General Government Securities Money Market Funds NCSR Certified annual shareholder report (management investment company)

General Government Securities Money Market Funds N-CSRCertified 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- 3456

General Government Securities Money Market Funds, Inc.

(Exact name of Registrant as specified in charter)

c/o The Dreyfus Corporation

200 Park Avenue

New York, New York 10166

(Address of principal executive offices) (Zip code)

Michael A. Rosenberg, Esq.

200 Park Avenue

New York, New York 10166

(Name and address of agent for service)

Registrant's telephone number, including area code: (212) 922-6000

Date of fiscal year end:		11/30
Date of reporting period:		05/31/2008

FORM N-CSR

Item 1.

Reports to Stockholders.

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The views expressed in this report reflect those of the portfolio manager only through the end of the period covered and do not necessarily represent the views of Dreyfus or any other person in the Dreyfus organization. Any such views are subject to change at any time based upon market or other conditions and Dreyfus disclaims any responsibility to update such views.These views may not be relied on as investment advice and, because investment decisions for a Dreyfus fund are based on numerous factors, may not be relied on as an indication of trading intent on behalf of any Dreyfus fund.

Not FDIC-Insured • Not Bank-Guaranteed • May Lose Value

Contents

		THE FUND

2		A Letter from the CEO
3		Discussion of Fund Performance
6		Understanding Your Fund’s Expenses
6		Comparing Your Fund’s Expenses
		With Those of Other Funds
7		Statement of Investments
9		Statement of Assets and Liabilities
10		Statement of Operations
11		Statement of Changes in Net Assets
12		Financial Highlights
14		Notes to Financial Statements
FOR MORE INFORMATION

		Back Cover

The Fund

General Government Securities

Money Market Fund

A LETTER FROM THE CEO

Dear Shareholder:

We are pleased to present this semiannual report for General Government Securities Money Market Fund, covering the six-month period from December 1, 2007, through May 31, 2008.

Although the U.S. economy has teetered on the brink of recession and the financial markets have encountered heightened volatility in an ongoing credit crisis, we recently have seen signs of potential improve-ment.The Federal Reserve Board’s aggressive easing of monetary policy and innovative measures to inject liquidity into the banking system appear to have reassured many investors and economists.At Dreyfus, we believe that the current economic downturn is likely to be relatively brief by historical standards, but the ensuing recovery may be gradual and prolonged as financial deleveraging and housing price deflation continue to weigh on economic activity.

The Fed has aggressively reduced the overnight rate by 250 basis points — to 2% as of this reporting period — which has resulted in lower yields for virtually all true money market instruments. In addition, volatility in the stock and bond markets also has allowed the money markets to maintain record levels of demand, since money market funds are obligated under strict regulations to seek preservation of capital as their main function.Your financial advisor can help you assess current risks and your need for liquidity and take advantage of potential opportunities in other asset classes given your individual needs and financial goals.

For information about how the fund performed during the reporting period, as well as market perspectives, we have provided a Discussion of Fund Performance given by the fund’s Portfolio Manager.

Thank you for your continued confidence and support.

DISCUSSION OF FUND PERFORMANCE

For the period of December 1, 2007, through May 31, 2008, as provided by Bernard W. Kiernan, Jr., Senior Portfolio Manager

Fund and Market Performance Overview

For the six-month period ended May 31, 2008, General Government Securities Money Market Fund’s Class A shares produced an annualized yield of 2.74%, and its Class B shares produced an annualized yield of 2.53% .Taking into account the effects of compounding, the fund’s Class A and Class B shares produced annualized effective yields of 2.78% and 2.56%, respectively.¹

Money market yields declined over much of the reporting period as the Federal Reserve Board (the “Fed”) reduced short-term interest rates in an attempt to stimulate U.S. economic growth.

The Fund’s Investment Approach

The fund seeks as high a level of current income as is consistent with the preservation of capital and the maintenance of liquidity.

To pursue this goal, the fund invests in securities issued or guaranteed as to principal and interest by the U.S. government or its agencies or instrumentalities, and repurchase agreements (including tri-party repurchase agreements).These instruments include those backed by the full faith and credit of the U.S. government and those that are neither insured nor guaranteed by the U.S. government.

The Fed Addressed an Economic Slump and Credit Crisis

Turmoil in the sub-prime mortgage market, slumping U.S. housing markets and resurgent energy prices already had led to economic concerns by the start of the reporting period, causing investors to reassess their previously generous attitudes toward risk and sparking sharp declines among stocks and higher yielding bonds.The resulting tightness in credit markets and heavy sub-prime related losses among commercial and investment banks prompted the Fed to reduce short-term interest

The Fund 3

DISCUSSION OF FUND PERFORMANCE (continued)

rates. As a result, the reporting period began with an overnight federal funds rate of 4.50%, down from 5.25% three months earlier.

The economy continued to show signs of weakness in December 2007, as sales of existing homes fell sharply and longer-term fixed-income markets encountered heightened volatility.The Fed again reduced the federal funds rate to 4.25% in December, but investors appeared to be disappointed that the reduction was not larger. 2007 ended with an annualized economic growth rate of just 0.6% in the fourth quarter and 2.2% for the year overall.

