Seligman High Income Fund Series N-CSR Certified annual shareholder report (management investment company)

UNITED STATES SECURITIES AND EXCHANGE COMMISSION WASHINGTON, D.C. 20549 FORM N-CSR CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT INVESTMENT COMPANIES Investment Company Act file number 811-4103 Seligman High Income Fund Series (Exact name of Registrant as specified in charter) 100 Park Avenue New York, New York 10017 (Address of principal executive offices) (Zip code) Lawrence P. Vogel 100 Park Avenue New York, New York 10017 (Name and address of agent for service) Registrant's telephone number, including area code: (212) 850-1864 Date of fiscal year end: 12/31 Date of reporting period: 12/31/04 ITEM 1. REPORTS TO STOCKHOLDERS.

Seligman
High-Yield Bond Series

Annual Report
December 31, 2004

Seeking to Maximize
Current Income by
Investing in a Diversified
Portfolio of High-Yielding
Corporate Bonds

J. & W. SELIGMAN & CO.
INCORPORATED
ESTABLISHED 1864
100 Park Avenue, New York, NY 10017

Seligman

141 Years of Investment Experience

J. & W. Seligman Co. Incorporated is a firm with a long tradition of investment expertise, offering a broad array of investment choices to help today’s investors seek their long-term financial goals.

Established in 1864, Seligman has a history of providing financial services marked not by fanfare, but rather by a quiet and firm adherence to financial prudence. While the world has changed dramatically in the 141 years since Seligman first opened its doors, the firm has continued to offer its clients high-quality investment solutions through changing times.

In the late 19th century, as the country grew, Seligman helped finance the westward expansion of the railroads, the construction of the Panama Canal, and the launching of urban transit systems. In the early 20th century, the firm helped fund the growing capital needs of new industries, including the nascent automobile and steel industries.

With the formation of Tri-Continental Corporation in 1929 — today, one of the nation’s largest diversified publicly-traded closed-end equity investment companies — Seligman began shifting its emphasis to investment management. In 1930, Seligman established what would be the first in an impressive lineup of mutual funds.

Seligman is proud of its distinctive past and of the traditional values that continue to shape the firm’s business decisions and investment judgment. While much has changed over the years, the firm’s commitment to providing prudent investment management that seeks to build wealth for clients over time is an enduring value that will continue to guide Seligman.

Table of Contents
To The Shareholders	1
Interview With Your
Portfolio Manager	2
Performance Overview	4
Portfolio Overview	7
Understanding and
Comparing Your Fund’s
Expenses	9
Portfolio of Investments	10
Statement of Assets
and Liabilities	16
Statement of Operations	17
Statements of
Changes in Net Assets	18
Notes to Financial
Statements	19
Financial Highlights	26
Report of Independent
Registered Public
Accounting Firm	31
Trustees and
Executive Officers	32
Required Federal Income
Tax Information	36
For More Information	back
	cover

To The Shareholders

Your annual shareholder report for Seligman High-Yield Bond Series follows this letter. This report contains an interview with your Portfolio Manager, as well as investment results and audited financial statements, including a portfolio of investments.

For the year ended December 31, 2004, Seligman High-Yield Bond Series posted a total return of 7.03% based on the net asset value of Class A shares. During the same time period, the Lipper High Current Yield Funds Average returned 9.93%, and the Citigroup US High-Yield Market Index returned 10.79% .

Thank you for your continued support of Seligman High-Yield Bond Series. We look forward to serving your investment needs for many years to come.

By Order of the Trustees,

William C. Morris
Chairman

Brian T. Zino
President

February 23, 2005

Manager	Shareholder Service Agent	General Distributor
J. & W. Seligman & Co. Incorporated	Seligman Data Corp.	Seligman Advisors, Inc.
100 Park Avenue	100 Park Avenue	100 Park Avenue
New York, NY 10017	New York, NY 10017	New York, NY 10017
Independent Registered	General Counsel
Public Accounting Firm	Sullivan & Cromwell LLP
Deloitte & Touche LLP

1

Interview With Your Portfolio Manager

Kendall C. Peterson

Q:	How did Seligman High-Yield Bond Series perform during the year ended December 31, 2004?
A:	For the year ended December 31, 2004, Seligman High-Yield Bond Series delivered a total return of 7.03%, based on the net asset value of Class A shares. During the same time period, the Lipper High Current Yield Funds Average posted a total return of 9.93%, and the Citigroup US High-Yield Market Index returned 10.79%.
Q:	What market conditions and events materially affected the Fund’s performance during the period?
A:	Solid economic growth, improved business conditions, and contained inflation helped the high-yield market and the Fund deliver positive returns in 2004. A broad market sell-off in the first half of the year was followed by a general market recovery in the second half. The Fund lost ground during the sell-off early in the year as high new issue supply, high energy prices, and election uncertainty added to investor unease. The recovery took place even as the good economic news prompted the Federal Reserve Board to begin increasing the fed funds rate in June.
	The US economy continued to expand in 2004, posting four quarters of solid economic growth. Improved corporate profits and healthy cash balances allowed many companies to de-leverage their balance sheets and increase dividend payouts. The Fed, convinced that the economic recovery was on sound footing, raised the short-term federal funds rate from 1.00% to 2.25% during the course of the year. Higher short-term rates were not accompanied by higher rates across the yield curve, with intermediate-term interest rates finishing the year largely unchanged. Inflation remained under control despite a significant increase in energy prices during the year and a decline in the dollar against the major foreign currencies.
	After a slow start, high-yield bonds performed well in 2004, particularly in the second half of the year, though returns were not as strong as those posted in 2003. The high-yield market benefited from several factors, including investors’ increased appetite for risk, low corporate default rates, and a search for increased income in a low rate environment. Both supply and demand for high-yield bonds increased during the year, with demand driven by institutional investors. Yield spreads, the difference in high-yield bond yields compared to Treasury yields, narrowed significantly in 2004. Undeterred by tightening yield spreads, high-yield bonds rallied toward year-end even as Treasury yields moved higher.

A TEAM APPROACH

Seligman High-Yield Bond Series is managed by the Seligman Fixed Income Group, headed by Kendall C. Peterson, CFA. Mr. Peterson draws on a team of seasoned investment professionals to select companies whose bonds have the potential for high yields at acceptable levels of investment risk consistent with the Fund’s objective. Team members include Jeff Gallo, Paul Langlois, Christopher Mahony (head of the investment-grade bond team), and Sau Lin Wu (trader).

2

Interview With Your Portfolio Manager

Kendall C. Peterson

Q:

What investment strategies or techniques materially affected the Fund’s performance during the period?

A:

Our investment strategy during the year included two primary investment themes — one to take advantage of the economic recovery, and the other to take advantage of anticipated interest-rate movements. The Fund entered the year with a tilt toward economically sensitive sectors (such as specialty chemicals and metals and mining) and lower-quality CCC-rated bonds, anticipating some follow-through on the economic expansion that took place in 2003. While the economy and corporate earnings showed continued growth in early 2004, the high-yield market came under selling pressure from heavy new issue supply and higher energy prices, causing the Fund’s value to decline. By mid-year, the Fund adopted a more conservative posture and shorter duration as it became clear the Federal Reserve was about to shift policy from an accommodative stance to a more neutral monetary policy. The Fed went on to raise short-term rates at five consecutive meetings starting on June 30th. However, interest rates for intermediate bonds did not follow the fed funds rate higher, and our move to a shorter duration was not rewarded, causing the Fund to lag its benchmark index. The portfolio’s exposure to economically sensitive sectors and lower-rated holdings helped offset some of the drag from the portfolio’s short duration as the high-yield market continued to climb higher into year-end. The Fund’s performance was also helped by its investment in certain wi reless telecommunications companies that outperformed the overall market. Overall, the Fund’s defensive stance kept the Fund from fully participating in the high-yield market once it began to move higher, while its exposure to select cyclical industry debt was a positive contributor to the Fund’s return in 2004.

The views and opinions expressed are those of the Portfolio Manager(s), are provided for general information only, and do not constitute specific tax, legal, or investment advice to, or recommendations for, any person. There can be no guarantee as to the accuracy of market forecasts. Opinions, estimates, and forecasts may be changed without notice.

3

Performance Overview

This section of the Annual Report is intended to help you understand the performance of Seligman High-Yield Bond Series (the “Fund”) and to provide a summary of the Fund’s portfolio characteristics.

Performance data quoted in this Annual Report represents past performance and does not guarantee future investment results. The rates of return will vary and the principal value of an investment will fluctuate. Shares, if redeemed, may be worth more or less than their original cost. Current performance may be lower or higher than the performance data quoted. Total returns of the Fund as of the most recent month-end will be available at www.seligman.com¹ by the seventh business day following that month-end. Calculations assume reinvestment of distributions. Performance data quoted does not reflect the deduction of taxes that an investor may pay on distributions or the redemption of shares. With respect to Class I, J. & W. Seligman & Co. Incorporated (the “Manager”) voluntarily reimbursed certain expenses in 2002 and 2001. Absent such reimbursements, total returns that included those periods would be lower.

Returns for Class A shares are calculated with and without the effect of the initial 4.75% maximum sales charge. Returns for Class B shares are calculated with and without the effect of the maximum 5% contingent deferred sales charge (“CDSC”), charged on redemptions made within one year of purchase, declining to 1% in the sixth year and 0% thereafter. Return from inception for Class B shares reflects automatic conversion to Class A shares approximately eight years after inception date. Returns for Class C shares are calculated with and without the effect of the initial 1% maximum sales charge and the 1% CDSC that is charged on redemptions made within 18 months of purchase. Returns for Class D and Class R shares are calculated with and without the effect of the 1% CDSC, charged on redemptions made within one year of purchase. Returns for Class I shares are calculated without any sales charges.

The chart on page 5 compares a $10,000 hypothetical investment made in Class A shares, with and without the initial 4.75% maximum sales charge, and in Class D shares, without the 1% CDSC, to a $10,000 investment made in the Citigroup High Yield Market Index for the 10-year period ended December 31, 2004. The performance of Class B, Class C, Class I and Class R shares, which commenced on later dates, and of Class A and Class D shares for other periods, with and without applicable sales charges and CDSCs, is not shown in this chart but is included in the total returns table that follows the chart. The performance of Class B, Class C, Class I, and Class R shares will differ from the performance shown for Class A and Class D shares, based on the differences in sales charges and fees paid by shareholders. The Citigroup High-Yield Market Index excludes the effect of taxes, fees and sales charges.

1 The reference to Seligman’s website is an inactive textual reference and information contained in or otherwise accessible through Seligman’s website does not form a part of this report or the Seligman Portfolios’ prospectus.

4

Performance Overview

Investment Results

Total Returns
For Periods Ended December 31, 2004

Average Annual

Class B

Class C

Class I

Class R

Since

Since

Since

Since

Six

One

Five

Ten

Inception

Inception

Inception

Inception

Months*

Year

Years

Years

4/22/96

5/27/99

11/30/01

4/30/03

Class A

With Sales Charge

2.43

%

1.86

%

(2.29

)%

3.64

%

n/a

n/a

n/a

n/a

Without Sales Charge

7.56

7.03

(1.34

)

4.15

n/a

n/a

n/a

n/a

Class B

With CDSC†

2.48

1.58

(2.32

)

n/a

n/a

n/a

n/a

n/a

Without CDSC

7.48

6.53

(2.08

)

n/a

1.26

%##

n/a

n/a

n/a

Class C

With Sales Charge

and CDSCø

5.23

4.07

(2.31

)

n/a

n/a

(2.31

)%

n/a

n/a

Without Sales Charge

and CDSC

7.16

6.22

(2.12

)

n/a

n/a

(2.13

)

n/a

n/a

Class D

With 1% CDSC

6.16

5.24

n/a

n/a

n/a

n/a

n/a

n/a

Without CDSC

7.16

6.22

(2.12

)

3.35

n/a

n/a

n/a

n/a

Class I

7.78

7.46

n/a

n/a

n/a

n/a

7.11

%

n/a

Class R

With 1% CDSC

6.43

5.77

n/a

n/a

n/a

n/a

n/a

n/a

Without CDSC

7.43

6.76

n/a

n/a

n/a

n/a

n/a

10.66

%

Citigroup High-Yield

Market Index**

9.49

10.79

7.22

8.45

7.37

††

6.39

†††

11.92

14.48

Lipper High Current

Yield Funds Average**

8.62

9.93

4.95

6.50

5.49

#

4.57

10.18

13.51

See footnotes on page 6.

5

Performance Overview

				Dividend and Capital Gain
				Per Share and Yield Information
Net Asset Value Per Share				For Periods Ended December 31, 2004
					SEC 30-Day
	12/31/04	6/30/04	12/31/03	Dividends Paidøø	Yieldsøøø		Capital Gain‡
Class A	$3.51	$3.39	$3.55	$0.2747	5.53	%	Realized	$0.003
Class B	3.52	3.39	3.55	0.2494	5.01		Unrealized	0.251	‡‡
Class C	3.52	3.40	3.56	0.2494	4.99
Class D	3.52	3.40	3.56	0.2494	5.04
Class I	3.51	3.39	3.55	0.2888	6.26
Class R	3.51	3.39	3.55	0.2660	5.69

*	Returns for periods of less than one year are not annualized.
**	The Citigroup High Yield Bond Index and the Lipper High Current Yield Funds Average are unmanaged benchmarks that
	assume reinvestment of all distributions and exclude the effect of taxes and sales charges, and the Citigroup High Yield
	Bond Index also excludes the effect of fees. The Lipper High Current Yield Funds Average aims at high (relative) current
	yield from fixed income securities, has no quality or maturity restrictions, and tends to invest in lower grade debt instru-
	ments. The Citigroup High Yield Market Index captures the performance of below investment-grade debt issues of corpora-
	tions domiciled in the United States or Canada. Investors cannot invest directly in an average or an index.
ø	The CDSC is 1% for periods up to 18 months.
øø	Represents per share amount paid or declared during the year ended December 31, 2004.
øøø	Current yield, representing the annualized yield for the 30-day period ended December 31, 2004, has been computed in
	accordance with SEC regulations and will vary.
†	The CDSC is 5% for periods of one year or less and 2% for the five-year period.
††	From April 30, 1996.
†††	From May 31, 1999.
#	From April 25, 1996.
##	Return from inception of Class B shares reflects automatic conversion to Class A shares approximately eight years after
	inception date.
‡	Information does not reflect effect of capital loss carryforwards that are available to offset these and future net realized
	capital gains. See Note 5 to Financial Statements.
‡‡	Represents the per share amount of net unrealized appreciation of portfolio securities as of December 31, 2004.

6

Portfolio Overview

Largest Industries
December 31, 2004

Largest Portfolio Changes

During Past Six Months

Largest Purchases	Largest Sales
Corporate Bonds:	Corporate Bonds:
Calpine 9.625%, 9/30/2014*	Nextel Communications 9.375%, 11/15/2009**
EchoStar DBS 5.75%, 10/1/2008*	BE Aerospace 9.5%, 11/1/2008**
Centenial Communications 8.125%, 2/1/2014*	Foamex 10.75%, 4/1/2009**
Rite Aid 8.125%, 5/1/2010	Rite Aid 7.7%, 2/15/2027**
American Tower 7.5%, 5/1/2012*	EchoStar DBS 10.375%, 10/1/2007**
Reddy Ice Holdings 10.5%, 11/1/2012*	Williams Companies 6.75%, 4/15/2009**
UCAR Finance 10.25%, 2/15/2012*	Dura Operating 9%, 5/1/2009**
Hexcel 9.875%, 10/1/2008*	Potlatch 10%, 7/15/2011**
Nextel Communications 7.375%, 8/1/2015*	EchoStar DBS 6.375%, 10/1/2012**
Town Sports International 9.625%, 4/15/2011*	K&F Industries 9.625%, 12/15/2010**

Largest portfolio changes from the previous period to the current period are based on cost of purchases and proceeds from sales of securities, listed in descending order.

*	Position added during the period.
**	Position eliminated during the period.

7

Portfolio Overview

Top Ten Companies
December 31, 2004

		Percent of
Security	Value	Net Assets
Qwest	$17,094,250	2.8
Charter Communications	16,274,750	2.7
Calpine	11,976,812	2.0
Dex Media East	11,870,688	2.0
Owens-Illinois	11,145,687	1.8
SBA Telecommunications	10,826,812	1.8
Georgia-Pacific	10,387,625	1.7
Huntsman ICI Chemicals	9,292,513	1.5
Rite Aid	7,570,312	1.2
AES	7,472,000	1.2

The amounts shown for the top ten companies represent the value of the Fund’s investments in securities of all types issued by the companies or their affiliates.

Ratings§			Weighted
December 31, 2004			Average Maturity
	Moody’s		6.54 years
BB	11.8	%
B	62.0
CCC	23.2
CC	1.7
Non-rated	1.3
§   Percentages based on current market values of long-term holdings.

8

Understanding and Comparing
Your Fund’s Expenses

As a shareholder of the Fund, you incur ongoing expenses, such as management fees, distribution and/or service (12b-1) fees, and other fund expenses. The information below is intended to help you understand your ongoing expenses (in dollars) of investing in the Fund and to compare them with the ongoing expenses of investing in other mutual funds. Please note that the expenses shown in the table are meant to highlight your ongoing expenses only and do not reflect any transactional costs, such as sales charges (also known as loads) on certain purchases or redemptions. Therefore, the table is useful in comparing ongoing expenses only, and will not help you to determine the relative total expenses of owning different funds. In addition, if transactional costs were included, your total expenses would have been higher.

The table is based on an investment of $1,000 invested at the beginning of July 1, 2004 and held for the entire six-month period ended December 31, 2004.

Actual Expenses

The table below provides information about actual expenses and actual account values. You may use the information, together with the amount you invested, to estimate the expenses that you paid over the period. Simply divide your account value at the beginning of the period by $1,000 (for example, an $8,600 account value divided by $1,000 = 8.6), then multiply the result by the number under the heading entitled “Expenses Paid During Period” for the Fund’s share class that you own to estimate the expenses that you paid on your account during the period.

Hypothetical Example for Comparison Purposes

The table below also provides information about hypothetical expenses and hypothetical account values based on the actual expense ratios of each class and an assumed rate of return of 5% per year before expenses, which is not the actual return of any class of the Fund. The hypothetical expenses and account values may not be used to estimate the ending account value or the actual expenses you paid for the period. You may use this information to compare the ongoing expenses of investing in the Fund and other mutual funds. To do so, compare this 5% hypothetical example with the 5% hypothetical examples that appear in the shareholder reports of the other mutual funds.

				Actual		Hypothetical
	Beginning			Ending		Ending
	Account	Annualized		Account	Expenses Paid	Account	Expenses Paid
	Value	Expense		Value	During Period**	Value	During Period**
	7/1/04	Ratio*		12/31/04	7/1/04 to 12/31/04	12/31/04	7/1/04 to 12/31/04
Class A	$1,000.00	1.28	%	$1,075.60	$  6.68	$1,018.70	$  6.50
Class B	1,000.00	2.03		1,074.80	10.59	1,014.93	10.28
Class C	1,000.00	2.03		1,071.60	10.57	1,014.93	10.28
Class D	1,000.00	2.03		1,071.60	10.57	1,014.93	10.28
Class I	1,000.00	0.85		1,077.80	4.44	1,020.86	4.32
Class R	1,000.00	1.53		1,074.30	7.98	1,017.44	7.76

*	Expenses of Class B, Class C, Class D, Class I and Class R shares differ from the expenses of Class A shares due to the differences in 12b-1 fees and other class-specific expenses paid by each share class. See the Fund’s prospectus for a description of each share class and its expenses and sales charges.
**	Expenses are equal to the annualized expense ratio based on actual expenses for the period July 1, 2004 to December 31, 2004, multiplied by the average account value over the period, multiplied by 184/366 (number of days in the period).

9

Portfolio of Investments
December 31, 2004

	Principal
	Amount		Value
Corporate Bonds 95.5%
Aerospace 2.5%
Hexcel 9.875%, 10/1/2008	$	3,550,000	$	3,958,250
K&F Industries 7.75%, 11/15/2014		2,450,000		2,541,875
Sequa 9%, 8/1/2009		5,375,000		6,087,188
TD Funding 8.375%, 7/15/2011		2,650,000		2,855,375
				15,442,688
Auto 3.1%
Cooper Standard Automotive:
7%, 12/15/2012*		425,000		433,500
8.375%, 12/15/2014*		1,325,000		1,328,312
Goodyear Tire & Rubber 7.857%, 8/15/2011		4,450,000		4,539,000
Stoneridge 11.5%, 5/1/2012		3,575,000		4,173,812
Tenneco Automotive 10.25%, 7/15/2013		2,675,000		3,169,875
TRW Automotive Acquisition:
9.375%, 2/15/2013		3,000,000		3,495,000
11%, 2/15/2013		1,203,000		1,455,630
				18,595,129
Broadcasting 2.7%
Granite Broadcasting 9.75%, 12/1/2010		3,600,000		3,456,000
Nextmedia Operating 10.75%, 7/1/2011		3,625,000		4,078,125
Paxson Communications 0% (12.25%†), 1/15/2009		1,725,000		1,621,500
Sinclair Broadcast Group 8%, 3/15/2012		2,300,000		2,455,250
Spanish Broadcasting Systems 9.625%, 11/1/2009		2,100,000		2,210,250
Young Broadcasting 10%, 3/1/2011		2,675,000		2,868,937
				16,690,062
Building Products 1.8%
Associated Materials 9.75%, 4/15/2012		2,775,000		3,114,938
Euramax International 8.5%, 8/15/2011		3,575,000		3,834,188
Texas Industries 10.25%, 6/15/2011		3,600,000		4,230,000
				11,179,126
Cable 4.2%
Charter Communications:
10.25%, 9/15/2010		8,750,000		9,318,750
0% (11.75%†), 5/15/2011		9,400,000		6,956,000
CSC Holdings 7.875%, 12/15/2007		3,725,000		4,013,688
Insight Midwest/Insight Capital 10.5%, 11/1/2010		2,625,000		2,887,500
Mediacom Broadband 11%, 7/15/2013		2,200,000		2,376,000
				25,551,938

See footnotes on page 15.

10

Portfolio of Investments
December 31, 2004

	Principal
	Amount		Value
Capital Goods 3.2%
Blount 8.875%, 8/1/2012	$	3,125,000	$	3,406,250
Columbus McKinnon 10%, 8/1/2010		3,500,000		3,955,000
JLG Industries 8.375%, 6/15/2012		3,525,000		3,789,375
NMHG Holding 10%, 5/15/2009		2,875,000		3,191,250
Norcross Safety Products 9.875%, 8/15/2011		3,100,000		3,441,000
Park-Ohio Industries 8.375%, 11/15/2014		1,350,000		1,356,750
				19,139,625
Chemicals 9.9%
ARCO Chemical 9.8%, 2/1/2020		4,950,000		5,667,750
Equistar Chemicals 10.125%, 9/1/2008		4,225,000		4,890,437
Huntsman ICI Chemicals 10.125%, 7/1/2009		5,810,000		6,144,075
Huntsman International 7.375%, 1/1/2015*		3,125,000		3,148,438
International Specialty Holdings 10.625%, 12/15/2009		5,825,000		6,480,312
KI Holdings 0% (9.875%†), 11/15/2014*		2,700,000		1,741,500
Koppers 9.875%, 10/15/2013		1,750,000		2,003,750
Lyondell Chemical 11.125%, 7/15/2012		5,350,000		6,379,875
Millennium America 9.25%, 6/15/2008		3,775,000		4,312,937
Nalco Finance Holdings 0% (9%†), 2/1/2014		4,714,000		3,511,930
Polyone 10.625%, 5/15/2010		3,500,000		3,955,000
Resolution Performance Products 9.5%, 4/15/2010		3,525,000		3,833,438
Rockwood Specialties Group 10.625%, 5/15/2011		3,525,000		4,071,375
Terra Capital 11.5%, 6/1/2010		3,283,000		3,759,035
				59,899,852
Consumer Products 2.3%
Jostens:
7.625%, 10/01/2012*		1,775,000		1,854,875
0% (10.25%†), 12/1/2013*		6,200,000		4,433,000
Playtex Products 9.375%, 6/1/2011		3,500,000		3,753,750
Rayovac 8.5%, 10/1/2013		3,575,000		3,986,125
				14,027,750
Containers 4.4%
Anchor Glass Container 11%, 2/15/2013		2,650,000		2,848,750
BWAY 10%, 10/15/2010		2,675,000		2,795,375
Crown Cork & Seal 8%, 4/15/2023		1,900,000		1,881,000
Crown European Holdings 9.5%, 3/1/2011		2,825,000		3,234,625
Owens-Illinois:
7.5%, 5/15/2010		8,150,000		8,689,937
7.8%, 5/15/2018		2,350,000		2,455,750
Pliant:
0% (11.125%†), 6/15/2009		2,900,000		2,693,375
11.125%, 9/1/2009		1,875,000		2,053,125
				26,651,937

See footnotes on page 15.

11

Portfolio of Investments
December 31, 2004

	Principal
	Amount		Value
Diversified Telecommunication 2.8%
Qwest 7.875%, 9/1/2011*	$	2,500,000	$	2,725,000
Qwest Services 13.5%, 12/15/2010*		11,900,000		14,369,250
				17,094,250
Electric 1.0%
CMS Energy 9.875%, 10/15/2007		1,775,000		1,992,437
MSW Energy Holdings 8.5%, 9/1/2010		3,600,000		3,960,000
				5,952,437
Energy 4.8%
Dynegy Holdings 8.75%, 2/15/2012		6,125,000		6,446,563
El Paso 7.875%, 6/15/2012		5,375,000		5,650,469
El Paso Production Holdings 7.75%, 6/1/2013		4,550,000		4,788,875
Frontier Oil 6.625%, 10/1/2011*		1,750,000		1,793,750
Harvest Operations 7.875%, 10/15/2011*		1,750,000		1,771,875
Reliant Energy 6.75%, 12/15/2014		3,125,000		3,121,094
Williams Companies 8.125%, 3/15/2012		4,650,000		5,394,000
				28,966,626
Environmental 0.4%
Allied Waste North America 8.5%, 12/1/2008		2,400,000		2,556,000
Finance 1.0%
Western Financial Bank 9.625%, 5/15/2012		5,075,000		5,810,875
Food and Beverage 2.8%
Land O’ Lakes 8.75%, 11/15/2011		3,550,000		3,550,000
Pilgrim’s Pride 9.25%, 11/15/2013		5,725,000		6,440,625
Seminis Vegetable seeds 10.25%, 10/1/2013		3,525,000		3,983,250
UAP Holding 0% (12%†), 7/15/2012*		4,175,000		3,298,250
				17,272,125
Food and Drug 1.8%
Rite Aid 8.125%, 5/1/2010		7,125,000		7,570,312
Roundy’s 8.875%, 6/15/2012*		3,125,000		3,429,688
				11,000,000
Gaming 1.9%
Harrah’s Operating 7.875%, 12/15/2005		3,675,000		3,831,187
Mandalay Resort Group 9.375%, 2/15/2010		2,675,000		3,129,750
MGM Grand 9.75%, 6/1/2007		2,000,000		2,230,000
Park Place Entertainment 9.375%, 2/15/2007		2,000,000		2,210,000
				11,400,937
Health Care Facilities and Supplies 1.9%
Alliance Imaging 7.25%, 12/15/2012		3,575,000		3,655,438
Medex 8.875%, 5/15/2013		3,550,000		4,153,500
Universal Hospital Services 10.125%, 11/1/2011		3,525,000		3,683,625
				11,492,563

See footnotes on page 15.

12

Portfolio of Investments
December 31, 2004

	Principal
	Amount		Value
Industrials 0.8%
Reddy Ice Holdings 10.5%, 11/1/2012	$	6,650,000	$	4,621,750
Leisure 1.5%
Intrawest 7.5%, 10/15/2013*		1,775,000		1,897,031
Six Flags 8.875%, 2/1/2010		3,175,000		3,230,562
Town Sports International 9.625%, 4/15/2011		3,575,000		3,780,563
				8,908,156
Lodging 2.3%
Host Marriot 9.5%, 1/15/2007		2,400,000		2,640,000
John Q. Hammons Hotels 8.875%, 5/15/2012		2,325,000		2,638,875
MeriStar Hospitality 9.125%, 1/15/2011		4,750,000		5,153,750
Starwood Hotels and Resorts 7.375%, 5/1/2007		3,575,000		3,829,719
				14,262,344
Metals and Mining 6.1%
AK Steel 7.875%, 2/15/2009		5,350,000		5,477,063
Earle M. Jorgensen 9.75%, 6/1/2012		3,050,000		3,446,500
Gerdau AmeriSteel 10.375%, 7/15/2011		3,500,000		4,121,250
IMCO Recycling:
10.375%, 10/15/2010		5,250,000		5,985,000
9%, 11/15/2014*		450,000		470,250
Neenah Foundry 11%, 9/30/2010		3,950,000		4,384,500
Ryerson Tull 8.25%, 12/15/2011*		2,000,000		2,030,000
UCAR Finance 10.25%, 2/15/2012		3,475,000		3,987,562
United States Steel 10.75%, 8/1/2008		5,830,000		6,893,975
				36,796,100
Paper and Forest Products 5.9%
Ainsworth Lumber 7.25%, 10/1/2012*		1,750,000		1,789,375
Buckeye Technologies 8%, 10/15/2010		3,550,000		3,567,750
Caraustar Industries 9.875%, 4/1/2011		3,450,000		3,760,500
Georgia-Pacific:
7.5%, 5/15/2006		6,650,000		6,999,125
8.875%, 5/15/2031		2,700,000		3,388,500
Jefferson Smurfit 8.25%, 10/1/2012		4,250,000		4,653,750
Longview Fibre 10%, 1/15/2009		3,600,000		3,951,000
Newark Group 9.75%, 3/15/2014		3,500,000		3,745,000
Tembec Industries 8.5%, 2/1/2011		3,725,000		3,762,250
				35,617,250
Publishing 4.4%
Dex Media 0% (9%†), 11/15/2013*		15,050,000		11,870,688
Houghton Mifflin 9.875%, 2/1/2013		4,425,000		4,867,500
Primedia 8.875%, 5/15/2011		4,850,000		5,153,125
Vertis:
10.875%, 6/15/2009		2,575,000		2,806,750
13.5%, 12/7/2009*		1,750,000		1,852,813
				26,550,876

See footnotes on page 15.

13

Portfolio of Investments
December 31, 2004

	Principal
	Amount		Value
Restaurants 1.6%
Buffets 11.25%, 7/15/2010	$	2,650,000	$	2,848,750
Denny’s 10%, 10/1/2012*		2,650,000		2,865,312
Domino’s 8.25%, 7/1/2011		1,386,000		1,521,135
Landry’s Restaurants 7.5%, 12/15/2014*		2,675,000		2,668,313
				9,903,510
Satellite 0.9%
EchoStar DBS 5.75%, 10/1/2008		5,375,000		5,469,062
Services 1.5%
Cenveo 9.625%, 3/15/2012		2,675,000		2,949,188
Mobile Mini 9.5%, 7/1/2013		1,350,000		1,579,500
URS 11.50%, 9/15/2009		1,170,000		1,351,350
Williams Scotsman:
9.875%, 6/1/2007		1,725,000		1,733,625
10%, 8/15/2008		1,325,000		1,477,375
				9,091,038
Stores 1.9%
Asbury Auto Group 9%, 6/15/2012		3,575,000		3,771,625
Central Garden & Pet 9.125%, 2/1/2013		2,675,000		2,969,250
Hollywood Entertainment 9.625%, 3/15/2011		4,625,000		4,925,625
				11,666,500
Technology 1.8%
Advanced Micro Devices 7.75%, 11/1/2012*		3,550,000		3,714,187
AMI Semiconductor 10.75%, 2/1/2013		3,559,000		4,199,620
Xerox 9.75%, 1/15/2009		2,625,000		3,097,500
				11,011,307
Textiles and Apparel 0.7%
Russell 9.25%, 5/1/2010		3,800,000		4,094,500
Tower 4.1%
American Tower:
9.375%, 2/1/2009		845,000		897,812
7.5%, 5/1/2012		4,450,000		4,694,750
7.125%, 10/15/2012*		1,775,000		1,823,813
Crown Castle International 10.75%, 8/1/2011		6,175,000		6,730,750
SBA Telecommunications 0% (9.75%†), 12/15/2011		12,775,000		10,826,812
				24,973,937
Utilities 4.5%
AES 9.375%, 9/15/2010		6,400,000		7,472,000
Calpine:
8.50%, 7/15/2010*		5,325,000		4,592,812
9.625%, 9/30/2014*		7,100,000		7,384,000
Edison Mission Energy 7.73%, 6/15/2009		5,525,000		5,967,000
National Waterworks (Series B) 10.5%, 12/1/2012		1,775,000		2,005,750
				27,421,562

See footnotes on page 15.

14

Portfolio of Investments
December 31, 2004

	Principal Amount, Shares or Warrants
			Value
Wireless 5.0%
Alamosa Holdings 11%, 7/31/2010	$	5,400,000	$	6,385,500
Centenial Cellular Operating 10.75%, 12/15/2008		1,450,000		1,511,625
Centenial Communications 8.125%, 2/1/2014		4,725,000		4,878,563
Nextel Communications 7.375%, 8/1/2015		3,575,000		3,950,375
Nextel Partners:
12.5%, 11/15/2009		1,770,000		2,013,375
8.125%, 7/1/2011		1,750,000		1,951,250
Rural Cellular 9.875%, 2/1/2010		3,550,000		3,629,875
Western Wireless 9.25%, 7/15/2013		5,350,000		5,844,875
				30,165,438
Total Corporate Bonds (Cost $536,452,419)		583,156,160		579,277,250
Preferred Stocks 0.6%
Publishing 0.6%
Primedia 8.625% (Cost $3,404,000)		37,000 shs.		3,404,000
Asset Backed Securities 0.3%
Utilities 0.3%
Midland Funding 11.75%, 7/23/2005 (Cost $1,543,532)	$	1,531,469		1,597,812
Warrants 0.1%
Tower 0.1%
American Tower* (Cost $238,723)		3,125 wts.		720,312
Repurchase Agreement 1.4%
State Street Bank & Trust 1.4%, dated 12/31/2004,
maturing 1/3/2005 in the amount of $8,427,983,
collateralized by: $7,510,000 US Treasury Notes 6.5%,
2/15/2010, with a fair market value of
(Cost $8,427,000)	$	8,427,000		8,427,000
Total Investments (Cost $550,065,674) 97.9%				593,426,374
Other Assets Less Liabilities 2.1%				12,987,587
Net Assets 100.0%			$	606,413,961

*	Rule 144A security.
†	Deferred-interest debentures pay no interest for a stipulated number of years, after which they pay the indicated
	coupon rate.

See Notes to Financial Statements.

15

Statement of Assets and Liabilities
December 31, 2004

Assets:
Investments, at value:
Corporate bonds (cost $536,452,419)	$	579,277,250
Preferred stocks (cost $3,404,000)		3,404,000
Asset-backed securities (cost $1,543,532)		1,597,812
Warrants (cost $238,723)		720,312
Repurchase agreement (cost $8,427,000)		8,427,000
Total investments (cost $550,065,674)		593,426,374
Cash		3,989,573
Receivable for dividends and interest		11,584,509
Receivable for securities sold		1,860,379
Receivable for shares of Beneficial Interest sold		321,775
Expenses prepaid to shareholder service agent		136,557
Other		121,642
Total Assets		611,440,809
Liabilities:
Payable for shares of Beneficial Interest repurchased		2,690,625
Dividends payable		1,477,772
Distribution and service fees payable		372,627
Management fee payable		338,675
Accrued expenses and other		147,149
Total Liabilities		5,026,848
Net Assets	$	606,413,961
Composition of Net Assets:
Shares of Beneficial Interest, at par (unlimited shares authorized;
$0.001 par value; 172,520,858 shares outstanding):
Class A	$	63,511
Class B		64,894
Class C		13,631
Class D		28,428
Class I		1,852
Class R		205
Additional paid-in capital		2,023,137,305
Dividends in excess of net investment income		(1,312,800	)
Accumulated net realized loss		(1,458,943,765	)
Net unrealized appreciation of investments		43,360,700
Net Assets	$	606,413,961

Net Asset Value Per Share:
Class A ($222,827,494 ÷ 63,511,267 shares)	$3.51	Class D ($100,124,815 ÷ 28,427,870 shares)	$3.52
Class B ($228,228,887 ÷ 64,893,457 shares)	$3.52	Class I ($6,500,056 ÷ 1,851,987 shares)	$3.51
Class C ($48,012,297 ÷ 13,631,030 shares)	$3.52	Class R ($720,412 ÷ 205,247 shares)	$3.51

See Notes to Financial Statements.

16

Statement of Operations
For the Year Ended December 31, 2004

Investment Income:
Interest	$	59,110,455
Dividends		933,691
Other income		317,583
Total Investment Income		60,361,729
Expenses:
Distribution and service fees		4,915,755
Management fee		4,330,661
Shareholder account services		1,937,976
Custody and related services		203,045
Registration		132,693
Auditing and legal fees		90,813
Shareholder reports and communications		83,119
Trustees’ fees and expenses		25,870
Miscellaneous		47,702
Total Expenses		11,767,634
Net Investment Income		48,594,095
Net Realized and Unrealized Gain (Loss) on Investments:
Net realized gain on investments		485,357
Net change in unrealized appreciation of investments		(9,176,202	)
Net Loss on Investments		(8,690,845	)
Increase in Net Assets from Operations	$	39,903,250

See Notes to Financial Statements.