January 2008 saw more disappointing economic news,including the first monthly job losses in more than four years. Congress passed legislation designed to stimulate the economy, and the Fed reduced the federal funds rate by 125 basis points to 3% in two separate moves during the latter part of January. However, more job losses were reported in February, and pressures on U.S. financial institutions remained intense from additional sub-prime related losses, deleveraging of institutional investment portfolios and the repricing of real estate.

In March, non-farm payrolls shrank by another 80,000 jobs, driving the total number of lost jobs during the first quarter of 2008 to 232,000.The unemployment rate climbed to 5.1% in March from 4.8% in February. The Fed continued to take aggressive policy action during the month, reducing the federal funds rate to 2.25% . In addition, the Fed announced an expansion of its Term Securities Lending Facility, making $200 billion of Treasury securities available to Wall Street firms. In an unprecedented move apparently designed to prevent further damage to the U.S. financial system, the Fed allowed borrowers to use certain mortgage-backed securities as collateral for these loans.The first quarter ended with a 0.9% GDP growth rate, according to revised government estimates.

More job losses followed in April, and the Fed continued to reduce the federal funds rate, implementing a cut of 25 basis points that left the overnight rate at 2% by the end of the reporting period. Moreover, inflationary pressures increased along with crude oil prices, and businesses attempted to pass along higher input costs for a variety of products.

Economic data in May proved to be mixed. On one hand, the U.S. economy lost an additional 49,000 jobs, and the unemployment rate jumped to 5.5% . Inflation worries also intensified as the average cost of gasoline in the United States hit $4.00 per gallon. On the other hand, retail sales improved by an unexpected 1% during the month, suggesting that tax rebate checks might be having the desired effect of boosting consumer spending.

Longer Maturities Captured Higher Yields

As the credit crisis unfolded and the Fed cut short-term interest rates, yield differences widened along the market’s maturity range, creating more attractive opportunities among longer-dated money market instruments. Moreover, demand for money market instruments surged from investors engaged in a “flight to quality.” In this environment, we increased the fund’s weighted average maturity toward a position we considered longer than industry averages.

Whether recent signs of a more stable economy portend a longer-term trend remains an open question.The Fed and market participants will be closely watching economic data for signs of economic strength and a moderation of inflation. In the meantime, we intend to maintain the fund’s conservative credit posture and a relatively long weighted average maturity.

June 16, 2008

		An investment in the fund is not insured or guaranteed by the FDIC or any other government
		agency. Although the fund seeks to preserve the value of your investment at $1.00 per share, it is
		possible to lose money by investing in the fund.
¹		Annualized effective yield is based upon dividends declared daily and reinvested monthly. Past
		performance is no guarantee of future results.Yields fluctuate.Yields provided for the fund’s Class
		B shares reflect the absorption of certain fund expenses by The Dreyfus Corporation pursuant to
		an undertaking in effect that may be extended, terminated or modified at any time. Had these
		expenses not been absorbed, the fund’s Class B shares would have produced an annualized yield
		of 2.51% and an annualized effective yield of 2.54%.

The Fund 5

UNDERSTANDING YOUR FUND’S EXPENSES (Unaudited)

As a mutual fund investor, you pay ongoing expenses, such as management fees and other expenses. Using the information below, you can estimate how these expenses affect your investment and compare them with the expenses of other funds.You also may pay one-time transaction expenses, including sales charges (loads) and redemption fees, which are not shown in this section and would have resulted in higher total expenses. For more information, see your fund’s prospectus or talk to your financial adviser.

Review your fund’s expenses

The table below shows the expenses you would have paid on a $1,000 investment in General Government Securities Money Market Fund from December 1, 2007 to May 31, 2008. It also shows how much a $1,000 investment would be worth at the close of the period, assuming actual returns and expenses.

Expenses and Value of a $1,000 Investment
assuming actual returns for the six months ended May 31, 2008
	Class A	Class B

Expenses paid per $1,000 ^†	$ 4.08	$ 5.08
Ending value (after expenses)	$1,013.80	$ 1,012.70

COMPARING YOUR FUND’S EXPENSES

WITH THOSE OF OTHER FUNDS (Unaudited)

Using the SEC’s method to compare expenses

The Securities and Exchange Commission (SEC) has established guidelines to help investors assess fund expenses. Per these guidelines, the table below shows your fund’s expenses based on a $1,000 investment, assuming a hypothetical 5% annualized return. You can use this information to compare the ongoing expenses (but not transaction expenses or total cost) of investing in the fund with those of other funds.All mutual fund shareholder reports will provide this information to help you make this comparison. Please note that you cannot use this information to estimate your actual ending account balance and expenses paid during the period.

Expenses and Value of a $1,000 Investment
assuming a hypothetical 5% annualized return for the six months ended May 31, 2008
	Class A	Class B

Expenses paid per $1,000 ^†	$ 4.09	$ 5.10
Ending value (after expenses)	$1,020.95	$ 1,019.95

^†Expenses are equal to the fund’s annualized expense ratio of .81% for Class A shares and 1.01% for Class B shares,

multiplied by the average account value over the period, multiplied by 183/366 (to reflect the one-half year period).