17

Statements of Changes in Net Assets

		Year Ended December 31,
	2004			2003
Operations:
Net investment income	$	48,594,095		$	57,838,777
Net realized gain on investments		485,357			52,924,456
Net change in unrealized appreciation of investments		(9,176,202	)		39,644,062
Increase in Net Assets from Operations		39,903,250			150,407,295
Distributions to Shareholders:
Net investment income:*
Class A		(17,359,276	)		(20,541,568	)
Class B		(19,048,076	)		(23,309,524	)
Class C		(3,778,097	)		(4,052,841	)
Class D		(7,890,350	)		(9,584,885	)
Class I		(481,679	)		(349,882	)
Class R		(36,617	)		(77	)
Total		(48,594,095	)		(57,838,777	)
Dividends in excess of net investment income:*
Class A		(402,543	)		(972,847	)
Class B		(441,705	)		(1,103,937	)
Class C		(87,610	)		(191,942	)
Class D		(182,968	)		(453,939	)
Class I		(11,169	)		(16,570	)
Class R		(849	)		(4	)
Total		(1,126,844	)		(2,739,239	)
Decrease in Net Assets from Distributions		(49,720,939	)		(60,578,016	)
Capital Share Transactions:
Net proceeds from sales of shares		37,308,067			91,960,373
Investment of dividends		25,652,341			30,359,362
Exchanged from associated funds		32,527,537			132,697,242
Total		95,487,945			255,016,977
Cost of shares repurchased		(195,607,794	)		(221,949,382	)
Exchanged into associated funds		(45,731,586	)		(133,080,952	)
Total		(241,339,380	)		(355,030,334	)
Decrease in Net Assets from Capital Share Transactions		(145,851,435	)		(100,013,357	)
Decrease in Net Assets		(155,669,124	)		(10,184,078	)
Net Assets:
Beginning of year		762,083,085			772,267,163
End of Year (includes dividends in excess of net investment
income of $1,312,800 and $3,398,362, respectively)	$	606,413,961		$	762,083,085

*	For tax purposes, these distributions are considered ordinary income.
	See Notes to Financial Statements.

18

Notes to Financial Statements

1.	Multiple Classes of Shares — Seligman High-Yield Bond Series (the “Fund”) is a series of Seligman High Income Fund Series (the “Series”). The Fund offers the following six classes of shares:
	Class A shares are sold with an initial sales charge of up to 4.75% and a continuing service fee of up to 0.25% on an annual basis. Class A shares purchased in an amount of $1,000,000 or more are sold without an initial sales charge but are subject to a contingent deferred sales charge (“CDSC”) of 1% on redemptions within 18 months of purchase.
	Class B shares are sold without an initial sales charge but are subject to a distribution fee of 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 5% on redemptions in the first year of purchase, declining to 1% in the sixth year and 0% thereafter. Class B shares will automatically convert to Class A shares during the month that precedes the eighth anniversary of their date of purchase. If Class B shares of the Fund are exchanged for Class B shares of another Seligman mutual fund, the holding period of the shares exchanged will be added to the holding period of the shares acquired, both for determining the applicable CDSC and the conversion of Class B shares to Class A shares.
	Class C shares are sold primarily with an initial sales charge of up to 1%, and a CDSC, if applicable, of 1% imposed on redemptions made within 18 months of purchase. Shares purchased through certain financial intermediaries may be bought without an initial sales charge and with a 1% CDSC on redemptions made within 12 months of purchase. All Class C shares are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis.
	Class D shares are sold without an initial sales charge but are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% imposed on redemptions made within one year of purchase.
	Class I shares are offered to certain institutional clients. Class I shares are sold without any sales charges and are not subject to distribution and service fees.
	Class R shares are offered to certain employee benefit plans and are not available to all investors. They are sold without an initial sales charge, but are subject to a distribution fee of up to 0.25% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% on redemptions made within one year of a plan’s initial purchase of Class R shares.
	All classes of shares represent interests in the same portfolio of investments, have the same rights and are generally identical in all respects except that each class bears its own class-specific expenses, and has exclusive voting rights with respect to any matter on which a separate vote of any class is required.
2.	Significant Accounting Policies — The financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America which require management to make certain estimates and assumptions at the date of the financial statements. Actual results may differ from these estimates. The following summarizes the significant accounting policies of the Fund:
	a.	Security Valuation — Securities traded on an exchange are valued at the last sales price on the primary exchange or market on which they are traded. Securities not listed on an exchange or security market are valued by independent pricing services based on bid prices, which consider such factors as coupons, maturities, credit ratings, liquidity, specific terms and features, and the US Treasury yield curve, or are valued by J. & W. Seligman & Co. Incorporated (the “Manager”) based on quotations provided by primary market makers in such securities. Securities for which market quotations are not readily available or (are otherwise no longer valid or reliable) are valued at fair value determined in accordance with procedures approved by the Trustees. This can occur in the event of, among other things, natural disasters, acts of terrorism, market disruptions, intra-day trading halts, and extreme market volatility in the US markets. Short-term holdings maturing in 60 days or less are valued at amortized cost.

19

Notes to Financial Statements

b.	Federal Taxes — There is no provision for federal income tax. The Fund has elected to be taxed as a regulated investment company and intends to distribute substantially all taxable net income and net gain realized.
c.	Security Transactions and Related Investment Income — Investment transactions are recorded on trade dates. Identified cost of investments sold is used for both financial reporting and federal income tax purposes. Dividends receivable are recorded on ex-dividend dates. Interest income is recorded on an accrual basis. The Fund amortizes discount and premium on portfolio securities for financial reporting purposes.
d.	Repurchase Agreements — The Fund may enter into repurchase agreements with commercial banks and with broker/dealers deemed to be creditworthy by the Manager. Securities received as collateral subject to repurchase agreements are deposited with the Fund’s custodian and, pursuant to the terms of the repurchase agreement, must have an aggregate market value greater than or equal to the repurchase price plus accrued interest at all times. Procedures have been established to monitor, on a daily basis, the market value of repurchase agreements’ underlying securities to ensure the existence of the proper level of collateral.
e.	Multiple Class Allocations — All income, expenses (other than class-specific expenses), and realized and unrealized gains or losses are allocated daily to each class of shares based upon the relative value of shares of each class. Class-specific expenses, which include distribution and service fees and any other items that are specifically attributable to a particular class, are charged directly to such class. For the year ended December 31, 2004, distribution and service fees, shareholder account services and registration expenses were class-specific expenses.
f.	Distributions to Shareholders — Dividends are declared daily and paid monthly. Other distributions paid by the Fund are recorded on ex-dividend dates.

3.	Purchases and Sales of Securities — Purchases and sales of portfolio securities, excluding short-term investments, for the year ended December 31, 2004, amounted to $341,569,439 and $494,283,274, respectively.
4.	Management Fee, Distribution Services, and Other Transactions — The Manager manages the affairs of the Fund and provides the necessary personnel and facilities. Compensation of all officers of the Fund, all trustees of the Fund who are employees of the Manager, and all personnel of the Fund and the Manager is paid by the Manager. The Manager receives a fee, calculated daily and payable monthly, equal to 0.65% per annum of the first $1 billion of the Fund’s average daily net assets and 0.55% per annum of the Fund’s average daily net assets in excess of $1 billion. The management fee reflected in the Statement of Operations represents 0.65% per annum of the Fund’s average daily net assets.
	Seligman Advisors, Inc. (the “Distributor”), agent for the distribution of the Fund’s shares, and an affiliate of the Manager, received concessions of $15,695 from sales of Class A shares. Commissions of $124,099 and $26,145 were paid to dealers from sales of Class A and Class C shares, respectively.
	The Fund has an Administration, Shareholder Services and Distribution Plan (the “Plan”) with respect to distribution of its shares. Under the Plan, with respect to Class A shares, service organizations can enter into agreements with the Distributor and receive a continuing fee of up to 0.25% on an annual basis, payable monthly, of the average daily net assets of the Class A shares attributable to the particular service organizations for providing personal services and/or the maintenance of shareholder accounts. The Distributor charges such fees to the Fund pursuant to the Plan. For the year ended December 31, 2004, fees incurred under the Plan aggregated $555,344 or 0.25% per annum of the average daily net assets of Class A shares.

20   

Notes to Financial Statements

Under the Plan, with respect to Class B shares, Class C shares, Class D shares, and Class R shares, service organizations can enter into agreements with the Distributor and receive a continuing fee for providing personal services and/or the maintenance of shareholder accounts of up to 0.25% on an annual basis of the average daily net assets of the Class B, Class C, Class D, and Class R shares for which the organizations are responsible; and, for Class C, Class D, and Class R shares, fees for providing other distribution assistance of up to 0.75% (0.25%, in the case of Class R shares) on an annual basis of such average daily net assets. Such fees are paid monthly by the Fund to the Distributor pursuant to the Plan.

With respect to Class B shares, a distribution fee of 0.75% on an annual basis of average daily net assets is payable monthly by the Fund to the Distributor; however, the Distributor has sold its rights to this fee with respect to a substantial portion of Class B shares to third parties (the “Purchasers”), which provide funding to the Distributor to enable it to pay commissions to dealers at the time of the sale of the related Class B shares.

For the year ended December 31, 2004, fees incurred under the Plan, equivalent to 1% per annum of the average daily net assets of Class B, Class C, and Class D shares, and 0.50% per annum of average daily net assets of Class R shares, amounted to $2,700,191, $537,273, $1,120,488, and $2,459, respectively.

The Distributor is entitled to retain any CDSC imposed on certain redemptions of Class A , Class C, Class D and Class R shares. For the year ended December 31, 2004, such charges amounted to $80,342.

The Distributor has sold its rights to collect any CDSC imposed on redemptions of Class B shares to the Purchasers. In connection with the sale of its rights to collect any CDSC and the distribution fees with respect to Class B shares described above, prior to August 1, 2004, the Distributor received payments from the Purchasers based on the value of Class B shares sold. The aggregate of such payments and distribution fees retained by the Distributor, for the year ended December 31, 2004, amounted to $14,566.

Seligman Services, Inc., an affiliate of the Manager, is eligible to receive commissions from certain sales of shares of beneficial interest of the Fund, as well as distribution and service fees pursuant to the Plan. For the year ended December 31, 2004, Seligman Services, Inc. received commissions of $2,226 from the sales of shares of the Fund. Seligman Services, Inc. also received distribution and service fees of $23,085, pursuant to the Plan.

Seligman Data Corp., which is owned by certain associated investment companies, charged the Fund at cost $1,937,976 for shareholder account services in accordance with a methodology approved by the Fund’s trustees. Class I shares receive more limited shareholder services than the Fund’s other classes of shares (the “Retail Classes”). Seligman Data Corp. does not allocate to Class I the costs of any of its departments that do not provide services to the Class I shareholders.

Costs of Seligman Data Corp. directly attributable to the Retail Classes of the Fund were charged to those classes in proportion to their respective net asset values. Costs directly attributable to Class I shares were charged to Class I. The remaining charges were allocated to the Retail Classes and Class I by Seligman Data Corp. pursuant to a formula based on their net assets, shareholder transaction volumes and number of shareholder accounts.

The Series and certain other associated investment companies (together, the “Guarantors”) have severally but not jointly guaranteed the performance and observance of all the terms and conditions of two leases entered into by Seligman Data Corp., including the payment of rent by Seligman Data Corp. (the “Guaranties”). The leases and the Guaranties expire in September 2008 and January 2009. The obligation of the Series to pay any amount due under either Guaranty is limited to a specified percentage of the full amount, which generally is based on the Series’ percentage of the expenses billed by Seligman Data Corp. to all Guarantors in the preceding calendar quarter. As of December 31, 2004, the Series’ potential

21

Notes to Financial Statements

	obligation under the Guaranties is $459,600. As of December 31, 2004, no event has occurred which would result in the Series becoming liable to make any payment under a Guaranty. The Fund would bear a portion of any payments made by the Series under the Guaranties. A portion of rent paid by Seligman Data Corp. is charged to the Fund as part of Seligman Data Corp.’s shareholder account services cost. Certain officers and trustees of the Fund are officers or directors of the Manager, the Distributor, Seligman Services, Inc., and/or Seligman Data Corp. The Fund has a compensation arrangement under which trustees who receive fees may elect to defer receiving such fees. Trustees may elect to have their deferred fees accrue interest or earn a return based on the performance of the Fund or other funds in the Seligman Group of Investment Companies. The cost of such fees and earnings/loss accrued thereon is included in trustees’ fees and expenses, and the accumulated balance thereof at December 31, 2004, of $27,236 is included in accrued expenses and other liabilities. Deferred fees and related accrued earnings are not deductible by the Fund for federal income tax purposes until such amounts are paid.
5.	Federal Tax Information — Certain components of income, expense and realized capital gain and loss are recognized at different times or have a different character for federal income tax purposes and for financial reporting purposes. Where such differences are permanent in nature, they are reclassified in the components of net assets based on their characterization for federal income tax purposes. Any such reclassifications will have no effect on net assets, results of operations or net asset value per share of the Fund. As a result of the differences described above, the treatment for financial reporting purposes of distributions made during the year from net investment income or net realized gains may differ from their treatment for federal income tax purposes. Further, the cost of investments also can differ for federal income tax purposes.
	At December 31, 2004, the cost of investments for federal income tax purposes was $552,454,923. The tax basis cost was greater than the cost for financial reporting purposes due to the tax deferral of losses on wash sales in the amount of $385,379 and the amortization of premium for financial reporting purposes of $2,003,870.
	At December 31, 2004, the tax basis components of accumulated losses were as follows:

Gross unrealized appreciation of portfolio securities	$	42,629,385
Gross unrealized depreciation of portfolio securities		(1,657,934	)
Net unrealized depreciation of portfolio securities		40,971,451
Capital loss carryforward		(1,458,558,386	)
Undistributed income		718,306
Total accumulated losses	$	(1,416,868,629	)

At December 31, 2004, the Fund had a net capital loss carryforward for federal income tax purposes of $1,458,558,386, which is available for offset against future taxable net capital gains, with $88,447,879 expiring in 2007, $255,659,981 expiring in 2008, $668,622,539 expiring in 2009, $444,283,739 expiring in 2010, and $1,544,248 expiring in 2012. The amount was determined after adjustments for certain differences between financial reporting and tax purposes, such as wash sale losses. Accordingly, no capital gain distributions are expected to be paid to shareholders until net capital gains have been realized in excess of the available capital loss carryforward.

6.

Committed Line of Credit — The Fund is a participant in a joint $425 million committed line of credit that is shared by substantially all open-end funds in the Seligman Group of Investment Companies. The trustees have currently limited the Fund’s borrowings to 10% of its net assets. Borrowings pursuant to the credit facility are subject to interest at a rate equal to the overnight federal funds rate plus 0.50%. The Fund incurs a commitment fee of 0.10% per annum on its share of the unused portion of the credit facil-

22

Notes to Financial Statements

	ity. The credit facility may be drawn upon only for temporary purposes and is subject to certain other customary restrictions. The credit facility commitment expires in June 2005, but is renewable annually with the consent of the participating banks. For the year ended December 31, 2004, the Fund did not borrow from the credit facility.
7.	Transactions in Shares of Beneficial Interest — The Fund has authorized unlimited shares of $0.001 par value Shares of Beneficial Interest. Transactions in Shares of Beneficial Interest were as follows:

	Year Ended December 31,
	2004					2003
Class A	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	6,970,061		$	24,300,202		19,750,005		$	64,845,052
Investment of dividends	2,679,139			9,278,265		3,372,353			11,257,976
Exchanged from associated funds	6,850,834			23,699,984		29,714,802			98,511,770
Converted from Class B**	5,156,128			17,770,888		—			—
Total	21,656,162			75,049,339		52,837,160			174,614,798
Cost of shares repurchased	(20,375,894	)		(70,767,341	)	(30,635,465	)	(102,529,746		)
Exchanged into associated funds	(7,964,360	)		(27,599,893	)	(32,468,232	)	(107,935,587		)
Total	(28,340,254	)		(98,367,234	)	(63,103,697	)	(210,465,333		)
Decrease	(6,684,092	)	$	(23,317,895	)	(10,266,537	)	$	(35,850,535	)
Class B	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	981,042		$	3,427,329		2,392,996		$	8,001,358
Investment of dividends	2,586,426			8,978,336		3,241,500			10,864,949
Exchanged from associated funds	1,482,105			5,149,932		7,082,946			23,575,331
Total	5,049,573			17,555,597		12,717,442			42,441,638
Cost of shares repurchased	(21,273,936	)		(73,910,560	)	(20,972,117	)		(70,334,266	)
Exchanged into associated funds	(3,576,498	)		(12,429,316	)	(4,978,261	)		(16,519,189	)
Converted to Class A**	(5,137,476	)		(17,747,493	)	—			—
Total	(29,987,910	)	(104,087,369		)	(25,950,378	)		(86,853,455	)
Decrease	(24,938,337	)	$	(86,531,772	)	(13,232,936	)	$	(44,411,817	)
Class C	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	1,158,719		$	4,083,443		4,172,255		$	13,957,406
Investment of dividends	626,767			2,177,803		635,232			2,132,580
Exchanged from associated funds	350,697			1,225,061		1,534,952			5,162,235
Total	2,136,183			7,486,307		6,342,439			21,252,221
Cost of shares repurchased	(4,538,222	)		(15,763,557	)	(4,832,192	)		(16,224,882	)
Exchanged into associated funds	(795,234	)		(2,769,302	)	(1,301,150	)		(4,330,091	)
Total	(5,333,456	)		(18,532,859	)	(6,133,342	)		(20,554,973	)
Increase (decrease)	(3,197,273	)	$	(11,046,552	)	209,097		$	697,248

See footnotes on page 24.

23

Notes to Financial Statements

	Year Ended December 31,
	2004					2003
Class D	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	883,302		$	3,072,468		971,003		$	3,242,054
Investment of dividends	1,350,531			4,693,220		1,714,869			5,744,394
Exchanged from associated funds	687,056			2,410,932		1,631,198			5,447,906
Total	2,920,889			10,176,620		4,317,070			14,434,354
Cost of shares repurchased	(9,776,462	)		(34,014,496	)	(9,663,490	)		(32,471,269	)
Exchanged into associated funds	(847,479	)		(2,933,075	)	(1,276,564	)		(4,296,085	)
Total	(10,623,941	)		(36,947,571	)	(10,940,054	)		(36,767,354	)
Decrease	(7,703,052	)	$	(26,770,951	)	(6,622,984	)	$	(22,333,000	)
Class I	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	481,981		$	1,683,385		575,349		$	1,913,003
Investment of dividends	141,815			490,350		107,251			359,386
Total	623,796			2,173,735		682,600			2,272,389
Cost of shares repurchased	(315,154	)		(1,074,498	)	(115,864	)		(389,219	)
Increase	308,642		$	1,099,237		566,736		$	1,883,170
	Year Ended					April 30, 2003* to
	December 31, 2004					December 31, 2003
Class R	Shares		Amount			Shares		Amount
Net proceeds from sales of shares	205,237		$	717,845		445		$	1,500
Investment of dividends	10,004			34,367		23			77
Exchanged from associated funds	11,894			41,628		—			—
Increase	227,135			793,840		468			1,577
Cost of shares repurchased	(22,356	)		(77,342	)	—			—
Increase	204,779		$	716,498		468		$	1,577

*	Commencement of offering of shares.
**	Automatic conversion of Class B shares to Class A shares approximately eight years after the initial purchase date. The amount of dividends accrued on Class B shares between the last dividend payment date and the conversion date is invested in Class A shares and is included in the conversion from Class B amount.

8.

Other Matters — The Manager conducted an extensive internal review in response to developments regarding disruptive or illegal trading practices within the mutual fund industry. As of September 2003, the Manager had one arrangement that permitted frequent trading in the Seligman registered investment companies (“Seligman Funds”). This arrangement was in the process of being closed down by the Manager before the first proceedings relating to trading practices within the mutual fund industry were publicly announced. Based on a review of the Manager’s records for 2001 through 2003, the Manager identified three other arrangements that had permitted frequent trading in the Seligman Funds. All three had already been terminated prior to the end of September 2002. The Securities and Exchange Commission (the “SEC”), the NASD and the Attorney General of the State of New York also are reviewing these matters.