STATEMENT OF INVESTMENTS

May 31, 2008 (Unaudited)

	Annualized
	Yield on
	Date of	Principal
U.S. Government Agencies—91.9%	Purchase (%)	Amount ($)	Value ($)

Federal Farm Credit Bank:
9/15/09	2.05	100,000,000 ^a	99,993,798
3/12/10	2.20	54,180,000 ^a	54,093,626
Federal Home Loan Bank System:
6/18/08	4.23	125,000,000	124,755,625
7/16/08	3.42	150,000,000	149,370,000
8/15/08	2.13	50,000,000	49,779,167
9/5/08	2.09	29,800,000	29,635,504
9/24/08	2.12	40,000,000	39,731,667
2/13/09	1.90	100,000,000	100,423,933
2/27/09	2.58	35,000,000	35,009,875
3/5/09	2.55	40,000,000	40,004,857
4/14/09	2.25	65,100,000	65,092,063
5/7/09	2.35	20,000,000	20,025,896
5/19/09	2.50	50,000,000	50,007,185
9/4/09	2.12	150,000,000 ^a	150,000,000
9/18/09	2.14	66,000,000 ^a	66,008,433
Federal Home Loan Mortgage Corp.:
6/13/08	3.88	175,000,000	174,777,167
7/1/08	4.31	100,000,000	99,650,833
1/12/09	2.14	40,000,000	40,710,113
2/17/09	2.16	1,200,000	1,221,914
Federal National Mortgage Association:
6/2/08	2.25	175,000,000 ^a	175,000,000
8/20/08	2.11	30,000,000	29,860,667
Total U.S. Government Agencies
(cost $1,595,152,323)		1,595,152,323



Repurchase Agreements—8.0%

Barclays Financial LLC
dated 5/30/08, due 6/2/08 in the
amount of $38,007,347 (fully collateralized
by $38,869,000 Federal National Mortgage
Association, 0%, due 7/16/08,
value $38,760,167)	2.32	38,000,000	38,000,000

The Fund 7

STATEMENT OF INVESTMENTS (Unaudited) (continued)

	Annualized
	Yield on
	Date of	Principal
Repurchase Agreements (continued)	Purchase (%)	Amount ($)	Value ($)

HSBC USA Inc.
dated 5/30/08, due 6/2/08 in the
amount of $50,009,708 (fully collateralized
by $105,458,167 Federal Home Loan Mortgage
Corp., 3.214%-5.50%, due 1/15/22-3/15/34,
value $20,378,326 and $60,250,000 Federal
National Mortgage Association, 4.50%-6.25%,
due 9/25/33-12/25/35, value $30,624,216)	2.33	50,000,000	50,000,000
Merrill Lynch & Co. Inc.
dated 5/30/08, due 6/2/08 in the
amount of $50,009,833 (fully collateralized
by $51,015,000 Government National
Mortgage Association, 5.50%, due 5/15/38,
value $51,003,841)	2.36	50,000,000	50,000,000
Total Repurchase Agreements
(cost $138,000,000)			138,000,000


Total Investments (cost $1,733,152,323)		99.9%	1,733,152,323

Cash and Receivables (Net)		.1%	2,259,988

Net Assets		100.0%	1,735,412,311

Variable rate security—interest rate subject to periodic change.

^†Based on net assets.

See notes to financial statements.

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2008 (Unaudited)

	Cost	Value

Assets ($):
Investments in securities—See Statement of Investments	1,733,152,323	1,733,152,323
Interest receivable		5,464,642
Prepaid expenses		80,243
		1,738,697,208

Liabilities ($):
Due to The Dreyfus Corporation and affiliates—Note 2(c)		1,470,557
Cash overdraft due to Custodian		1,761,093
Payable for shares of Common Stock redeemed		14,656
Accrued expenses		38,591
		3,284,897

Net Assets ($)		1,735,412,311

Composition of Net Assets ($):
Paid-in capital		1,735,720,563
Accumulated net realized gain (loss) on investments		(308,252)

Net Assets ($)		1,735,412,311

Net Asset Value Per Share
	Class A	Class B

Net Assets ($)	67,242,691	1,668,169,620
Shares Outstanding	67,481,683	1,668,254,645

Net Asset Value Per Share ($)	1.00	1.00

See notes to financial statements.

The Fund 9

STATEMENT OF OPERATIONS

Six Months Ended May 31, 2008 (Unaudited)

Investment Income ($):
Interest Income		29,282,847
Expenses:
Management fee—Note 2(a)		4,159,666
Shareholder servicing costs—Note 2(c)		2,444,813
Distribution fees, service and prospectus fees—Note 2(b)		1,672,115
Registration fees		80,036
Custodian fees—Note 2(c)		73,417
Directors’ fees and expenses—Note 2(d)		38,860
Professional fees		31,358
Shareholders’ reports		6,513
Miscellaneous		14,784
Total Expenses		8,521,562
Less—reduction in shareholder servicing
costs due to undertaking—Note 2(c)		(186,301)
Less—reduction in fees due to
earnings credits—Note 1(b)		(1,128)
Net Expenses		8,334,133
Investment Income-Net		20,948,714

Net Realized Gain (Loss) on Investments—Note 1(b) ($)		94,500
Net Increase in Net Assets Resulting from Operations		21,043,214

See notes to financial statements.