The Manager also has reviewed its practice of placing some of the Seligman Funds’ orders to buy and sell portfolio securities with brokerage firms in recognition of their sales of Seligman Funds. At the time such orders were placed, this practice was permissible when done properly; however, the Manager believes that it may have violated applicable requirements for certain of such orders as a result of compensation arrangements the Manager had with certain brokerage firms. The Manager discontinued this practice entirely in October 2003. The Manager is confident that the execution of all such orders was consistent

24

Notes to Financial Statements

with its best execution obligations and that the Seligman Funds did not pay higher brokerage commissions than they would otherwise have paid for comparable transactions. The Manager has also responded fully to information requests from the SEC and the NASD relating to the Manager’s use of revenue sharing and fund portfolio brokerage commissions and will continue to provide additional information if, and as, requested.

The results of the Manager’s internal reviews were presented to the Independent Trustees of the Seligman Funds. In order to resolve matters with the Independent Trustees relating to the four arrangements that permitted frequent trading, which did not adversely affect Seligman High-Yield Bond Series, the Manager has made payments to three funds and has agreed to waive a portion of its management fee with respect to another fund. In order to resolve matters with the Independent Trustees with regard to portfolio brokerage commissions, in May 2004, the Manager made payments to each of twenty-four funds in an amount equal to the commissions paid by each such fund during the period from 1998 through 2003 to certain brokerage firms in recognition of sales of fund shares. Seligman High-Yield Bond Series generally does not pay brokerage commissions and thus did not receive any payment from the Manager.

25

Financial Highlights

The tables below are intended to help you understand each Class’s financial performance for the periods presented. Certain information reflects financial results for a single share of Beneficial Interest of a Class that was held throughout the periods shown. Per share amounts are calculated using average shares outstanding. “Total return” shows the rate that you would have earned (or lost) on an investment in each Class, assuming you reinvested all your dividends and capital gain distributions. Total returns do not reflect any taxes or sales charges and are not annualized for periods of less than one year.

Class A
	Year Ended December 31,
	2004		2003		2002		2001ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$3.55		$3.16		$3.69		$4.99		$6.26
Income (Loss) from Investment Operations:
Net investment income	0.27		0.26		0.28		0.47		0.64
Net realized and unrealized gain (loss)
on investments	(0.04	)	0.40		(0.47	)	(1.21	)	(1.21	)
Total from Investment Operations	0.23		0.66		(0.19	)	(0.74	)	(0.57	)
Less Distributions:
Dividends from net investment income	(0.27	)	(0.26	)	(0.28	)	(0.47	)	(0.64	)
Dividends in excess of net investment income	—	øø	(0.01	)	—		—		(0.02	)
Return of capital	—		—		(0.06	)	(0.09	)	(0.04	)
Total Distributions	(0.27	)	(0.27	)	(0.34	)	(0.56	)	(0.70	)
Net Asset Value, End of Year	$3.51		$3.55		$3.16		$3.69		$4.99
Total Return	7.03	%	21.84	%	(5.35	)%	(15.91	)%	(10.02	)%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$222,827		$248,869		$254,191		$360,394		$584,944
Ratio of expenses to average net assets	1.28	%	1.30	%	1.31	%	1.16	%	1.09	%
Ratio of net investment income to average net assets	7.78	%	7.88	%	8.53	%	10.61	%	11.08	%
Portfolio turnover rate	53.38	%	141.00	%	117.82	%	53.04	%	27.45	%

See footnotes on page 30.

26

Financial Highlights

Class B
			Year Ended December 31,
	2004		2003		2002		2001ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$3.55		$3.17		$3.70		$5.00		$6.26
Income (Loss) from Investment Operations:
Net investment income	0.24		0.24		0.26		0.43		0.59
Net realized and unrealized gain (loss) on investments	(0.02	)	0.39		(0.48	)	(1.21	)	(1.20	)
Total from Investment Operations	0.22		0.63		(0.22	)	(0.78	)	(0.61	)
Less Distributions:
Dividends from net investment income	(0.24	)	(0.24	)	(0.25	)	(0.43	)	(0.59	)
Dividends in excess of net investment income	(0.01	)	(0.01	)	—		—		(0.02	)
Return of capital	—		—		(0.06	)	(0.09	)	(0.04	)
Total Distributions	(0.25	)	(0.25	)	(0.31	)	(0.52	)	(0.65	)
Net Asset Value, End of Year	$3.52		$3.55		$3.17		$3.70		$5.00
Total Return	6.53	%	20.64	%	(6.07	)%	(16.58	)%	(10.66	)%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$228,229		$319,267		$326,688		$483,041		$723,751
Ratio of expenses to average net assets	2.03	%	2.05	%	2.06	%	1.91	%	1.84	%
Ratio of net investment income to average net assets	7.03	%	7.13	%	7.78	%	9.86	%	10.33	%
Portfolio turnover rate	53.38	%	141.00	%	117.82	%	53.04	%	27.45	%

See footnotes on page 30.

27

Financial Highlights

Class C
			Year Ended December 31,
	2004		2003		2002		2001ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$3.56		$3.17		$3.70		$5.00		$6.27
Income (Loss) from Investment Operations:
Net investment income	0.24		0.24		0.26		0.43		0.59
Net realized and unrealized gain (loss) on investments	(0.03	)	0.40		(0.48	)	(1.21	)	(1.21	)
Total from Investment Operations	(0.21	)	0.64		(0.22	)	(0.78	)	(0.62	)
Less Distributions:
Dividends from net investment income	(0.24	)	(0.24	)	(0.25	)	(0.43	)	(0.59	)
Dividends in excess of net investment income	(0.01	)	(0.01	)	—		—		(0.02	)
Return of capital	—		—		(0.06	)	(0.09	)	(0.04	)
Total Distributions	(0.25	)	(0.25	)	(0.31	)	(0.52	)	(0.65	)
Net Asset Value, End of Year	$3.52		$3.56		$3.17		$3.70		$5.00
Total Return	6.22	%	20.98	%	(6.08	)%	(16.59	)%	(10.81	)%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$48,012		$59,892		$52,709		$78,721		$87,204
Ratio of expenses to average net assets	2.03	%	2.05	%	2.06	%	1.91	%	1.84	%
Ratio of net investment income to average net assets	7.03	%	7.13	%	7.78	%	9.86	%	10.33	%
Portfolio turnover rate	53.38	%	141.00	%	117.82	%	53.04	%	27.45	%

See footnotes on page 30.

28

Financial Highlights

Class D
	Year Ended December 31,
	2004		2003		2002		2001ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$3.56		$3.17		$3.70		$5.00		$6.27
Income (Loss) from Investment Operations:
Net investment income	0.24		0.24		0.26		0.43		0.59
Net realized and unrealized gain (loss) on investments	(0.03	)	0.40		(0.48	)	(1.21	)	(1.21	)
Total from Investment Operations	0.21		0.64		(0.22	)	(0.78	)	(0.62	)
Less Distributions:
Dividends from net investment income	(0.24	)	(0.24	)	(0.25	)	(0.43	)	(0.59	)
Dividends in excess of net investment income	(0.01	)	(0.01	)	—		—		(0.02	)
Return of capital	—		—		(0.06	)	(0.09	)	(0.04	)
Total Distributions	(0.25	)	(0.25	)	(0.31	)	(0.52	)	(0.65	)
Net Asset Value, End of Year	$3.52		$3.56		$3.17		$3.70		$5.00
Total Return	6.22	%	20.98	%	(6.08	)%	(16.59	)%	(10.81	)%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$100,125		$128,582		$135,595		$217,133		$369,286
Ratio of expenses to average net assets	2.03	%	2.05	%	2.06	%	1.91	%	1.84	%
Ratio of net investment income to average net assets	7.03	%	7.13	%	7.78	%	9.86	%	10.33	%
Portfolio turnover rate	53.38	%	141.00	%	117.82	%	53.04	%	27.45	%

See footnotes on page 30.

29

Financial Highlights

Class I									Class R
	Year Ended December 31,						11/30/01*		Year		4/30/03*
							to		Ended		to
	2004		2003		2002		12/31/01ø		12/31/04		12/31/03
Per Share Data:
Net Asset Value, Beginning of Period	$3.55		$3.16		$3.69		$3.77		$3.55		$3.37
Income (Loss) from
Investment Operations:
Net investment income	0.29		0.28		0.29		0.02		0.25		0.17
Net realized and unrealized gain (loss)
on investments	(0.04	)	0.40		(0.47	)	(0.05	)	(0.02	)	0.19
Total from Investment Operations	0.25		0.68		(0.18	)	(0.03	)	0.23		0.36
Less Distributions:
Dividends from net investment income	(0.29	)	(0.28	)	(0.29	)	(0.01	)	(0.25	)	(0.17	)
Dividends in excess of net
investment income	—	øø	(0.01	)	—		—		(0.02	)	(0.01	)
Return of capital	—		—		(0.06	)	(0.04	)	—		—
Total Distributions	(0.29	)	(0.29	)	(0.35	)	(0.05	)	(0.27	)	(0.18	)
Net Asset Value, End of Period	$3.51		$3.55		$3.16		$3.69		$3.51		$3.55
Total Return	7.46	%	22.38	%	(5.02	)%	(0.91	)%	6.76	%	10.99	%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)	$6,500		$5,472		$3,085		$53		$720		$2
Ratio of expenses to average net assets	0.85	%	0.95	%	0.93	%	0.78	%†	1.53	%	1.56	%†
Ratio of net investment income
to average net assets	8.21	%	8.23	%	8.91	%	11.48	%†	7.53	%	7.64	%†
Portfolio turnover rate	53.38	%	141.00	%	117.82	%	53.04	%**	53.38	%	141.00	%‡
Without expense reimbursement:‡‡
Ratio of expenses to average net assets	—		—		0.98	%	1.43	%†
Ratio of net investment income
to average net assets	—		—		8.86	%	10.83	%†

†	Annualized.
*	Commencement of offering of shares.
**	For the year ended December 31, 2001.
‡	For the year ended December 31, 2003.
‡‡	The Manager, at its discretion, reimbursed certain expenses of Class I shares.
ø	As required, effective January 1, 2001, the Fund adopted the provisions of the AICPA Audit and Accounting Guide for
	Investment Companies and began amortizing premium on debt securities. The effect of this change for the year ended
	December 31, 2001, was to decrease net investment income per share by $0.01 for Classes A, B, C and D, decrease net
	realized and unrealized loss on investments per share by $0.01 for Classes A, B, C and D, and decrease the ratios of net
	investment income to average net assets from 10.77% to 10.61% for Class A, from 10.02% to 9.86% for Classes B, C, and
	D, and from 11.53% to 11.48% for Class I. The effect of this change per share for Class I was less than $0.01. The ratios
	for periods prior to January 1, 2001, have not been restated.
øø	Less than + or - $0.01

See Notes to Financial Statements.

30

Report of Independent Registered
Public Accounting Firm

The Trustees and Shareholders,
Seligman High-Yield Bond Series of
Seligman High Income Fund Series:

We have audited the accompanying statement of assets and liabilities of Seligman High-Yield Bond Series, one of the funds constituting Seligman High Income Fund Series (the “Fund”), including the portfolio of investments, as of December 31, 2004, and the related statement of operations for the year then ended, the statements of changes in net assets for each of the two years in the period then ended, and the financial highlights for each of the periods presented. These financial statements and financial highlights are the responsibility of the Fund’s management. Our responsibility is to express an opinion on these financial statements and financial highlights based on our audits.

We conducted our audits in accordance with the standards of the Public Company Accounting Oversight Board (United States). Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements and financial highlights are free of material misstatement. An audit includes consideration of internal control over financial reporting as a basis for designing audit procedures that are appropriate in the circumstances, but not for the purpose of expressing an opinion on the effectiveness of the Fund’s internal control over financial reporting. Accordingly, we express no such opinion. An audit also includes examining, on a test basis, evidence supporting the amounts and disclosures in the financial statements, assessing the accounting principles used and significant estimates made by management, as well as evaluating the overall financial statement presentation. Our procedures included confirmation of securities owned as of December 31, 2004, by correspondence with the Fund’s custodian and brokers; where replies were not received from brokers, we performed other auditing procedures. We believe that our audits provide a reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to above present fairly, in all material respects, the financial position of Seligman High-Yield Bond Series of Seligman High Income Fund Series as of December 31, 2004, the results of its operations for the year then ended, the changes in its net assets for each of the two years in the period then ended, and the financial highlights for the respective stated periods, in conformity with accounting principles generally accepted in the United States of America.

DELOITTE & TOUCHE LLP
New York, New York
February 23, 2005

31

Trustees and Officers

Information pertaining to the Trustees and Officers of Seligman High-Yield Bond Series is set forth below.

Independent Trustees

Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
Robert B. Catell (67)2,3	Chairman, Chief Executive Officer and Director, KeySpan Corporation (diver-
• Trustee: 2003 to Date	sified energy, gas and electric company); Director or Trustee of each of the
• Oversees 60 Portfolios in	investment companies of the Seligman Group of Funds† (except Seligman
Fund Complex	Cash Management Fund, Inc.); Director or Trustee, Alberta Northeast Gas,
	Ltd., Boundary Gas Inc., The Houston Exploration Company (oil and gas
	exploration, development and production companies); Edison Electric
	Institute, New York State Energy Research and Development Authority,
	Independence Community Bank, Business Council of New York State, Inc.,
	New York City Partnership, and the Long Island Association (business and
	civic organizations).
John R. Galvin (75)1,3	Dean Emeritus, Fletcher School of Law and Diplomacy at Tufts
• Trustee: 1995 to Date	University; Director or Trustee of each of the investment companies of
• Oversees 61 Portfolios in	the Seligman Group of Funds†; and Chairman Emeritus, American
Fund Complex	Council on Germany. Formerly, Governor of the Center for Creative
	Leadership; Director, Raytheon Co. (defense and commercial electronics)
	and USLIFE Corporation (life insurance). From June 1987 to June 1992,
	Mr. Galvin was the Supreme Allied Commander, Europe and the
	Commander-in-Chief, United States European Command.
Alice S. Ilchman (69)2,3	President Emerita, Sarah Lawrence College; Director or Trustee of each of
• Trustee: 1991 to Date	the investment companies of the Seligman Group of Funds†; Director,
• Oversees 61 Portfolios in	Jeannette K. Watson Summer Fellowship (summer internships for college
Fund Complex	students); Trustee, Save the Children (non-profit child-assistance organi-
	zation) and the Committee for Economic Development; Governor, Court
	of Governors, London School of Economics; and Director, Public
	Broadcasting Service (PBS). Formerly, Chairman, The Rockefeller
	Foundation (charitable foundation) and Director, New York Telephone
	Company.
Frank A. McPherson (71)2,3	Retired Chairman of the Board and Chief Executive Officer of Kerr-McGee
• Trustee: 1995 to Date	Corporation (diversified energy and chemical company); Director or
• Oversees 61 Portfolios in	Trustee of each of the investment companies of the Seligman Group of
Fund Complex	Funds†; Director, ConocoPhillips (integrated international oil corpora-
	tion), Integris Health (owner of various hospitals), BOK Financial (bank
	holding company), Oklahoma Chapter of the Nature Conservancy,
	Oklahoma Medical Research Foundation, Boys and Girls Clubs of
	Oklahoma, Oklahoma City Public Schools Foundation and Oklahoma
	Foundation for Excellence in Education. Formerly, Director, Kimberly-Clark
	Corporation (consumer products) and the Federal Reserve System’s
	Kansas City Reserve Bank.

See footnotes on page 35.

32

Trustees and Officers

Independent Trustees (continued)

Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
John E. Merow (75)1,3	Retired Chairman and Senior Partner, Sullivan & Cromwell LLP (law firm);
• Trustee: 1984 to Date	Director or Trustee of each of the investment companies of the Seligman
• Oversees 61 Portfolios	Group of Funds†; Director, Aleris International, Inc. (aluminum and zinc
in Fund Complex	recycler and aluminum rolled products); Director Emeritus, the Municipal
	Art Society of New York; Executive Committee Member and Secretary,
	the U.S. Council for International Business; Trustee and Vice Chairman,
	New York-Presbyterian Healthcare System, Inc.; Trustee, New York-
	Presbyterian Hospital; and Member of the American Law Institute and
	Council on Foreign Relations.
Betsy S. Michel (62)1,3	Attorney; Director or Trustee of each of the investment companies of the
• Trustee: 1984 to Date	Seligman Group of Funds†; Trustee, The Geraldine R. Dodge Foundation
• Oversees 61 Portfolios	(charitable foundation). Formerly, Chairman of the Board of Trustees of
in Fund Complex	St. George’s School (Newport, RI) and Trustee, World Learning, Inc.
	(international educational training).
Leroy C. Richie (63)1,3	Chairman and Chief Executive Officer, Q Standards Worldwide, Inc. (library
• Trustee: 2000 to Date	of technical standards); Director or Trustee of each of the investment com-
• Oversees 60 Portfolios	panies of the Seligman Group of Funds†(except Seligman Cash Manage-
in Fund Complex	ment Fund, Inc.); Director, Kerr-McGee Corporation (diversified energy and
	chemical company) and Infinity, Inc. (oil and gas services and exploration);
	Director and Chairman, Highland Park Michigan Economic Development
	Corp. Formerly, Trustee, New York University Law Center Foundation; Vice
	Chairman, Detroit Medical Center and the Detroit Economic Growth Corp.;
	Chairman and Chief Executive Officer, Capital Coating Technologies, Inc.
	(applied coating technologies); and Vice President and General Counsel,
	Automotive Legal Affairs, Chrysler Corporation.
Robert L. Shafer (72)2,3	Retired Vice President, Pfizer Inc. (pharmaceuticals); Director or Trustee
• Trustee: 1984 to Date	of each of the investment companies of the Seligman Group of Funds†
• Oversees 61 Portfolios	and Ambassador and Permanent Observer of the Sovereign and Military
in Fund Complex	Order of Malta to the United Nations. Formerly, Director, USLIFE
	Corporation (life insurance).
James N. Whitson (69)1,3	Retired Executive Vice President and Chief Operating Officer, Sammons
• Trustee: 1993 to Date	Enterprises, Inc. (a diversified holding company); Director or Trustee of each
• Oversees 61 Portfolios	of the investment companies of the Seligman Group of Funds†; Director,
in Fund Complex	CommScope, Inc. (manufacturer of coaxial cable). Formerly, Director and
	Consultant, Sammons Enterprises, Inc. and Director, C-SPAN (cable televi-
	sion network).

See footnotes on page 35.