STATEMENT OF CHANGES IN NET ASSETS

	Six Months Ended
	May 31, 2008	Year Ended
	(Unaudited)	November 30, 2007

Operations ($):
Investment income—net	20,948,714	54,001,184
Net realized gain (loss) on investments	94,500	18,863
Net Increase (Decrease) in Net Assets
Resulting from Operations	21,043,214	54,020,047

Dividends to Shareholders from ($):
Investment income—net:
Class A Shares	(964,189)	(6,827,626)
Class B Shares	(19,984,525)	(47,173,558)
Total Dividends	(20,948,714)	(54,001,184)

Capital Stock Transactions ($1.00 per share):
Net proceeds from shares sold:
Class A Shares	164,423,895	1,301,604,325
Class B Shares	2,418,212,168	4,177,326,486
Dividends reinvested:
Class A Shares	942,087	6,008,008
Class B Shares	19,941,701	46,674,892
Cost of shares redeemed:
Class A Shares	(164,483,989)	(1,601,638,284)
Class B Shares	(2,196,264,454)	(3,887,546,069)
Increase (Decrease) in Net Assets
from Capital Stock Transactions	242,771,408	42,429,358
Total Increase (Decrease) in Net Assets	242,865,908	42,448,221

Net Assets ($):
Beginning of Period	1,492,546,403	1,450,098,182
End of Period	1,735,412,311	1,492,546,403

See notes to financial statements.

The Fund 11

FINANCIAL HIGHLIGHTS

The following tables describe the performance for each share class for the fiscal periods indicated. All information reflects financial results for a single fund share. Total return shows how much your investment in the fund would have increased (or decreased) during each period, assuming you had reinvested all dividends and distributions.These figures have been derived from the fund’s financial statements.

	Six Months Ended
	May 31, 2008		Year Ended November 30,

Class A Shares	(Unaudited)	2007	2006	2005	2004	2003

Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.014	.043	.041	.022	.005	.005
Distributions:
Dividends from investment
income—net	(.014)	(.043)	(.041)	(.022)	(.005)	(.005)
Net asset value, end of period	1.00	1.00	1.00	1.00	1.00	1.00

Total Return (%)	2.75^a	4.44	4.16	2.24	.52	.52

Ratios/Supplemental Data (%):
Ratio of total expenses
to average net assets	.81^a	.78	.80	.79	.79	.77
Ratio of net expenses
to average net assets ^b	.81^a	.78	.80	.79	.79	.77
Ratio of net investment income
to average net assets	2.78^a	4.45	4.06	2.18	.51	.52

Net Assets, end of period
($ x 1,000)	67,243	66,357	360,382	443,079	517,063	565,857

^a		Annualized.
^b		Expense waivers and/or reimbursements amounted to less than .01%.
See notes to financial statements.

	Six Months Ended
	May 31, 2008		Year Ended November 30,

Class B Shares	(Unaudited)	2007	2006	2005	2004	2003

Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.013	.042	.039	.020	.003	.003
Distributions:
Dividends from investment
income—net	(.013)	(.042)	(.039)	(.020)	(.003)	(.003)
Net asset value, end of period 1.00		1.00	1.00	1.00	1.00	1.00

Total Return (%)	2.55^a	4.25	3.95	2.02	.32	.29

Ratios/Supplemental Data (%):
Ratio of total expenses
to average net assets	1.03^a	1.04	1.03	1.04	1.04	1.03
Ratio of net expenses
to average net assets	1.01^a	1.01	1.01	1.01	.98	1.00
Ratio of net investment income
to average net assets	2.51^a	4.16	3.89	1.96	.30	.29

Net Assets, end of period
($ x 1,000)	1,668,170	1,426,190	1,089,717	1,061,190	719,095	933,041

^aAnnualized.

See notes to financial statements.

The Fund 13

NOTES TO FINANCIAL STATEMENTS ( U n a u d i t e d )

NOTE 1—Significant Accounting Policies:

General Government Securities Money Market Fund (the “fund”) is a separate diversified series of General Government Securities Money Market Funds, Inc. (the “Company”) which is registered under the Investment Company Act of 1940, as amended (the “Act”), as an open-end management investment company and operates as a series company, currently offering two series, including the fund.The fund’s investment objective is to provide investors with as high a level of current income as is consistent with the preservation of capital and the maintenance of liquidity. The Dreyfus Corporation (the “Manager” or “Dreyfus”), a wholly-owned subsidiary of The Bank of New York Mellon Corporation (“BNY Mellon”), serves as the fund’s investment adviser.

MBSC Securities Corporation (the “Distributor”), a wholly-owned subsidiary of the Manager, is the distributor of the fund’s shares. The fund is authorized to issue 16 billion shares of $.001 par value Common Stock. The fund currently offers two classes of shares: Class A (10 billion shares authorized) and Class B (6 billion shares authorized). Class A shares and Class B shares are identical except for the services offered to and the expenses borne by each class, the allocation of certain transfer agency costs and certain voting rights. Class A shares are subject to a Service Plan adopted pursuant to Rule 12b-1 under the Act, Class B shares are subject to a Distribution Plan adopted pursuant to Rule 12b-1 under the Act and Class A and Class B shares are subject to a Shareholder Services Plan. In addition, Class B shares are charged directly for sub-accounting services provided by Service Agents (a securities dealer, financial institution or other industry professional) at an annual rate of .05% of the value of the average daily net assets of Class B shares. During the period ended May 31, 2008, sub-accounting service fees amounted to $398,604 for Class B shares and are included in shareholder servicing costs. Income, expenses (other than expenses attributable to a specific class), and realized and unrealized gains or losses on investments are allocated to each class of shares based on its relative net assets.

The Company accounts separately for the assets, liabilities and operations of each series. Expenses directly attributable to each series are charged to that series’ operations; expenses which are applicable to all series are allocated among them on a pro rata basis.

It is the fund’s policy to maintain a continuous net asset value per share of $1.00; the fund has adopted certain investment, portfolio valuation and dividend and distribution policies to enable it to do so.There is no assurance, however, that the fund will be able to maintain a stable net asset value per share of $1.00.

The fund’s financial statements are prepared in accordance with U.S. generally accepted accounting principles, which may require the use of management estimates and assumptions. Actual results could differ from those estimates.

The fund enters into contracts that contain a variety of indemnifications. The fund’s maximum exposure under these arrangements is unknown.The fund does not anticipate recognizing any loss related to these arrangements.

(a) Portfolio valuation: Investments in securities are valued at amortized cost in accordance with Rule 2a-7 of the Act, which has been determined by the Board of Directors to represent the fair value of the fund’s investments.

The Financial Accounting Standards Board (“FASB”) released Statement of Financial Accounting Standards No. 157 “Fair Value Measurements” (“FAS 157”). FAS 157 establishes an authoritative definition of fair value, sets out a framework for measuring fair value, and requires additional disclosures about fair-value measurements.The application of FAS 157 is required for fiscal years beginning after November 15, 2007 and interim periods within those fiscal years.

Various inputs are used in determining the value of the fund’s investments relating to FAS 157.

The Fund 15

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

These inputs are summarized in the three broad levels listed below.

Level 1—quoted prices in active markets for identical securities.

Level 2—other significant observable inputs (including quoted prices for similar securities, interest rates, prepayment speeds, credit risk, etc.)

Level 3—significant unobservable inputs (including fund’s own assumptions in determining the fair value of investments).

The inputs or methodology used for valuing securities are not necessarily an indication of the risk associated with investing in those securities. For example, money market securities are valued using amortized cost, in accordance with rules under the Act. Generally, amortized cost approximates the current fair value of a security, but since the value is not obtained from a quoted price in an active market, such securities are reflected as Level 2.

The following is a summary of the inputs used as of May 31, 2008 in valuing the fund’s investments carried at fair value:

		Investments in
Valuation Inputs		Securities ($)

Level 1—Quoted Prices		0
Level 2—Other Significant Observable Inputs		1,733,152,323
Level 3—Significant Unobservable Inputs		0
Total		1,733,152,323

(b) Securities transactions and investment income: Securities transactions are recorded on a trade date basis. Interest income, adjusted for accretion of discount and amortization of premium on investments, is earned from settlement date and recognized on the accrual basis. Realized gains and losses from securities transactions are recorded on the identified cost basis. Cost of investments represents amortized cost.

In March 2008, the FASB released Statement of Financial Accounting Standards No. 161 “Disclosures about Derivative Instruments and Hedging Activities” (“FAS 161”). FAS 161 requires qualitative disclosures about objectives and strategies for using derivatives, quantitative

disclosures about fair value amounts of gains and losses on derivative instruments and disclosures about credit-risk-related contingent features in derivative agreements.The application of FAS 161 is required for fiscal years beginning after November 15, 2008 and interim periods within those fiscal years.At this time, management is evaluating the implications of FAS 161 and its impact on the financial statements and the accompanying notes has not yet been determined.

The fund has arrangements with the custodian and cash management banks whereby the fund may receive earnings credits when positive cash balances are maintained, which are used to offset custody and cash management fees. For financial reporting purposes, the fund includes net earnings credits as an expense offset in the Statement of Operations.

The fund may enter into repurchase agreements with financial institutions, deemed to be creditworthy by the fund’s Manager, subject to the seller’s agreement to repurchase and the fund’s agreement to resell such securities at a mutually agreed upon price. Securities purchased 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. If the value of the underlying securities falls below the value of the repurchase price plus accrued interest, the fund will require the seller to deposit additional collateral by the next business day. If the request for additional collateral is not met, or the seller defaults on its repurchase obligation, the fund maintains the right to sell the underlying securities at market value and may claim any resulting loss against the seller.

(c) Dividends to shareholders: It is the policy of the fund to declare dividends from investment income-net on each business day; such dividends are paid monthly. Dividends from net realized capital gains, if any, are normally declared and paid annually, but the fund may make distributions on a more frequent basis to comply with the distribution requirements of the Internal Revenue Code of 1986, as amended (the “Code”).

The Fund 17

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

To the extent that net realized capital gains can be offset by capital loss carryovers, it is the policy of the fund not to distribute such gains.

(d) Federal income taxes: It is the policy of the fund to continue to qualify as a regulated investment company, if such qualification is in the best interests of its shareholders, by complying with the applicable provisions of the Code, and to make distributions of taxable income sufficient to relieve it from substantially all federal income and excise taxes.

During the current year, the fund adopted FASB Interpretation No. 48 “Accounting for Uncertainty in Income Taxes” (“FIN 48”). FIN 48 provides guidance for how uncertain tax positions should be recognized, measured, presented and disclosed in the financial statements. FIN 48 requires the evaluation of tax positions taken or expected to be taken in the course of preparing the fund’s tax returns to determine whether the tax positions are “more-likely-than-not” of being sustained by the applicable tax authority. Tax positions not deemed to meet the more likely-than-not threshold would be recorded as a tax expense in the current year. The adoption of FIN 48 had no impact on the operations of the fund for the period ended May 31, 2008.