33

Trustees and Officers

Interested Trustees and Principal Officers

Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
William C. Morris (66)*	Chairman, J. & W. Seligman & Co. Incorporated; Chairman of the Board
• Trustee and Chairman of	and Director or Trustee of each of the investment companies of the
the Board: 1988 to Date	Seligman Group of Funds†; Chairman, Seligman Advisors, Inc., Seligman
• Oversees 61 Portfolios in	Services, Inc., and Carbo Ceramics Inc. (manufacturer of ceramic prop-
Fund Complex	pants for oil and gas industry); Director, Seligman Data Corp.; and
	President and Chief Executive Officer, The Metropolitan Opera Associa-
	tion. Formerly, Director, Kerr-McGee Corporation (diversified energy and
	chemical company) and Chief Executive Officer of each of the investment
	companies of the Seligman Group of Funds.
Brian T. Zino (52)*	Director and President, J. & W. Seligman & Co. Incorporated; Chief
• Trustee: 1993 to Date	Executive Officer, President and Director or Trustee of each of the invest-
• President: 1995 to Date	ment companies of the Seligman Group of Funds†; Director, Seligman
• Chief Executive Officer:	Advisors, Inc. and Seligman Services, Inc.; Chairman, Seligman Data
2002 to Date	Corp.; Member of the Board of Governors of the Investment Company
	Institute; and Director, ICI Mutual Insurance Company.
• Oversees 61 Portfolios in
Fund Complex
Eleanor T. M. Hoagland (53)	Managing Director and Senior Vice President, Risk Manager, J. & W.
• Vice President and Chief	Seligman & Co. Incorporated; Vice President and Chief Compliance
Compliance Officer:	Officer for each of the investment companies of the Seligman Group of
July 2004 to Date	Funds†. Formerly, Managing Director, Partner and Chief Portfolio
	Strategist, AMT Capital Management from 1994 to 2000.
Kendall C. Peterson (48)	Managing Director, J. & W. Seligman & Co. Incorporated since 2001; Vice
• Vice President and	President of Seligman Portfolios, Inc. and Portfolio Manager of its High-
Portfolio Manager:	Yield Bond Portfolio. Formerly, Vice President and Portfolio Manager and
2001 to Date	Desk Head for High Yield Mutual Funds with Fortis, Inc. since 1999.
	From 1985 through 1999, served in a variety of capacities with The
	Prudential Insurance Company of America, the last six years of which he
	was Vice President and Portfolio Manager for High Yield Mutual Funds.
Thomas G. Rose (47)	Chief Financial Officer, Senior Vice President, Finance, and Treasurer,
• Vice President:	J. & W. Seligman & Co. Incorporated, Senior Vice President, Finance,
2000 to Date	Seligman Advisors, Inc. and Seligman Data Corp.; Vice President of each
	of the investment companies of the Seligman Group of Funds†; and of
	Seligman Services, Inc. and Seligman International, Inc. Formerly,
	Treasurer of the investment companies of the Seligman Group of Funds
	and Seligman Data Corp.

See footnotes on page 35.

34

Trustees and Officers

Interested Trustees and Principal Officers (continued)

Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
Lawrence P. Vogel (48)	Senior Vice President and Treasurer, Investment Companies, J. & W.
• Vice President:	Seligman & Co. Incorporated; Vice President and Treasurer of each of the
1992 to Date	investment companies of the Seligman Group of Funds†; and Treasurer,
• Treasurer: 2000 to Date	Seligman Data Corp. Formerly, Senior Vice President, Finance, J. & W.
	Seligman & Co. Incorporated, Seligman Advisors, Inc., Seligman
	International, Inc. and Seligman Data Corp.; Vice President, Seligman
	Services, Inc. and Treasurer, Seligman International, Inc.
Frank J. Nasta (40)	Managing Director, General Counsel and Corporate Secretary, J. & W.
• Secretary: 1994 to Date	Seligman & Co. Incorporated; Secretary of each of the investment compa-
	nies of the Seligman Group of Funds†, and Corporate Secretary,
	Seligman Advisors, Inc., Seligman Services, Inc., Seligman International,
	Inc. and Seligman Data Corp. Formerly, Senior Vice President, Law and
	Regulation Department, J. & W. Seligman & Co. Incorporated.

The Fund’s Statement of Additional Information (SAI) includes additional information about Fund trustees and is available, without charge, upon request. You may call toll-free (800) 221-2450 in the US or collect (212) 682-7600 outside the US to request a copy of the SAI, to request other information about the Fund, or to make shareholder inquiries.

ø	The address for each of the trustees and officers is 100 Park Avenue, 8th floor, New York, NY 10017. Each Trustee serves for
	an indefinite term, until the election and qualification of a successor or until his or her earlier death, resignation or removal.
	Each officer is elected annually by the Trustees.
†	The Seligman Group of Funds consists of 23 registered investment companies.
*	Mr. Morris and Mr. Zino are considered “interested persons” of the Fund, as defined in the Investment Company Act of 1940,
	as amended, by virtue of their positions with J. & W. Seligman & Co. Incorporated and its affiliates.

Member:	1 Audit Committee
	2 Trustee Nominating Committee
	3 Board Operations Committee

35

Required Federal Income Tax
Information (unaudited)

Of ordinary dividends paid to shareholders during the Fund’s fiscal year ended December 31, 2004, 1.88% is eligible for the dividends received deduction for corporations.

For the fiscal year ended December 31, 2004, the Fund designates 1.88%, or the maximum amount allowable, of its distributions as qualified dividend income.

36

For More Information

ImportantTelephoneNumbers

(800) 221-2450	Shareholder  Services
(800) 445-1777	Retirement Plan Services
(212) 682-7600	Outside the United States
(800) 622-4597	24-Hour Automated Telephone Access Service

QuarterlySchedule of Investments

A complete schedule of portfolio holdings owned by the Fund will be filed with the SEC for the first and third quarters of each fiscal year on Form N-Q, and will be available to shareholders (i) without charge, upon request, by calling toll-free (800) 221-2450 in the US or collect (212) 682-7600 outside the US or (ii) on the SEC’s website at www.sec.gov. In addition, the Form N-Q may be reviewed and copied at the SEC’s Public Reference Room in Washington, D.C. Information on the operation of the Public Reference Room may be obtained by calling (800) SEC-0330. Certain of the information contained in the Fund’s Form N-Q is also made available to shareholders on Seligman’s website at www.seligman.com.¹

Proxy VotingPolicies and Procedures

A description of the policies and procedures used by the Fund to determine how to vote proxies relating to portfolio securities as well as information regarding how the Fund voted proxies relating to portfolio securities during the most recent 12-month period ended June 30, is available (i) without charge, upon request, by calling toll-free (800) 221-2450 in the US or collect (212) 682-7600 outside the US and (ii) on the SEC’s website at www.sec.gov.

This report is intended only for the information of shareholders or those who have received the offering prospectus covering shares of Beneficial Interest of Seligman High-Yield Bond Series, which contains information about the sales charges, management fee, and other costs. Please read the prospectus carefully before investing or sending money.

¹      The reference to Seligman’s website is an inactive textual reference and information contained in or otherwise accessible through Seligman’s website does not form a part of this report or the Fund’s prospectus.

TXHY2 12/04

Seligman
U.S. Government
Securities Series

Annual Report  
December 31, 2004

Seeking High Current
Income by Investing in
US Government Securities

J. & W. SELIGMAN & CO.
INCORPORATED
ESTABLISHED 1864
100 Park Avenue, New York, NY 10017

Seligman

141 Years of Investment Experience

J. & W. Seligman & Co. Incorporated is a firm with a long tradition of investment expertise, offering a broad array of investment choices to help today’s investors seek their long-term financial goals.

Established in 1864, Seligman has a history of providing financial services marked not by fanfare, but rather by a quiet and firm adherence to financial prudence. While the world has changed dramatically in the 141 years since Seligman first opened its doors, the firm has continued to offer its clients high-quality investment solutions through changing times.

In the late 19th century, as the country grew, Seligman helped finance the westward expansion of the railroads, the construction of the Panama Canal, and the launching of urban transit systems. In the early 20th century, the firm helped fund the growing capital needs of new industries, including the nascent automobile and steel industries.

With the formation of Tri-Continental Corporation in 1929 — today, one of the nation’s largest diversified publicly-traded closed-end equity investment companies — Seligman began shifting its emphasis to investment management. In 1930, Seligman established what would be the first in an impressive lineup of mutual funds.

Seligman is proud of its distinctive past and of the traditional values that continue to shape the firm’s business decisions and investment judgment. While much has changed over the years, the firm's commitment to providing prudent investment management that seeks to build wealth for clients over time is an enduring value that will continue to guide Seligman.

Table of Contents
To The Shareholders	1
Interview With Your Portfolio Manager	2
Performance Overview	4
Portfolio Overview	6
Understanding and Comparing Your  Fund’s Expenses	7
Portfolio of Investments	8
Statement of  Assets and Liabilities	10
Statement of Operations	11
Statements of Changes in Net Assets	12
Notes to Financial Statements	13
Financial Highlights	19
Report of Independent
Registered Public
Accounting Firm	24
Trustees and Executive Officers	25
For More Information	back
	cover

To The Shareholders

Your annual shareholder report for Seligman U.S. Government Securities Series follows this letter. This report contains an interview with your Fund’s Portfolio Manager, as well as your Fund’s investment results and financial statements, including a portfolio of investments.

During the year ended December 31, 2004, Seligman U.S. Government Securities Series delivered a total return of 1.09% based on the net asset value of Class A shares. During the same time, the Lipper General US Government Bond Funds Average returned 3.22% and the Lehman Brothers Government Bond Index returned 3.48% .

We thank you for your continued support of Seligman U.S. Government Securities Series and look forward to serving your investment needs for many years to come.

By Order of the Trustees,

William C. Morris
Chairman

Brian T. Zino
President

February 23, 2005

Manager	Shareholder Service Agent	General Distributor
J. & W. Seligman & Co. Incorporated	Seligman Data Corp.	Seligman Advisors, Inc.
100 Park Avenue	100 Park Avenue	100 Park Avenue
New York, NY 10017	New York, NY 10017	New York, NY 10017
Independent Registered	General Counsel
Public Accounting Firm	Sullivan & Cromwell LLP
Deloitte & Touche LLP

1

Interview With Your Portfolio Manager

Christopher J. Mahony

Q:	How did Seligman U.S. Government Securities Series perform for the fiscal year ended December 31, 2004?
A:	During the year ended December 31, 2004, Seligman U.S. Government Securities Series delivered a total return of 1.09% based on the net asset value of Class A shares. During the same time, the Lipper General US Government Bond Funds Average returned 3.22% and the Lehman Brothers Government Bond Index returned 3.48%.
Q:	What market conditions and events materially affected the Fund’s performance during the period?
A:	Aside from a brief period of rising rates in the Spring of 2004, the US government bond market was surprisingly stable during the Fund’s past fiscal year, and yields ended 2004 almost unchanged from the year’s beginning. At the start of 2004, the 10-year US Treasury bond was yielding 4.27%, and at year-end the yield stood at 4.24%.
	This stability in longer-term yields took place amid a series of Federal Reserve Board increases in the short-term federal funds rate. Despite the fact that short-term rates moved to their highest levels in more than three years, longer-term rates held steady as a result of continued demand for US Treasury securities by foreign investors, and an environment of continued low inflation and subdued job growth.
	The Federal Reserve Board also played a role in stabilizing the bond market. The Fed issues regular statements regarding their views on the state of the economy, whether or not they actually increase rates. These statements have prepared market participants for increases for some time, and the increases are thus often priced into bond yields even before the Fed raises rates. In addition, the Fed assured market participants that although they were raising rates, rates were still accommodative of economic growth, and they were simply attempting to contain inflationary pressures before they arise. The Fed’s “measured pace” approach, whereby they have not shocked the market with sudden and significant rate increases, has gone a long way toward keeping longer-term rates steady. This stability allowed the Fund’s holdings to maintain principal value better than they may have, had long-term rates risen sharply. However, the yields available to the Fund have re mained historically low.

A TEAM APPROACH

Seligman U.S. Government Securities Series is managed by the investment-grade team of Seligman’s Fixed Income Team. The investment-grade team is led by Christopher Mahony, who is assisted in the management of the Fund by seasoned research professionals who are responsible for identifying quality money market instruments in order to preserve capital and to maximize liquidity and current income. The Seligman Fixed Income Team is led by Kendall Peterson. Team members include Jeff Gallo, Paul Langlois, and Sau Lin Wu (trader).

2

Interview With Your Portfolio Manager

Christopher J. Mahony

Q:	What investment strategies or techniques materially affected the Fund’s performance during the period?
A:	In 2004, we continued to reduce the Fund’s exposure to US Treasuries, from 12.4% to 6.8%, while increasing exposure to Ginnie Mae (Government National Mortgage Association) CMOs (Collateralized Mortgage Obligations), from 62.1% to 76.5%. While Ginnie Mae CMOs are full faith and credit obligations of the US government, they offer higher yields than direct obligation Treasuries and, as spread products, they typically perform better in a rising-rate environment. While rates did not rise over the course of the year as we had anticipated, the Ginnie Mae CMOs did provide the Fund with some additional yield.
	In 2004, the bond market continued to favor lower-quality debt, although this sector of the market did not experience the strong rally that it did in 2003. Such an environment is not optimal for the Fund, which maintains a very high-quality portfolio.

The Fund’s average duration was 3.74 years in 2004, shorter than the duration of the Lehman Index. Duration is a measure of a portfolio’s sensitivity to changing interest rates, with shorter durations being more defensive in an environment of rising interest rates. A shorter duration is achieved by holding shorter maturity bonds. This had a negative effect on the Fund’s performance in 2004 because longer-maturity bonds delivered greater price increases than did shorter maturities.

The views and opinions expressed are those of the Portfolio Manager(s), are provided for general information only, and do not constitute specific tax, legal, or investment advice to, or recommendations for, any person. There can be no guarantee as to the accuracy of market forecasts. Opinions, estimates, and forecasts may be changed without notice.

3

Performance Overview

This section of the Annual Report is intended to help you understand the performance of Seligman US Government Securities Series (the “Fund”) and to provide a summary of the Fund’s portfolio characteristics.

Performance data quoted in this Annual Report represents past performance and does not guarantee future investment results. The rates of return will vary and the principal value of an investment will fluctuate. Shares, if redeemed, may be worth more or less than their original cost. Current performance may be lower or higher than the performance data quoted. Total returns of the Fund as of the most recent month-end will be available at www.seligman.com¹ by the seventh business day following that month-end. Calculations assume reinvestment of distributions. Performance data quoted does not reflect the deduction of taxes that an investor may pay on distributions or the redemption of shares.

Returns for Class A shares are calculated with and without the effect of the initial 4.75% maximum sales charge. Returns for Class B shares are calculated with and without the effect of the maximum 5% contingent deferred sales charge (“CDSC”), charged on redemptions made within one year of purchase, declining to 1% in the sixth year and 0% thereafter. Return from inception for Class B shares reflects automatic conversion to Class A shares approximately eight years after inception date. Returns for Class C shares are calculated with and without the effect of the initial 1% maximum sales charge and the 1% CDSC that is charged on redemptions made within 18 months of purchase. Returns for Class D and Class R shares are calculated with and without the effect of the 1% CDSC, charged on redemptions made within one year of purchase.

The chart on page 5 compares a $10,000 hypothetical investment made in Class A shares, with and without the initial 4.75% maximum sales charge, and in Class D shares, without the 1% CDSC, to a $10,000 investment made in the Lehman Brothers Government Bond Index for the 10-year period ended December 31, 2004. The performance of Class B, Class C and Class R shares, which commenced on later dates, and of Class A and Class D shares for other periods, with and without applicable sales charges and CDSCs, is not shown in this chart but is included in the total returns table that follows the chart. The performance of Class B, Class C, and Class R shares will differ from the performance shown for Class A and Class D shares, based on the differences in sales charges and fees paid by shareholders. The Lehman Brothers Government Bond Index excludes the effect of taxes, fees and sales charges.

¹      The reference to Seligman’s website is an inactive textual reference and information contained in or otherwise accessible through Seligman’s website does not form a part of this report or the Fund’s prospectus.

4

Performance Overview

Investment Results
Total Returns
For Periods Ended December 31, 2004

							Average Annual
									Class B		Class C		Class R
									Since		Since		Since
	Six		One		Five		Ten		Inception		Inception		Inception
	Months*		Year		Years		Years		1/1/97		5/27/99		4/30/03
Class A
With Sales Charge	(2.88	)%	(3.70	)%	4.95	%	5.45	%	n/a		n/a		n/a
Without Sales Charge	1.93		1.09		5.96		5.96		n/a		n/a		n/a
Class B
With CDSC†	(3.45	)	(4.57	)	4.87		n/a		n/a		n/a		n/a
Without CDSC	1.55		0.34		5.20		n/a		4.51	%#	n/a		n/a
Class C
With Sales Charge and CDSC††	(0.44	)	(1.73	)	4.95		n/a		n/a		4.14	%	n/a
Without Sales Charge and CDSC	1.55		0.20		5.17		n/a		n/a		4.33		n/a
Class D
With 1% CDSC	0.55		(0.64	)	n/a		n/a		n/a		n/a		n/a
Without CDSC	1.55		0.34		5.17		5.15		n/a		n/a		n/a
Class R
With 1% CDSC	0.60		(0.16	)	n/a		n/a		n/a		n/a		n/a
Without CDSC	1.60		0.82		n/a		n/a		n/a		n/a		0.46	%
Lehman Brothers
Government Bond Index**	3.61		3.48		7.48		7.46		6.76		6.63	‡	4.31
Lipper General US
Government Funds Average**	3.59		3.22		6.48		6.49		5.76		5.57		2.03

See footnotes on page 6.

5

Performance Overview

				Dividends Per Share and Yield Information
Net Asset Value Per Share				For the Year Ended December 31, 2004
	12/31/04	6/30/04	12/31/03	Dividends Paidø	SEC 30-Day Yieldsøø
Class A	$7.10	$7.07	$7.23	$0.208	2.79	%
Class B	7.12	7.09	7.25	$0.155	2.19
Class C	7.11	7.08	7.25	$0.155	2.17
Class D	7.11	7.08	7.24	$0.155	2.18
Class R	7.10	7.08	7.23	$0.192	2.68

Weighted Average Maturity 21.1 years

*	Returns for periods of less than one year are not annualized.
**	The Lehman Brothers Government Bond Index and the Lipper General US Government Bond Funds Average are unman-
	aged benchmarks that assume reinvestment of dividends and exclude the effect of taxes and sales charges. The Lehman
	Brothers Government Bond Index also excludes the effect of fees. The Lipper General US Government Bond Funds Average
	invests at least 65% of its assets in US government and government agency issues. The Lehman Brothers Government
	Bond Index is a benchmark index made up of the Treasury Bond Index and the Agency Bond Index as well as the 1-3 Year
	Government Index and 20+ Year Treasury Index. Investors cannot invest directly in an average or an index.
†	The CDSC is 5% for periods of one year or less, and 2% for the five-year period.
††	The CDSC is 1% for periods up to 18 months.
‡	From May 28, 1999.
#	Returns from inception for Class B shares reflects automatic conversion to Class A shares approximately eight years after
	inception date.
ø	Represents per share amount paid or declared for the year ended December 31, 2004.
øø	Current yield, representing the annualized yield for the 30-day period ended December 31, 2004, has been computed in
	accordance with SEC regulations and will vary.

An investment in the Fund is not insured by the Federal Deposit Insurance Corporation or any other government agency.