As of and during the period ended May 31, 2008, the fund did not have any liabilities for any unrecognized tax benefits.The fund recognizes interest and penalties, if any, related to unrecognized tax benefits as income tax expense in the Statement of Operations. During the period, the fund did not incur any interest or penalties.

Each of the tax years in the three-year period ended November 30, 2007, remains subject to examination by the Internal Revenue Service and state taxing authorities.

The fund has an unused capital loss carryover of $402,752 available for federal income tax purposes to be applied against future net securities profit, if any, realized subsequent to November 30, 2007. If not applied, $40,129 of the carryover expires in fiscal 2008, $13,107 expires in fiscal 2011, $25,250 expires in fiscal 2012 and $324,266 expires in fiscal 2013.

The tax character of distributions paid to shareholders during the fiscal year ended November 30, 2007 was all ordinary income. The tax character of current year distributions will be determined at the end of the current fiscal year.

At May 31, 2008, the cost of investments for federal income tax purposes was substantially the same as the cost for financial reporting purposes (see the Statement of Investments).

NOTE 2—Management Fee and Other Transactions with Affiliates:

(a) Pursuant to a management agreement (“Agreement”) with the Manager, the management fee is computed at the annual rate of .50% of the value of the fund’s average daily net assets and is payable monthly. The Agreement provides that if in any full fiscal year the aggregate expenses of the fund, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed 1¹/₂% of the value of the fund’s average net assets, the fund may deduct from payments to be made to the Manager, or the Manager will bear such excess expense. During the period ended May 31, 2008, there was no expense reimbursement pursuant to the Agreement.

(b) Under the Service Plan with respect to Class A shares (the “Plan”), adopted pursuant to Rule 12b-1 under the Act, Class A shares bear directly the costs of preparing, printing and distributing prospectuses and statements of additional information and of implementing and operating the Plan, such aggregate amount not to exceed in any fiscal year of the fund, the greater of $100,000 or .005% of the average daily net assets of Class A. In addition, Class A shares pay the Distributor for distributing Class A shares, servicing shareholder accounts (“Servicing”) and advertising and marketing relating to Class A shares at an aggregate annual rate of .20% of the value of the average daily net assets of Class A.The Distributor may pay one or more Service Agents a fee in respect of Class A shares owned by shareholders with whom the Service Agent

The Fund 19

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

has a Servicing relationship or for whom the Service Agent is the dealer or holder of record.The schedule of such fees and the basis upon which such fees will be paid shall be determined from time to time by the Distributor. If a holder of Class A shares ceases to be a client of a Service Agent, but continues to hold Class A shares, the Distributor will be permitted to act as a Service Agent in respect of such fund shareholders and receive payments under the Plan for Servicing.The fees payable for Servicing are payable without regard to actual expenses incurred. During the period ended May 31, 2008, Class A shares were charged $69,794 pursuant to the Plan.

Under the Distribution Plan with respect to Class B shares (“Class B Distribution Plan”), adopted pursuant to Rule 12b-1 under the Act, Class B shares bear directly the costs of preparing, printing and distributing prospectuses and statements of additional information and of implementing and operating the Class B Distribution Plan, such aggregate amount not to exceed in any fiscal year of the fund, the greater of $100,000 or .005% of the average daily net assets of Class B. In addition, Class B shares reimburse the Distributor for payments made to third parties for distributing Class B shares at an aggregate annual rate not to exceed .20% of the value of the average daily net assets of Class B. During the period ended May 31, 2008, Class B shares were charged $1,602,321 pursuant to the Class B Distribution Plan.

Under the Shareholder Services Plan with respect to Class B (“Class B Shareholder Services Plan”), Class B shares pay the Distributor at an annual rate of .25% of the value of the average daily net assets of Class B for servicing shareholder accounts. The services provided may include personal services relating to shareholder accounts, such as answering shareholder inquiries regarding Class B shares and providing reports and other information, and services related to the maintenance of shareholder accounts.The Distributor may make payments to Service Agents in respect of these services.The Distributor determines the amounts to be paid to Service Agents.

The Manager had undertaken from December 1, 2007 through May 31, 2008, to reduce the expenses of Class B shares, if the aggregate expenses of Class B shares of the fund, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed an annual rate of 1.01% of the value of the average daily net assets of Class B shares. Such expense limitations are voluntary, temporary and may be terminated at anytime. During the period ended May 31, 2008, Class B shares were charged $1,993,019 pursuant to the Class B Shareholder Services Plan, of which $186,301 was reimbursed by the Manager.

The fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the Manager, under a transfer agency agreement, for providing personnel and facilities to perform transfer agency services for the fund. During the period ended May 31, 2008, the fund was charged $17,079, pursuant to the transfer agency agreement.

The fund compensates The Bank of New York, a subsidiary of BNY Mellon and a Dreyfus affiliate, under a cash management agreement for performing cash management services related to fund subscriptions and redemptions. During the period ended May 31, 2008, the fund was charged $1,128 pursuant to the cash management agreement.

The fund compensates The Bank of New York, under a custody agreement for providing custodial services for the fund. During the period

The Fund 21

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

ended May 31, 2008, the fund was charged $73,417 pursuant to the custody agreement.

During the period ended May 31, 2008, the fund was charged $2,820 for services performed by the Chief Compliance Officer.

The components of “Due to The Dreyfus Corporation and affiliates” in the Statement of Assets and Liabilities consist of: management fees $725,245, Rule 12b-1 distribution plan fees $290,098, shareholder services plan fees $418,311, custodian fees $56,374, chief compliance officer fees $2,350 and transfer agency per account fees $5,392, which are offset against an expense reimbursement currently in effect in the amount of $27,213.

(d) Each Board member also serves as a Board member of other funds within the Dreyfus complex. Annual retainer fees and attendance fees are allocated to each fund based on net assets.

NOTE 3—Subsequent Event:

Effective July 1, 2008, BNY Mellon has reorganized and consolidated a number of its banking and trust company subsidiaries. As a result of the reorganization, any services previously provided to the fund by Mellon Bank, N.A. or Mellon Trust of New England, N.A. are now provided by The Bank of New York, which has changed its name to The Bank of New York Mellon.

NOTES

Not FDIC-Insured • Not Bank-Guaranteed • May Lose Value

Contents

		THE FUND

2		A Letter from the CEO
3		Discussion of Fund Performance
6		Understanding Your Fund’s Expenses
6		Comparing Your Fund’s Expenses
		With Those of Other Funds
7		Statement of Investments
8		Statement of Assets and Liabilities
9		Statement of Operations
10		Statement of Changes in Net Assets
11		Financial Highlights
13		Notes to Financial Statements
FOR MORE INFORMATION

		Back Cover

The Fund

General Treasury Prime

Money Market Fund

A LETTER FROM THE CEO

Dear Shareholder:

We are pleased to present this semiannual report for General Treasury Prime Money Market Fund, covering the six-month period from December 1, 2007, through May 31, 2008.

The Fed has aggressively reduced the overnight rate by 250 basis points — to 2% as of this reporting period — which has resulted in lower yields for virtually all true money market instruments. In addition, volatility in the stock and bond markets also has allowed the money markets to maintain record levels of demand, since money market funds are obligated under strict regulations to seek preservation of capital as their main func-tion.Your financial advisor can help you assess current risks and your need for liquidity and take advantage of potential opportunities in other asset classes given your individual needs and financial goals.

For information about how the fund performed during the reporting period, as well as market perspectives, we have provided a Discussion of Fund Performance given by the fund’s Portfolio Manager.

Thank you for your continued confidence and support.

DISCUSSION OF FUND PERFORMANCE

For the period of December 1, 2007, through May 31, 2008, as provided by Bernard W. Kiernan, Jr., Senior Portfolio Manager

Fund and Market Performance Overview

For the six-month period ended May 31, 2008, General Treasury Prime Money Market Fund’s Class A shares produced an annualized yield of 1.90%, and its Class B shares produced an annualized yield of 1.68% . Taking into account the effects of compounding, the fund’s Class A and Class B shares produced annualized effective yields of 1.92% and 1.69%, respectively.¹

Money market yields declined over much of the reporting period as the Federal Reserve Board (the “Fed”) reduced short-term interest rates in an attempt to stimulate U.S. economic growth, and investor demand increased in the midst of a credit crisis.

The Fund’s Investment Approach

The fund seeks as high a level of current income as is consistent with the preservation of capital and the maintenance of liquidity.To pursue this goal, the fund normally invests substantially all of its assets in U.S.Treasury securities.

The Fed Addressed an Economic Slump and Credit Crisis

Turmoil in the sub-prime mortgage market, slumping U.S. housing markets and resurgent energy prices already had led to economic concerns by the start of the reporting period. These factors had caused investors to reassess their previously generous attitudes toward risk, sparking sharp declines among stocks and higher yielding bonds.

The resulting tightness in credit markets, as well as reports of heavy sub-prime related losses among commercial and investment banks, prompted the Fed to intervene by reducing short-term interest rates. As a result, the reporting period began with an overnight federal funds rate of 4.50%, down from 5.25% approximately three months earlier.

The Fund 3

DISCUSSION OF FUND PERFORMANCE (continued)

The economy continued to show signs of weakness in December 2007, as sales of existing homes fell sharply and longer-term fixed-income markets encountered heightened volatility. The Fed again reduced the federal funds rate by 25 basis points in December — to 4.25% — but investors appeared to be disappointed that the reduction was not larger. 2007 ended with an annualized economic growth rate of just 0.60% in the fourth quarter and 2.20% for the year overall.

January 2008 saw more disappointing economic news, including the first monthly job losses in more than four years. Congress passed legislation designed to stimulate the economy, and the Fed reduced the federal funds rate by 125 basis points to 3% in two separate moves during the latter part of January. However, more job losses were reported in February, and pressures on U.S. financial institutions remained intense from additional sub-prime related losses, deleveraging of institutional investment portfolios and the repricing of real estate.

In March, non-farm payrolls shrank by another 80,000 jobs, driving the total number of lost jobs during the first quarter of 2008 to 232,000.The unemployment rate climbed to 5.10% in March from 4.80% in February. The Fed continued to take aggressive policy action during the month, reducing the federal funds rate to 2.25% . In addition, the Fed announced an expansion of its Term Securities Lending Facility, making $200 billion of Treasury securities available to Wall Street firms. In an unprecedented move apparently designed to prevent further damage to the U.S. financial system, the Fed allowed borrowers to use certain mortgage-backed securities as collateral for these loans.The first quarter ended with a 0.90% GDP growth rate, according to revised government estimates.