Portfolio Overview

Composition of Net Assets

December 31, 2004

	Percent of Portfolio
	12/31/04	12/31/03
US Treasury	6.8	12.4
US Obligations	83.3	69.7
Agency Obligations	6.6	13.0
Short-Term	3.3	4.9
Total	100.0	100.0

6

Understanding and Comparing
Your Fund’s Expenses

As a shareholder of the Fund, you incur ongoing expenses, such as management fees, distribution and/or service (12b-1) fees, and other fund expenses. The information below is intended to help you understand your ongoing expenses (in dollars) of investing in the Fund and to compare them with the ongoing expenses of investing in other mutual funds. Please note that the expenses shown in the table are meant to highlight your ongoing expenses only and do not reflect any transactional costs, such as sales charges (also known as loads) on certain purchases or redemptions. Therefore, the table is useful in comparing ongoing expenses only, and will not help you to determine the relative total expenses of owning different funds. In addition, if transactional costs were included, your total expenses would have been higher.

The table is based on an investment of $1,000 invested at the beginning of July 1, 2004 and held for the entire six-month period ended December 31, 2004.

Actual Expenses

The table below provides information about actual expenses and actual account values. You may use the information, together with the amount you invested, to estimate the expenses that you paid over the period. Simply divide your account value at the beginning of the period by $1,000 (for example, an $8,600 account value divided by $1,000 = 8.6), then multiply the result by the number under the heading entitled “Expenses Paid During Period” for the Fund’s share class that you own to estimate the expenses that you paid on your account during the period.

Hypothetical Example for Comparison Purposes

The table below also provides information about hypothetical expenses and hypothetical account values based on the actual expense ratios of each class and an assumed rate of return of 5% per year before expenses, which is not the actual return of any class of the Fund. The hypothetical expenses and account values may not be used to estimate the ending account value or the actual expenses you paid for the period. You may use this information to compare the ongoing expenses of investing in the Fund and other mutual funds. To do so, compare this 5% hypothetical example with the 5% hypothetical examples that appear in the shareholder reports of the other mutual funds.

				Actual			Hypothetical
	Beginning			Ending		Ending
	Account	Annualized		Account	Expenses Paid	Account		Expenses Paid
	Value	Expense		Value	During Period**	Value		During Period**
	7/1/04	Ratio*		12/31/04	7/1/04 to 12/31/04	12/31/04		7/1/04 to 12/31/04
Class A	$1,000.00	1.29	%	$1,019.30	$6.55	$	1,018.65	$6.55
Class B	1,000.00	2.04	%	1,015.50	10.34		1,014.88	10.33
Class C	1,000.00	2.04	%	1,015.50	10.34		1,014.88	10.33
Class D	1,000.00	2.04	%	1,015.50	10.34		1,014.88	10.33
Class R	1,000.00	1.54	%	1,016.00	7.80		1,017.39	7.81

*	Expenses of Class B, Class C, Class D and Class R shares differ from the expenses of Class A shares due to the differences in 12b-1 fees paid by each share class. See the Fund’s prospectus for a description of each share class and its expenses and sales charges.
**	Expenses are equal to the annualized expense ratio based on actual expenses for the period July 1, 2004 to December 31, 2004, multiplied by the average account value over the period, multiplied by 184/366 (number of days in the period).

7

Portfolio of Investments
December 31, 2004

		Principal
		Amount		Value
US Full Faith and Credit Obligations 90.0%
US Treasury Notes:
4.375%, 5/15/2007	$	1,400,000	$	1,439,321
3.125%, 4/15/2009		5,000,000		4,925,785
Government National Mortgage Association (“Ginnie Mae”):*
5%, 4/16/2018		4,250,961		4,356,694
5%, 5/20/2025		8,350,000		8,097,567
4.25%, 7/20/2027		4,786,212		4,789,646
4%, 12/16/2028		4,176,359		4,162,779
4.5%, 6/20/2028		4,862,629		4,903,742
6%, 5/20/2029		84,118		84,367
5%, 5/20/2029		14,940,176		15,225,716
2.71%, 2/20/2031		8,000,000		7,969,098
5.5%, 2/20/2033		4,270,013		4,403,713
3.625%, 4/16/2033		4,949,169		4,780,037
5.5%, 11/20/2033		8,000,000		7,992,145
4%, 1/20/2034		1,932,816		1,918,166
4.5%, 5/20/2034		2,689,775		2,722,419
Small Business Administration
5.199%, 8/1/2012		1,801,698		1,841,560
US Government Guaranteed Title XI (Vessel Management)
6.75% 7/15/2025		1,680,000		1,929,633
US Trade Funding
4.26% 11/15/2014		1,824,609		1,828,184
Veteran Affairs Vendee Mortgage Trust*
7.5% 12/15/2006		616,368		618,836
Total US Full Faith and Credit Obligations (Cost $84,184,659)				83,989,408
Agency Obligations 6.6%
Federal Home Loan Mortgage (“Freddie Mac”)*
6%, 11/1/2010		245,918		259,542
Federal National Mortgage Association (“Fannie Mae”)
5%, 7/25/2024		6,000,000		5,892,007
Total Agency Obligations (Cost $6,081,653)				6,151,549

See footnotes on page 9.

8

Portfolio of Investments

December 31, 2004

	Principal
	Amount	Value
Short-Term Investments 3.2%
Federal Home Loan Bank 2.1059%, 1/19/2005	$ 160,000	$159,823
Repurchase agreement, State Street Bank & Trust 1.4%,
dated 12/31/2004 maturing 1/3/2005 in the amount of
$2,867,334, collateralized by $2,970,000 US Treasury
Notes 2.625%, due 11/15/2006, with a fair market value
of $2,955,150	2,867,000	2,867,000
Total Short-Term Investments (Cost $3,026,823)		3,026,823
Total Investments (Cost 93,293,135) 99.8%		93,167,780
Other Asset Less Liabilities 0.2%		190,167
Net Assets 100.0%		93,357,947

*      Investments in mortgage-backed securities are subject to principal paydowns. As a result of prepayments from refinancing or satisfaction of the underlying mortgage instruments, the average life may be less than the original maturity. This in turn may impact the ultimate yield realized from these securities.

See Notes to Financial Statements.

9

Statement of Assets and Liabilities

December 31, 2004

Assets:
Investments, at value:
US Full Faith and Credit Obligations (cost $84,184,659)		$  83,989,408
Agency Obligations (cost $6,081,653)		6,151,549
Short-term investments (cost $3,026,823)		3,026,823
Total investments (cost $93,293,135)		93,167,780
Cash		5,224
Receivable for interest		389,402
Receivable for shares of Beneficial Interest sold		233,815
Expenses prepaid to shareholder service agent		25,487
Other		4,549
Total Assets		93,826,257
Liabilities:
Payable for shares of Beneficial Interest repurchased		207,944
Dividends payable		106,374
Distribution and service fees payable		48,931
Management fee payable		39,664
Accrued expenses and other		65,397
Total Liabilities		468,310
Net Assets		$  93,357,947
Composition of Net Assets:
Shares of Beneficial Interest, at par ($0.001 par value; unlimited shares authorized;
13,136,141 shares outstanding):
Class A		$  6,697
Class B		3,379
Class C		1,373
Class D		1,625
Class R		62
Additional paid-in capital		99,913,542
Dividends in excess of net investment income		(50,600	)
Accumulated net realized loss		(6,392,776	)
Net unrealized depreciation of investments		(125,355	)
Net Assets		$  93,357,947
Net Asset Value Per Share:
Class A	($47,552,711 ÷ 6,697,627 shares)	7.10
Class B	($24,044,970 ÷ 3,379,328 shares)	7.12
Class C	($9,764,255 ÷ 1,372,672 shares)	7.11
Class D	($11,556,420 ÷ 1,624,643 shares)	7.11
Class R	($439,591 ÷ 61,871 shares)	7.10

See Notes to Financial Statements.

10

Statement of Operations
For the Year Ended December 31, 2004

Investment Income:
Interest	$	4,361,400
Expenses:
Distribution and service fees		696,713
Management fee		548,459
Shareholder account services		412,582
Registration		90,035
Auditing and legal fees		36,974
Custody and related services		34,514
Shareholder reports and communications		20,297
Trustees’ fees and expenses		10,174
Miscellaneous		15,121
Total Expenses		1,864,869
Net Investment Income		2,496,531
Net Realized and Unrealized Gain (Loss) on Investments:
Net realized loss on investments		(2,198,295	)
Net change in unrealized depreciation of investments		437,869
Net Loss on Investments		(1,760,426	)
Increase in Net Assets from Operations	$	736,105

See Notes to Financial Statements.

11

Statements of Changes in Net Assets

		Year Ended December 31,
		2004			2003
Operations:
Net investment income	$	2,496,531		$	3,367,059
Net realized gain (loss) on investments		(2,198,295	)		1,190,290
Net change in unrealized appreciation/depreciation of investments		437,869			(4,425,134	)
Increase in Net Assets from Operations		736,105			132,215
Distribution to Shareholders:
Net investment income:*
Class A		(1,387,965	)		(1,683,740	)
Class B		(600,395	)		(948,534	)
Class C		(250,925	)		(397,431	)
Class D		(249,344	)		(337,333	)
Class R		(7,902	)		(21	)
Total		(2,496,531	)		(3,367,059	)
Dividends in excess of net investment income:*
Class A		(159,849	)		(365,851	)
Class B		(69,146	)		(206,102	)
Class C		(28,898	)		(86,356	)
Class D		(28,716	)		(73,297	)
Class R		(910	)		(4	)
Total		(287,519	)		(731,610	)
Decrease in Net Assets from Distributions		(2,784,050	)		(4,098,669	)
Capital Share Transactions:
Net proceeds from sales of shares		7,388,003			35,976,490
Investment of dividends		2,188,905			3,112,959
Exchanged from associated funds		16,694,284			71,077,284
Total		26,271,192			110,166,733
Cost of shares repurchased		(41,135,646	)		(73,839,727	)
Exchanged into associated funds		(23,578,197	)		(94,886,553	)
Total		(64,713,843	)		(168,726,280	)
Decrease in Net Assets from Capital Share Transactions		(38,442,651	)		(58,559,547	)
Decrease in Net Assets		(40,490,596	)		(62,526,001	)
Net Assets:
Beginning of year		133,848,543			196,374,544
End of Year (net of dividends in excess of
net investment income of $50,600 and $203,725, respectively)	$	93,357,947		133,848,543

* For tax purposes, these distributions are considered ordinary income. 

See Notes to Financial Statements. 

12

Notes to Financial Statements

1.	Multiple Classes of Shares — Seligman U.S. Government Securities Series (the “Fund”) is a series of Seligman High Income Fund Series (the “Series”). The Fund offers the following five classes of shares:
	Class A shares are sold with an initial sales charge of up to 4.75% and a continuing service fee of up to 0.25% on an annual basis. Class A shares purchased in an amount of $1,000,000 or more are sold without an initial sales charge but are subject to a contingent deferred sales charge (“CDSC”) of 1% on redemptions within 18 months of purchase.
	Class B shares are sold without an initial sales charge but are subject to a distribution fee of 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 5% on redemptions in the first year of purchase, declining to 1% in the sixth year and 0% thereafter. Class B shares will automatically convert to Class A shares during the month that precedes the eighth anniversary of their date of purchase. If Class B shares of the Fund are exchanged for Class B shares of another Seligman mutual fund, the holding period of the shares exchanged will be added to the holding period of the shares acquired, both for determining the applicable CDSC and the conversion of Class B shares to Class A shares.
	Class C shares are sold primarily with an initial sales charge of up to 1%, and a CDSC, if applicable, of 1% imposed on redemptions made within 18 months of purchase. Shares purchased through certain financial intermediaries may be bought without an initial sales charge and with a 1% CDSC on redemptions made within 12 months of purchase. All Class C shares are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis.
	Class D shares are sold without an initial sales charge but are subject to a distribution fee of up to 0.75% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% imposed on redemptions made within one year of purchase.
	Class R shares are offered to certain employee benefit plans and are not available to all investors. They are sold without an initial sales charge, but are subject to a distribution fee of up to 0.25% and a service fee of up to 0.25% on an annual basis, and a CDSC, if applicable, of 1% on redemptions made within one year of a plan’s initial purchase of Class R shares.
	All classes of shares represent interests in the same portfolio of investments, have the same rights and are generally identical in all respects except that each class bears its separate distribution and certain other class-specific expenses, and has exclusive voting rights with respect to any matter on which a separate vote of any class is required.
2.	Significant Accounting Policies — The financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America which require management to make certain estimates and assumptions at the date of the financial statements. Actual results may differ from these estimates. The following summarizes the significant accounting policies of the Fund:
	a.	Security Valuation — Investments in US Government and Government agency obligations are valued at current market values or, in their absence, at fair values determined in accordance with procedures approved by the trustees. Securities traded on an exchange are valued at last sales prices or, in their absence and in the case of over-the-counter securities, at the mean of bid and asked prices. Short-term holdings maturing in 60 days or less are valued at amortized cost.
	b.	Federal Taxes — There is no provision for federal income tax. The Fund has elected to be taxed as a regulated investment company and intends to distribute substantially all taxable net income and net realized gain.

13

Notes to Financial Statements

c.	Security Transactions and Related Investment Income — Investment transactions are recorded on trade dates. Identified cost of investments sold is used for both financial reporting and federal income tax purposes. Interest income is recorded on an accrual basis. The Fund amortizes premiums and discounts on purchases of portfolio securities for financial reporting purposes.
d.	Repurchase Agreements — The Fund may enter into repurchase agreements with commercial banks and with broker/dealers deemed to be creditworthy by J. & W. Seligman & Co. Incorporated (the “Manager”). Securities received as collateral subject to repurchase agreements are deposited with the Fund’s custodian and, pursuant to the terms of the repurchase agreements, must have an aggregate market value greater than or equal to the repurchase price plus accrued interest at all times. Procedures have been established to monitor, on a daily basis, the market value of repurchase agreements’ underlying securities to ensure the existence of the proper level of collateral.
e.	Multiple Class Allocations — All income, expenses (other than class-specific expenses), and realized and unrealized gains or losses are allocated daily to each class of shares based upon the relative value of shares of each class. Class-specific expenses, which include distribution and service fees and any other items that are specifically attributable to a particular class, are charged directly to such class. For the year ended December 31, 2004, distribution and service fees were the only class-specific expenses.
f.	Distributions to Shareholders — Dividends and distributions to shareholders are recorded on ex-dividend dates.

3.	Purchases and Sales of Securities — Purchases and sales of portfolio securities, excluding short-term investments, for the year ended December 31, 2004, amounted to $136,258,516 and $171,451,729, respectively.
4.	Management Fee, Distribution Services, and Other Transactions — The Manager manages the affairs of the Fund and provides the necessary personnel and facilities. Compensation of all officers of the Fund, all directors of the Fund who are employees of the Manager, and all personnel of the Fund and the Manager is paid by the Manager. The Manager receives a fee, calculated daily and payable monthly, equal to 0.50% per annum of the Fund’s average daily net assets.
	Seligman Advisors, Inc. (the “Distributor”), agent for the distribution of the Fund’s shares and an affiliate of the Manager, received concessions of $1,391 from sales of Class A shares. Commissions of $11,039 and $3,802 were paid to dealers for sales of Class A and Class C shares, respectively.
	The Fund has an Administration, Shareholder Services and Distribution Plan (the “Plan”) with respect to distribution of its shares. Under the Plan, with respect to Class A shares, service organizations can enter into agreements with the Distributor and receive a continuing fee of up to 0.25% on an annual basis, payable quarterly, of the average daily net assets of the Class A shares attributable to the particular service organizations for providing personal services and/or the maintenance of shareholder accounts. The Distributor charges such fees to the Fund pursuant to the Plan. For the year ended December 31, 2004, fees incurred under the Plan aggregated $130,559, or 0.25% per annum of the average daily net assets of Class A shares.
	Under the Plan, with respect to Class B shares, Class C shares, Class D shares, and Class R shares, service organizations can enter into agreements with the Distributor and receive a continuing fee for providing personal services and/or the maintenance of shareholder accounts of up to 0.25% on an annual basis of the average daily net assets of the Class B, Class C, Class D, and Class R shares for which the organizations are responsible; and, for Class C, Class D, and Class R shares, fees for providing other distribution assistance of up to 0.75% (0.25%, in the case of Class R shares) on an annual basis of such average daily net assets. Such fees are paid mont hly by the Fund to the Distributor pursuant to the Plan.

14

Notes to Financial Statements

With respect to Class B shares, a distribution fee of 0.75% on an annual basis of average daily net assets is payable monthly by the Fund to the Distributor; however, the Distributor has sold its rights to this fee with respect to a substantial portion of Class B shares to third parties (the “Purchasers”), which provide funding to the Distributor to enable it to pay commissions to dealers at the time of the sale of the related Class B shares.

For the year ended December 31, 2004, fees incurred under the Plan, equivalent to 1% per annum of the average daily net assets of Class B, Class C, and Class D shares, and 0.50% per annum of average daily net assets of Class R shares amounted to $307,992, $128,458, $128,044, and $1,660, respectively.

The Distributor is entitled to retain any CDSC imposed on certain redemptions of Class A, Class C, Class D and Class R shares. For the year ended December 31, 2004, such charges amounted to $29,730.

The Distributor has sold its rights to collect any CDSC imposed on redemptions of Class B shares to the Purchasers. In connection with the sale of its rights to collect any CDSC and the distribution fees with respect to Class B shares described above, prior to August 1, 2004, the Distributor received payments from the Purchasers based on the value of Class B shares sold. The aggregate of such payments and distribution fees retained by the Distributor, for the year ended December 31, 2004, amounted to $2,878.

Seligman Services, Inc., an affiliate of the Manager, is eligible to receive commissions from certain sales of shares of the Fund, as well as distribution and service fees pursuant to the Plan. For the year ended December 31, 2004, Seligman Services, Inc. received commissions of $1,213 from the sales of shares of the Fund. Seligman Services, Inc. also received distribution and service fees of $12,369 pursuant to the Plan.

Seligman Data Corp., which is owned by certain associated investment companies, charged the Fund at cost $412,582 for shareholder account services in accordance with a methodology approved by the Fund’s trustees.

Costs of Seligman Data Corp. directly attributable to the Fund were charged to the Fund. The remaining charges were allocated to the Fund by Seligman Data Corp. pursuant to a formula based on the Fund’s net assets, shareholder transaction volume and number of shareholder accounts.

The Series and certain other associated investment companies (together, the “Guarantors”) have severally but not jointly guaranteed the performance and observance of all the terms and conditions of two leases entered into by Seligman Data Corp., including the payment of rent by Seligman Data Corp. (the “Guaranties”). The leases and the Guaranties expire in September 2008 and January 2009. The obligation of the Series to pay any amount due under either Guaranty is limited to a specified percentage of the full amount, which generally is based on the Series’ percentage of the expenses billed by Seligman Data Corp. to all Guarantors in the preceding calendar quarter. As of December 31, 2004, the Series’ potential obligation under the Guaranties is $459,600. As of December 31, 2004, no event has occurred which would result in the Series becoming liable to make any payment under a Guaranty. The Fund would bear a portion of any payments made by the Series under the Guaranties. A portion of rent paid by Seligman Data Corp. is charged to the Fund as part of Seligman Data Corp.’s shareholder account services cost.

Certain officers and trustees of the Fund are officers or directors of the Manager, the Distributor, Seligman Services, Inc., and/or Seligman Data Corp.

The Fund has a compensation arrangement under which trustees who receive fees may elect to defer receiving such fees. Trustees may elect to have their deferred fees accrue interest or earn a return based on the performance of the Fund or other funds in the Seligman Group of Investment Companies. The cost of such fees and earnings/loss accrued thereon is included in trustees’ fees and expenses and the accumulated balance thereof at December 31, 2004, of $16,137 is included in accrued expenses and other liabilities. Deferred fees and related accrued earnings are not deductible by the Fund for federal income tax purposes until such amounts are paid.

15

Notes to Financial Statements

5.	Committed Line of Credit — The Fund is a participant in a joint $425 million committed line of credit that is shared by substantially all open-end funds in the Seligman Group of Investment Companies. The trustees have currently limited the Fund’s borrowings to 10% of its net assets. Borrowings pursuant to the credit facility are subject to interest at a rate equal to the overnight federal funds rate plus 0.50%. The Fund incurs a commitment fee of 0.10% per annum on its share of the unused portion of the credit facility. The credit facility may be drawn upon only for temporary purposes and is subject to certain other customary restrictions. The credit facility commitment expires in June 2005, but is renewable annually with the consent of the participating banks. For the year ended December 31, 2004, the Fund did not borrow from the credit facility.
6.	Federal Tax Information — Certain components of income, expense and realized capital gain and loss are recognized at different times or have a different character for federal income tax purposes and for financial reporting purposes. Where such differences are permanent in nature, they are reclassified in the components of net assets based on their characterization for federal income tax purposes. Any such reclassifications will have no effect on net assets, results of operations or net asset value per share of the Fund. As a result of the differences described above, the treatment for financial reporting purposes of distributions made during the year from net investment income or net realized gains may differ from their treatment for federal income tax purposes. Further, the cost of investments also can differ for federal income tax purposes.
	At December 31, 2004, the cost of investments for federal income tax purposes was $93,343,735. The tax basis cost was greater than the cost for financial reporting purposes due to the amortization of premium for financial reporting purposes of $50,600.
	At December 31, 2004, the tax basis components of accumulated losses were as follows:

Gross unrealized appreciation of portfolio securities	$	419,485
Gross unrealized depreciation of portfolio securities		(595,440	)
Net unrealized depreciation of portfolio securities		(175,955	)
Capital loss carryforwards		(6,090,424	)
Timing differences (post-October losses)		(302,352	)
Total accumulated losses	$	(6,568,731	)
At December 31, 2004, the Fund had a net capital loss carryforward for federal income tax purposes of $6,090,424, which is available for offset against future taxable net capital gains, with $522,463 expiring in 2005, $1,359,544 expiring in 2007, $1,438,163 expiring in 2008 and $2,770,254 expiring in 2012. Accordingly, no capital gain distributions are expected to be paid to shareholders until net capital gains have been realized in excess of the available capital loss carryforward.
In addition, the Fund elected to defer until January 1, 2005, the recognition for tax purposes of net losses of $302,352 realized on sales of investments after October 31, 2004. These losses will be available to offset future taxable net gains.

16

Notes to Financial Statements

7.      Transactions in Shares of Beneficial Interest — The Fund has authorized unlimited shares of $0.001 par value Shares of Beneficial Interest. Transactions in Shares of Beneficial Interest were as follows:

				Year Ended December 31,
	2004					2003
Class A	Shares			Amount		Shares			Amount
Net proceeds from sales of shares	626,724		$	4,501,534		3,535,309		$	26,078,441
Investment of dividends	173,268			1,244,369		215,577			1,580,283
Exchanged from associated funds	1,708,703			12,328,090		7,650,469			56,313,073
Converted from Class B**	202,247			1,440,730		—			—
Total	2,710,942			19,514,723		11,401,355			83,971,797
Cost of shares repurchased	(2,175,736	)		(15,651,488	)	(4,959,470	)		(36,310,173	)
Exchanged into associated funds	(2,087,961	)		(15,016,179	)	(9,094,844	)		(66,782,844	)
Total	(4,263,697	)		(30,667,667	)	(14,054,314	)		(103,093,017	)
Decrease	(1,552,755	)	$	(11,152,944	)	(2,652,959	)	$	(19,121,220	)
Class B
Net proceeds from sales of shares	73,811		$	533,094		221,854		$	1,632,736
Investment of dividends	66,905			482,170		112,271			825,400
Exchanged from associated funds	235,238			1,695,274		1,111,952			8,197,545
Total	375,954			2,710,538		1,446,077			10,655,681
Cost of shares repurchased	(1,746,161	)		(12,527,793	)	(2,686,241	)		(19,685,826	)
Exchanged into associated funds	(658,913	)		(4,754,738	)	(2,138,628	)		(15,682,664	)
Converted to Class A**	(201,759	)		(1,440,139	)	—			—
Total	(2,606,833	)		(18,722,670	)	(4,824,869	)		(35,368,490	)
Decrease	(2,230,879	)	$	(16,012,132	)	(3,378,792	)	$	(24,712,809	)
Class C
Net proceeds from sales of shares	66,731		$	483,662		909,164		$	6,729,146
Investment of dividends	29,734			214,298		50,398			370,264
Exchanged from associated funds	131,313			941,842		413,452			3,047,914
Total	227,778			1,639,802		1,373,014			10,147,324
Cost of shares repurchased	(1,215,884	)		(8,753,403	)	(1,366,384	)		(10,021,066	)
Exchanged into associated funds	(225,660	)		(1,627,979	)	(863,433	)		(6,324,619	)
Total	(1,441,544	)		(10,381,382	)	(2,229,817	)		(16,345,685	)
Decrease	(1,213,766	)	$	(8,741,580	)	(856,803	)	$	(6,198,361	)
Class D
Net proceeds from sales of shares	195,546		$	1,404,763		209,195		$	1,534,328
Investment of dividends	33,323			239,801		45,864			336,987
Exchanged from associated funds	236,920			1,717,005		476,360			3,518,752
Total	465,789			3,361,569		731,419			5,390,067
Cost of shares repurchased	(580,541	)		(4,167,381	)	(1,068,878	)		(7,822,662	)
Exchanged into associated funds	(301,853	)		(2,179,301	)	(832,113	)		(6,096,426	)
Total	(882,394	)		(6,346,682	)	(1,900,991	)		(13,919,088	)
Decrease	(416,605	)	$	(2,985,113	)	(1,169,572	)	$	(8,529,021	)

See footnotes on page 18.

17

Notes to Financial Statements
	Year Ended				April 30, 2003* to
	December 31, 2004				December 31, 2003
Class R	Shares		Amount		Shares	Amount
Net proceeds from sales of shares	63,771		$464,359		251	$1,839
Investment of dividends	1,156		8,267		3	25
Exchanged from associated funds	1,696		12,073		—	—
Total	66,623		484,699		254	1,864
Cost of shares repurchased	(5,006	)	(35,581	)	—	—
Increase	61,617		449,118		254	1,864

*	Commencement of offering of shares.
**	Automatic conversion of Class B shares to Class A shares approximately eight years after the initial purchase date. The amount of dividends accrued on Class B shares between the last dividend payment date and the conversion date is invested in Class A shares and is included in the conversion from Class B amount.

8.	Other Matters —The Manager conducted an extensive internal review in response to developments regarding disruptive or illegal trading practices within the mutual fund industry. As of September 2003, the Manager had one arrangement that permitted frequent trading in the Seligman registered investment companies (“Seligman Funds”). This arrangement was in the process of being closed down by the Manager before the first proceedings relating to trading practices within the mutual fund industry were publicly announced. Based on a review of the Manager’s records for 2001 through 2003, the Manager identified three other arrangements that had permitted frequent trading in the Seligman Funds. All three had already been terminated prior to the end of September 2002. The Securities and Exchange Commission (the “SEC”), the NASD and the Attorney General of the State of New York also are reviewing these matters.
	The Manager also has reviewed its practice of placing some of the Seligman Funds’ orders to buy and sell portfolio securities with brokerage firms in recognition of their sales of Seligman Funds. At the time such orders were made, this practice was permissible when done properly; however, the Manager believes that it may have violated applicable requirements for certain of such orders as a result of compensation arrangements the Manager had with certain brokerage firms. The Manager discontinued this practice entirely in October 2003. The Manager is confident that the execution of all such orders was consistent with its best execution obligations and that the Seligman Funds did not pay higher brokerage commissions than they would otherwise have paid for comparable transactions. The Manager has also responded fully to information requests from the SEC and the NASD relating to the Manager’s use of revenue sharing and fund portfolio brokerage commissions and will continue to provide additional information if, and as, requested.
	The results of the Manager’s internal reviews were presented to the Independent Trustees of the Seligman Funds. In order to resolve matters with the Independent Trustees relating to the four arrangements that permitted frequent trading, which did not adversely affect Seligman U.S. Government Securities Series, the Manager has made payments to three funds and has agreed to waive a portion of its management fee with respect to another fund. In order to resolve matters with the Independent Trustees with regard to portfolio brokerage commissions, in May 2004, the Manager made payments to each of twenty-four funds in an amount equal to the commissions paid by each such fund during the period from 1998 through 2003 to certain brokerage firms in recognition of sales of fund shares. Seligman U.S. Government Securities Series does not pay brokerage commissions and thus did not receive any payment from the Manager.

18

Financial Highlights

The tables below are intended to help you understand each Class’s financial performance for the periods presented. Certain information reflects financial results for a single share of Beneficial Interest of a Class that was held throughout the periods shown. Per share amounts are calculated using average shares outstanding. ‘Total return’ shows the rate that you would have earned (or lost) on an investment in each Class, assuming you reinvested all your dividends. Total returns do not reflect any taxes or sales charges and are not annualized for periods of less than one year.

Class A
	Year Ended December 31,
		2004			2003			2002			2001	ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$	7.23		$	7.39		$	6.97		$	6.91		$	6.50
Income (Loss) from Investment Operations:
Net investment income		0.19			0.18			0.26			0.32			0.36
Net realized and unrealized gain (loss)
on investments		(0.11	)		(0.14	)		0.45			0.08			0.41
Total from Investment Operations		0.08			0.04			0.71			0.40			0.77
Less Distributions:
Dividends from net investment income		(0.19	)		(0.18	)		(0.26	)		(0.32	)		(0.36	)
Dividends in excess of net investment income		(0.02	)		(0.02	)		(0.03	)		(0.02	)		—
Total Distributions		(0.21	)		(0.20	)		(0.29	)		(0.34	)		(0.36	)
Net Asset Value, End of Year	$	7.10		$	7.23		$	7.39		$	6.97		$	6.91
Total Return		1.09	%		0.55	%		10.45	%		5.95	%		12.26	%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$	47,553		$	59,660		$	80,556		$	81,722		$	62,982
Ratio of expenses to average net assets		1.31	%		1.27	%		1.24	%		1.16	%		1.21	%
Ratio of net investment income to average net assets		2.66	%		2.38	%		3.68	%		4.59	%		5.49	%
Portfolio turnover rate		133.02	%		250.49	%		184.24	%		66.84	%		37.42	%

See footnotes on page 23.

19

Financial Highlights

Class B
	Year Ended December 31,
		2004			2003			2002			2001	ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$	7.25		$	7.40		$	6.98		$	6.93		$	6.51
Income (Loss) from Investment Operations:
Net investment income		0.14			0.12			0.21			0.27			0.32
Net realized and unrealized gain (loss)
on investments		(0.11	)		(0.13	)		0.45			0.07			0.42
Total from Investment Operations		0.03			(0.01	)		0.66			0.34			0.74
Less Distributions:
Dividends from net investment income		(0.14	)		(0.12	)		(0.21	)		(0.27	)		(0.32	)
Dividends in excess of net investment income		(0.02	)		(0.02	)		(0.03	)		(0.02	)		—
Total Distributions		(0.16	)		(0.14	)		(0.24	)		(0.29	)		(0.32	)
Net Asset Value, End of Year	$	7.12		$	7.25		$	7.40		$	6.98		$	6.93
Total Return		0.34	%		(0.08	)%		9.63	%		5.01	%		11.59	%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$	24,045		$	40,659		$	66,563		$	44,557		$	30,064
Ratio of expenses to average net assets		2.06	%		2.03	%		1.99	%		1.91	%		1.96	%
Ratio of net investment income to average net assets		1.91	%		1.62	%		2.93	%		3.84	%		4.74	%
Portfolio turnover rate		133.02	%		250.49	%		184.24	%		66.84	%		37.42	%

See footnotes on page 23.

20

Financial Highlights

Class C
	Year Ended December 31,
		2004			2003			2002			2001	ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$	7.25		$	7.40		$	6.98		$	6.92		$	6.51
Income (Loss) from Investment Operations:
Net investment income		0.14			0.12			0.21			0.27			0.32
Net realized and unrealized gain (loss)
on investments		(0.12	)		(0.13	)		0.45			0.08			0.41
Total from Investment Operations		0.02			(0.01	)		0.66			0.35			0.73
Less Distributions:
Dividends from net investment income		(0.14	)		(0.12	)		(0.21	)		(0.27	)		(0.32	)
Dividends in excess of net investment income		(0.02	)		(0.02	)		(0.03	)		(0.02	)		—
Total Distributions		(0.16	)		(0.14	)		(0.24	)		(0.29	)		(0.32	)
Net Asset Value, End of Year	$	7.11		$	7.25		$	7.40		$	6.98		$	6.92
Total Return		0.20	%		(0.08	)%		9.63	%		5.16	%		11.43	%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$	9,764		$	18,739		$	25,488		$	15,961		$	4,714
Ratio of expenses to average net assets		2.06	%		2.03	%		1.99	%		1.91	%		1.96	%
Ratio of net investment income to average net assets		1.91	%		1.62	%		2.93	%		3.84	%		4.74	%
Portfolio turnover rate		133.02	%		250.49	%		184.24	%		66.84	%		37.42	%

See footnotes on page 23.

21

Financial Highlights

Class D
	Year Ended December 31,
		2004			2003			2002			2001	ø		2000
Per Share Data:
Net Asset Value, Beginning of Year	$	7.24		$	7.40		$	6.98		$	6.92		$	6.51
Income (Loss) from Investment Operations:
Net investment income		0.14			0.12			0.21			0.27			0.32
Net realized and unrealized gain (loss)
on investments		(0.11	)		(0.14	)		0.45			0.08			0.41
Total from Investment Operations		0.03			(0.02	)		0.66			0.35			0.73
Less Distributions:
Dividends from net investment income		(0.14	)		(0.12	)		(0.21	)		(0.27	)		(0.32	)
Dividends in excess of net investment income		(0.02	)		(0.02	)		(0.03	)		(0.02	)		—
Total Distributions		(0.16	)		(0.14	)		(0.24	)		(0.29	)		(0.32	)
Net Asset Value, End of Year	$	7.11		$	7.24		$	7.40		$	6.98		$	6.92
Total Return		0.34	%		(0.22	)%		9.63	%		5.16	%		11.43	%
Ratios/Supplemental Data:
Net assets, end of year (000s omitted)	$	11,556		$	14,789		$	23,768		$	20,106		$	15,138
Ratio of expenses to average net assets		2.06	%		2.03	%		1.99	%		1.91	%		1.96	%
Ratio of net investment income to average net assets		1.91	%		1.62	%		2.93	%		3.84	%		4.74	%
Portfolio turnover rate		133.02	%		250.49	%		184.24	%		66.84	%		37.42	%

See footnotes on page 23.

22

Financial Highlights

Class R
	Year Ended			4/30/03 * to
	12/31/04			12/31/03
Per Share Data:
Net Asset Value, Beginning of Period	$	7.23		$	7.36
Income (Loss) from Investment Operations:
Net investment income		0.17			0.10
Net realized and unrealized gain (loss)
on investments		(0.11	)		(0.10	)
Total from Investment Operations		0.06			—
Less Distributions
Dividends from net investment income		(0.17	)		(0.10	)
Dividends in excess of net investment income		(0.02	)		(0.03	)
Total Distributions		(0.19	)		(0.13	)
Net Asset Value, End of Period	$	7.10		$	7.23
Total Return		0.82	%		(0.05	)%
Ratios/Supplemental Data:
Net assets, end of period (000s omitted)	$	440		$	2
Ratio of expenses to average net assets		1.56	%		1.57	%†
Ratio of net investment loss to average net assets		2.41	%		2.01	%†
Portfolio turnover rate		133.02	%		250.49	%††

*	Commencement of offering of shares.
†	Annualized.
††	For the year ended December 31, 2003.
ø	As required, effective January 1, 2001, the Fund adopted the provisions of the AICPA Audit and Accounting Guide for
	Investment Companies and began amortizing premium on debt securities. The effect of this change for the year ended
	December 31, 2001, was to decrease net investment income per share by $0.02, increase net realized and unrealized
	gain (loss) on investments by $0.02 for each class and decrease the ratios of net investment income to average net
	assets from 4.83% to 4.59% for Class A, and from 4.08% to 3.84% for Classes B, C, and D. The per share data and
	ratios for periods prior to January 1, 2001, have not been restated.

See Notes to Financial Statements.

23

Report of Independent Registered
Public Accounting Firm

The Trustees and Shareholders,
Seligman U.S. Government Securities Series of
Seligman High Income Fund Series:

We have audited the accompanying statement of assets and liabilities of Seligman U.S. Government Securities Series, one of the funds constituting Seligman High Income Fund Series (the “Fund”), including the portfolio of investments, as of December 31, 2004, and the related statement of operations for the year then ended, the statements of changes in net assets for each of the two years in the period then ended, and the financial highlights for each of the periods presented. These financial statements and financial highlights are the responsibility of the Fund’s management. Our responsibility is to express an opinion on these financial statements and financial highlights based on our audits.

We conducted our audits in accordance with the standards of the Public Company Accounting Oversight Board (United States). Those standards require that we plan and perform the audit to obtain reasonable assurance about whether the financial statements and financial highlights are free of material misstatement. An audit includes consideration of internal control over financial reporting as a basis for designing audit procedures that are appropriate in the circumstances, but not for the purpose of expressing an opinion on the effectiveness of the Fund’s internal control over financial reporting. Accordingly, we express no such opinion. An audit also includes examining, on a test basis, evidence supporting the amounts and disclosures in the financial statements, assessing the accounting principles used and significant estimates made by management, as well as evaluating the overall financial statement presentation. Our procedures included confirmation of securities owned as of December 31, 2004, by correspondence with the Fund’s custodian. We believe that our audits provide a reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to above present fairly, in all material respects, the financial position of Seligman U.S. Government Securities Series of Seligman High Income Fund Series as of December 31, 2004, the results of its operations for the year then ended, the changes in its net assets for each of the two years in the period then ended, and the financial highlights for the respective stated periods, in conformity with accounting principles generally accepted in the United States of America.

DELOITTE & TOUCHE LLP
New York, New York
February 23, 2005

24

Trustees and Officers

Information pertaining to the Trustees and Officers of Seligman U.S. Government Securities Series is set forth below.

Independent Trustees

Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
Robert B. Catell (67)2,3	Chairman, Chief Executive Officer and Director, KeySpan Corporation (diver-
• Trustee: 2003 to Date	sified energy, gas and electric company); Director or Trustee of each of the
• Oversees 60 Portfolios in	investment companies of the Seligman Group of Funds† (except Seligman
Fund Complex	Cash Management Fund, Inc.); Director or Trustee, Alberta Northeast Gas,
	Ltd., Boundary Gas Inc., The Houston Exploration Company (oil and gas
	exploration, development and production companies); Edison Electric
	Institute, New York State Energy Research and Development Authority,
	Independence Community Bank, Business Council of New York State, Inc.,
	New York City Partnership, and the Long Island Association (business and
	civic organizations).
John R. Galvin (75)1,3	Dean Emeritus, Fletcher School of Law and Diplomacy at Tufts
• Trustee: 1995 to Date	University; Director or Trustee of each of the investment companies of
• Oversees 61 Portfolios in	the Seligman Group of Funds†; and Chairman Emeritus, American
Fund Complex	Council on Germany. Formerly, Governor of the Center for Creative
	Leadership; Director, Raytheon Co. (defense and commercial electronics)
	and USLIFE Corporation (life insurance). From June 1987 to June 1992,
	Mr. Galvin was the Supreme Allied Commander, Europe and the
	Commander-in-Chief, United States European Command.
Alice S. Ilchman (69)2,3	President Emerita, Sarah Lawrence College; Director or Trustee of each of
• Trustee: 1991 to Date	the investment companies of the Seligman Group of Funds†; Director,
• Oversees 61 Portfolios in	Jeannette K. Watson Summer Fellowship (summer internships for college
Fund Complex	students); Trustee, Save the Children (non-profit child-assistance organi-
	zation) and the Committee for Economic Development; Governor, Court
	of Governors, London School of Economics; and Director, Public
	Broadcasting Service (PBS). Formerly, Chairman, The Rockefeller
	Foundation (charitable foundation) and Director, New York Telephone
	Company.
Frank A. McPherson (71)2,3	Retired Chairman of the Board and Chief Executive Officer of Kerr-McGee
• Trustee: 1995 to Date	Corporation (diversified energy and chemical company); Director or
• Oversees 61 Portfolios in	Trustee of each of the investment companies of the Seligman Group of
Fund Complex	Funds†; Director, ConocoPhillips (integrated international oil corpora-
	tion), Integris Health (owner of various hospitals), BOK Financial (bank
	holding company), Oklahoma Chapter of the Nature Conservancy,
	Oklahoma Medical Research Foundation, Boys and Girls Clubs of
	Oklahoma, Oklahoma City Public Schools Foundation and Oklahoma
	Foundation for Excellence in Education. Formerly, Director, Kimberly-Clark
	Corporation (consumer products) and the Federal Reserve System’s
	Kansas City Reserve Bank.

See footnotes on page 28.

25

Trustees and Officers

Independent Trustees (continued)

Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
John E. Merow (75)1,3	Retired Chairman and Senior Partner, Sullivan & Cromwell LLP (law firm);
• Trustee: 1984 to Date	Director or Trustee of each of the investment companies of the Seligman
• Oversees 61 Portfolios	Group of Funds†; Director, Aleris International, Inc. (aluminum and zinc
in Fund Complex	recycler and aluminum rolled products); Director Emeritus, the Municipal
	Art Society of New York; Executive Committee Member and Secretary,
	the U.S. Council for International Business; Trustee and Vice Chairman,
	New York-Presbyterian Healthcare System, Inc.; Trustee, New York-
	Presbyterian Hospital; and Member of the American Law Institute and
	Council on Foreign Relations.
Betsy S. Michel (62)1,3	Attorney; Director or Trustee of each of the investment companies of the
• Trustee: 1984 to Date	Seligman Group of Funds†; Trustee, The Geraldine R. Dodge Foundation
• Oversees 61 Portfolios	(charitable foundation). Formerly, Chairman of the Board of Trustees of
in Fund Complex	St. George’s School (Newport, RI); and Trustee, World Learning, Inc.
	(international educational training).
Leroy C. Richie (63)1,3	Chairman and Chief Executive Officer, Q Standards Worldwide, Inc. (library
• Trustee: 2000 to Date	of technical standards); Director or Trustee of each of the investment com-
• Oversees 60 Portfolios	panies of the Seligman Group of Funds†(except Seligman Cash Manage-
in Fund Complex	ment Fund, Inc.); Director, Kerr-McGee Corporation (diversified energy and
	chemical company) and Infinity, Inc. (oil and gas services and exploration);
	Director and Chairman, Highland Park Michigan Economic Development
	Corp. Formerly, Trustee, New York University Law Center Foundation; Vice
	Chairman, Detroit Medical Center and the Detroit Economic Growth Corp.;
	Chairman and Chief Executive Officer, Capital Coating Technologies, Inc.
	(applied coating technologies); and Vice President and General Counsel,
	Automotive Legal Affairs, Chrysler Corporation.
Robert L. Shafer (72)2,3	Retired Vice President, Pfizer Inc. (pharmaceuticals); Director or Trustee
• Trustee: 1984 to Date	of each of the investment companies of the Seligman Group of Funds†
• Oversees 61 Portfolios	and Ambassador and Permanent Observer of the Sovereign and Military
in Fund Complex	Order of Malta to the United Nations. Formerly, Director, USLIFE
	Corporation (life insurance).
James N. Whitson (69)1,3	Retired Executive Vice President and Chief Operating Officer, Sammons
• Trustee: 1993 to Date	Enterprises, Inc. (a diversified holding company); Director or Trustee of each
• Oversees 61 Portfolios	of the investment companies of the Seligman Group of Funds†; Director,
in Fund Complex	CommScope, Inc. (manufacturer of coaxial cable). Formerly, Director and
	Consultant, Sammons Enterprises, Inc. and Director C-SPAN (cable televi-
	sion network).

See footnotes on page 28.

26

Trustees and Officers

Interested Trustees and Principal Officers

Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
William C. Morris (66)*	Chairman, J. & W. Seligman & Co. Incorporated; Chairman of the Board
• Trustee and Chairman of	and Director or Trustee of each of the investment companies of the
the Board: 1988 to Date	Seligman Group of Funds†; Chairman, Seligman Advisors, Inc., Seligman
• Oversees 61 Portfolios in	Services, Inc., and Carbo Ceramics Inc. (manufacturer of ceramic prop-
Fund Complex	pants for oil and gas industry); Director, Seligman Data Corp.; and
	President and Chief Executive Officer, The Metropolitan Opera Associa-
	tion. Formerly, Director, Kerr-McGee Corporation (diversified energy and
	chemical company) and Chief Executive Officer of each of the investment
	companies of the Seligman Group of Funds.
Brian T. Zino (52)*	Director and President, J. & W. Seligman & Co. Incorporated; Chief
• Trustee: 1993 to Date	Executive Officer, President and Director or Trustee of each of the invest-
• President: 1995 to Date	ment companies of the Seligman Group of Funds†; Director, Seligman
• Chief Executive Officer:	Advisors, Inc. and Seligman Services, Inc.; Chairman, Seligman Data
2002 to Date	Corp.; Member of the Board of Governors of the Investment Company
	Institute; and Director, ICI Mutual Insurance Company.
• Oversees 61 Portfolios in
Fund Complex
Eleanor T. M. Hoagland (53)	Managing Director and Senior Vice President, Risk Manager, J. & W.
• Vice President and Chief	Seligman & Co. Incorporated; Vice President and Chief Compliance
Compliance Officer:	Officer for each of the investment companies of the Seligman Group of
July 2004 to Date	Funds†. Formerly, Managing Director, Partner and Chief Portfolio
	Strategist, AMT Capital Management from 1994 to 2000.
Christopher J. Mahony (41)	Senior Vice President, Investment Officer of J. & W. Seligman & Co.
• Vice President and	Incorporated, Vice President and Portfolio Manager of Seligman Cash
Portfolio Manager:	Management Fund, Inc., Seligman Investment Grade Fixed Income Fund,
2001 to Date	Inc., Vice President of Seligman Portfolios, Inc., and Portfolio Manager of
	its Cash Management Portfolio and Investment Grade Fixed Income
	Portfolio, and Co-Portfolio Manager of its Income and Growth Portfolio;
	Vice President and Co-Portfolio Manager of Seligman Income and
	Growth Fund, Inc. Formerly, Senior Portfolio Manager at Fort Washington
	Investment Advisors, Inc. since 1994; and Portfolio Manager, Neuberger
	and Berman from 1991 to 1994.

See footnotes on page 28.

27

Trustees and Officers
Interested Trustees and Principal Officers (continued)
Name, (Age), Position(s)	Principal Occupation(s) During Past Five Years, Directorships
held with Fundø	and Other Information
Thomas G. Rose (47)	Chief Financial Officer, Senior Vice President, Finance, and Treasurer,
• Vice President:	J. & W. Seligman & Co. Incorporated, Senior Vice President, Finance,
2000 to Date	Seligman Advisors, Inc. and Seligman Data Corp.; Vice President of each
	of the investment companies of the Seligman Group of Funds†; and of
	Seligman Services, Inc. and Seligman International, Inc. Formerly,
	Treasurer of the investment companies of the Seligman Group of Funds
	and Seligman Data Corp.
Lawrence P. Vogel (48)	Senior Vice President and Treasurer, Investment Companies, J. & W.
• Vice President:	Seligman & Co. Incorporated; Vice President and Treasurer of each of the
1992 to Date	investment companies of the Seligman Group of Funds†; and Treasurer,
• Treasurer:	Seligman Data Corp. Formerly, Senior Vice President, Finance, J. & W.
2000 to Date	Seligman & Co. Incorporated, Seligman Advisors, Inc., Seligman
	International, Inc. and Seligman Data Corp.; Vice President, Seligman
	Services, Inc. and Treasurer, Seligman International, Inc.
Frank J. Nasta (40)	Managing Director, General Counsel and Corporate Secretary, J. & W.
• Secretary: 1994 to Date	Seligman & Co. Incorporated; Secretary of each of the investment compa-
	nies of the Seligman Group of Funds†, and Corporate Secretary,
	Seligman Advisors, Inc., Seligman Services, Inc., Seligman International,
	Inc. and Seligman Data Corp. Formerly, Senior Vice President, Law and
	Regulation Department, J. & W. Seligman & Co. Incorporated.

The Fund’s Statement of Additional Information (SAI) includes additional information about Fund trustees and is available, without charge, upon request. You may call toll-free (800) 221-2450 in the US or collect (212) 682-7600 outside the US to request a copy of the SAI, to request other information about the Fund, or to make shareholder inquiries.

ø	The address for each of the trustees and officers is 100 Park Avenue, 8th floor, New York, NY 10017. Each Trustee serves for
	an indefinite term, until the election and qualification of a successor or until his or her earlier death, resignation or removal.
	Each officer is elected annually by the Trustees.
†	The Seligman Group of Funds consists of 23 registered investment companies.
*	Mr. Morris and Mr. Zino are considered “interested persons” of the Fund, as defined in the Investment Company Act of 1940,
	as amended, by virtue of their positions with J. & W. Seligman & Co. Incorporated and its affiliates.

Member:	1 Audit Committee
	2 Trustee Nominating Committee
	3 Board Operations Committee

28

For More Information

ImportantTelephoneNumbers

(800) 221-2450    Shareholder Services

(800) 445-1777    Retirement Plan Services

(212) 682-7600    Outside the United States

(800) 622-4597    24-Hour Automated Telephone Access Service

QuarterlySchedule of Investments

A complete schedule of portfolio holdings owned by the Fund will be filed with the SEC for the first and third quarters of each fiscal year on Form N-Q, and will be available to shareholders (i) without charge, upon request, by calling toll-free (800) 221-2450 in the US or collect (212) 682-7600 outside the US or (ii) on the SEC’s website at www.sec.gov. In addition, the Form N-Q may be reviewed and copied at the SEC’s Public Reference Room in Washington, D.C. Information on the operation of the Public Reference Room may be obtained by calling (800) SEC-0330. Certain of the information contained in the Fund’s form N-Q is also made available to shareholders on Seligman’s website at www.seligman. com.¹

Proxy VotingPolicies and Procedures

A description of the policies and procedures used by the Fund to determine how to vote proxies relating to portfolio securities as well as information regarding how the Fund voted proxies relating to portfolio securities during the most recent 12-month period ended June 30, is available (i) without charge, upon request, by calling toll-free (800) 221-2450 in the US or collect (212) 682-7600 outside the US and (ii) on the SEC’s website at www.sec.gov.

This report is intended only for the information of shareholders or those who have received the offering prospectus covering shares of Beneficial Interest of Seligman U.S. Government Securities Series, which contains information about the sales charges, management fee, and other costs. Please read the prospectus carefully before investing or sending money.

¹      The reference to Seligman’s website is an inactive textual reference and information contained in or otherwise accessible through Seligman’s website does not form a part of this report or the Fund’s prospectus.

TXUSG2 12/04

ITEM 2. CODE OF ETHICS. As of December 31, 2004, the registrant has adopted a code of ethics that applies to its principal executive and principal financial officers. ITEM 3. AUDIT COMMITTEE FINANCIAL EXPERT. The registrant's board of directors has determined that Mr. James N. Whitson, a member of its audit committee, is an audit committee financial expert. Mr. Whitson is "independent" as such term is defined in Form N-CSR. ITEM 4. PRINCIPAL ACCOUNTANT FEES AND SERVICES. (a) - (d) Aggregate fees billed to the registrant for the last two fiscal years for professional services rendered by the registrant's principal accountant were as follows: 2004 2003 ---------- ---------- Audit Fees $73,924 $70,396 Audit-Related Fees - - Tax Fees 4,400 4,200 All Other Fees 1,932 1,898 Audit fees include amounts related to the audit of the registrant's annual financial statements and services normally provided by the accountant in connection with statutory and regulatory filings. Tax fees include amounts related to tax compliance, tax planning, and tax advice. Other fees include the registrant's pro-rata share of amounts for services related to documentation of certain internal control procedures for the registrant and certain other associated investment companies. Aggregate fees billed by the registrant's principal accountant for the last two fiscal years for non-audit services provided to the registrant's investment adviser (not including a sub-adviser whose role is primarily portfolio management and is sub-contracted or overseen by another investment adviser) and any entity controlling, controlled by, or under common control with the investment adviser that provides ongoing services to the registered investment company, where the engagement relates directly to the operations and financial reporting of the registrant, were as follows: 2004 2003 ---------- ----------- Audit-Related Fees $118,630 $126,130 Tax Fees 13,703 7,500 All Other Fees 43,000 - Audit-related fees include amounts for (i) attestation services for the registrant's stockholder service agent; (ii) review of certain internal controls of such stockholder service agent's sub-agent; (iii) performance of certain agreed-upon procedures relating to certain services performed by the registrant's distributor; and (iv) actuarial services provided prior to May 6, 2003 to the registrant's investment adviser and stockholder service agent (such services were no longer permitted to be performed for the stockholder service agent after May 5, 2003). Tax fees include amounts related to tax compliance, tax planning, and tax advice for and an evaluation of certain tax reporting procedures of the registrant's stockholder service agent. Other fees relates to electronic communication processing services performed on behalf of outside counsel of the investment adviser. (e) (1) The Audit Committee is required to preapprove audit and non-audit services performed for the registrant by the principal accountant in order to assure that the provision of such services does not impair the principal accountant's independence. The Audit Committee also is required to preapprove certain non-audit services performed by the registrant's principal accountant for the registrant's investment adviser (not including any sub-adviser whose role is primarily portfolio management and is subcontracted with or overseen by another investment adviser) and certain of the adviser's affiliates that provide services directly related to the operations and financial reporting of the registrant. Unless a type of service to be provided by the principal accountant has received preapproval, it will require specific preapproval by the Audit Committee. The Audit Committee may delegate preapproval authority to one or more of its members. The member or members to whom such authority is delegated shall report any preapproval decisions to the Audit Committee at its next scheduled meeting. Notwithstanding the foregoing, under certain circumstances, preapproval of non-audit services of a de minimis amount is not required. (2) No services included in (b) - (d) above were approved pursuant to the waiver provisions of paragraphs (c)(7)(i)(C) or (c)(7)(ii) of Rule 2-01 of Regulation S-X. (f) Not applicable. (g) The aggregate fees billed for the most recent fiscal year and the preceding fiscal year by the registrant's principal accountant for non-audit services rendered to the registrant, its investment adviser (not including any sub-adviser whose role is primarily portfolio management and is subcontracted with or overseen by another investment adviser), and any entity controlling, controlled by, or under common control with the investment adviser that provides ongoing services to the registrant were $356,998 and $273,358, respectively. (h) All non-audit services rendered in (g) above were pre-approved by the registrant's audit committee. Accordingly, the audit committee considered whether these services were compatible with maintaining the principal accountant's independence. ITEM 5. AUDIT COMMITTEE OF LISTED REGISTRANTS. James N. Whitson, Chairman John R. Galvin Betsy S. Michel John E. Merow Leroy C. Richie ITEM 6. SCHEDULE OF INVESTMENTS. Included in Item 1 above. ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END MANAGEMENT INVESTMENT COMPANIES. Not applicable. ITEM 8. PORTFOLIO MANAGERS OF CLOSED-END MANAGEMENT INVESTMENT COMPANIES. Not applicable. ITEM 9. PURCHASES OF EQUITY SECURITIES BY CLOSED-END MANAGEMENT INVESTMENT COMPANY AND AFFILIATED PURCHASERS. Not applicable. ITEM 10 SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS. Not applicable. ITEM 11. CONTROLS AND PROCEDURES. (a) The registrant's principal executive officer and principal financial officer have concluded, based upon their evaluation of the registrant's disclosure controls and procedures as conducted within 90 days of the filing date of this report, that these disclosure controls and procedures provide reasonable assurance that material information required to be disclosed by the registrant in the report it files or submits on Form N-CSR is recorded, processed, summarized and reported, within the time periods specified in the Commission's rules and forms and that such material information is accumulated and communicated to the registrant's management, including its principal executive officer and principal financial officer, as appropriate, in order to allow timely decisions regarding required disclosure. (b) The registrant's principal executive officer and principal financial officer are aware of no changes in the registrant's internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that has materially affected, or is reasonably likely to materially affect, the registrant's internal control over financial reporting. ITEM 12. EXHIBITS. (a)(1) Code of Ethics for Principal Executive and Principal Financial Officers (a)(2) Certifications of principal executive officer and principal financial officer as required by Rule 30a-2(a) under the Investment Company Act of 1940. (a)(3) Not applicable. (b) Certifications of chief executive officer and chief financial officer as required by Rule 30a-2(b) under the Investment Company Act of 1940. SIGNATURES Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized. SELIGMAN HIGH INCOME FUND SERIES By: /s/ BRIAN T. ZINO --------------------------------- Brian T. Zino President and Chief Executive Officer Date: March 8, 2005 Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed below by the following persons on behalf of the registrant and in the capacities and on the dates indicated. By: /s/ BRIAN T. ZINO --------------------------------- Brian T. Zino President and Chief Executive Officer Date: March 8, 2005 By: /s/ LAWRENCE P. VOGEL --------------------------------- Lawrence P. Vogel Vice President, Treasurer and Chief Financial Officer Date: March 8, 2005 SELIGMAN HIGH INCOME FUND SERIES EXHIBIT INDEX (a)(1) Code of Ethics for Principal Executive and Principal Financial Officers (a)(2) Certifications of principal executive officer and principal financial officer as required by Rule 30a-2(a) under the Investment Company Act of 1940. (b) Certification of chief executive officer and chief financial officer as required by Rule 30a-2(b) of the Investment Company Act of 1940.