More job losses followed in April, but the unemployment rate ticked down to a modest 5%.The Fed continued to reduce the federal funds rate, implementing a cut of 25 basis points that left the overnight rate at 2% by the end of the reporting period. Moreover, inflationary pressures increased along with crude oil prices, and businesses attempted to pass along higher input costs.

Economic data in May proved to be mixed. On one hand, the U.S. economy lost an additional 49,000 jobs, and the unemployment rate jumped to 5.50% . Inflation worries also intensified as oil prices continued to set new record highs and the average cost of gasoline in the United States surpassed $4.00 per gallon. On the other hand, retail sales improved by an unexpected 1% during the month, suggesting that tax rebate checks might be having the desired effect of boosting consumer spending.

Longer Maturities Captured Higher Yields

As the credit crisis unfolded and the Fed cut short-term interest rates, demand for U.S.Treasury securities surged from investors engaged in a “flight to quality,” putting additional downward pressure on yields across the money market’s maturity spectrum. In this environment, we maintained the fund’s weighted average maturity in a position we considered in line with industry averages.

June 16, 2008

		An investment in the fund is not insured or guaranteed by the FDIC or any other government
		agency. Although the fund seeks to preserve the value of your investment at $1.00 per share, it is
		possible to lose money by investing in the fund.
¹		Annualized effective yield is based upon dividends declared daily and reinvested monthly. Past
		performance is no guarantee of future results.Yields fluctuate.Yields provided for the fund’s Class
		A and Class B shares reflect the absorption of certain fund expenses by The Dreyfus Corporation
		pursuant to an undertaking in effect that may be extended, terminated or modified at any time.
		Had these expenses not been absorbed, the fund’s Class A shares would have produced an annualized
		yield of 1.89% and an annualized effective yield of 1.91%, and the fund’s Class B shares
		would have produced an annualized yield of 1.60% and an annualized effective yield of 1.61%.

The Fund 5

UNDERSTANDING YOUR FUND’S EXPENSES (Unaudited)

Review your fund’s expenses

The table below shows the expenses you would have paid on a $1,000 investment in General Treasury Prime Money Market Fund from December 1, 2007 to May 31, 2008. It also shows how much a $1,000 investment would be worth at the close of the period, assuming actual returns and expenses.

Expenses and Value of a $1,000 Investment
assuming actual returns for the six months ended May 31, 2008
	Class A	Class B

Expenses paid per $1,000 ^†	$ 3.92	$ 5.02
Ending value (after expenses)	$1,009.60	$1,008.40

COMPARING YOUR FUND’S EXPENSES

WITH THOSE OF OTHER FUNDS (Unaudited)

Using the SEC’s method to compare expenses

Expenses and Value of a $1,000 Investment
assuming a hypothetical 5% annualized return for the six months ended May 31, 2008
	Class A	Class B

Expenses paid per $1,000 ^†	$ 3.94	$ 5.05
Ending value (after expenses)	$1,021.10	$1,020.00

†		Expenses are equal to the fund’s annualized expense ratio of .78% for Class A and 1.00% for Class B, multiplied
		by the average account value over the period, multiplied by 183/366 (to reflect the one-half year period).

STATEMENT OF INVESTMENTS

May 31, 2008 (Unaudited)

	Annualized
	Yield on
	Date of	Principal
U.S. Treasury Bills—94.7%	Purchase (%)	Amount ($)	Value ($)

6/5/08	1.54	6,100,000	6,098,955
6/12/08	3.19	35,522,000	35,487,919
6/16/08	2.03	11,000,000	10,990,696
6/19/08	1.94	44,982,000	44,938,403
7/3/08	3.15	4,000,000	3,988,978
7/10/08	1.80	47,300,000	47,208,719
7/17/08	1.15	74,000,000	73,891,159
7/24/08	0.87	25,000,000	24,967,979
7/31/08	1.55	761,000	759,047
8/14/08	2.03	6,000,000	5,975,210
8/21/08	2.04	18,000,000	17,918,392
8/28/08	1.25	12,000,000	11,963,627
9/4/08	1.33	65,240,000	65,013,119
10/2/08	1.53	42,000,000	41,782,085
Total U.S. Treasury Bills
(cost $390,984,288)			390,984,288


U.S. Treasury Note—5.4%

6/30/08
(cost $22,067,903)	1.21	22,000,000	22,067,903


Total Investments (cost $413,052,191)		100.1%	413,052,191
Liabilities, Less Cash and Receivables		(.1%)	(591,150)
Net Assets		100.0%	412,461,041

^†Based on net assets.

See notes to financial statements.

The Fund 7

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2008 (Unaudited)

	Cost	Value

Assets ($):
Investments in securities—See Statement of Investments	413,052,191	413,052,191
Interest receivable		473,922
Prepaid expenses		63,764
		413,589,877

Liabilities ($):
Due to The Dreyfus Corporation and affiliates—Note 2(c)		338,070
Cash overdraft due to Custodian		765,248
Accrued expenses		25,518
		1,128,836

Net Assets ($)		412,461,041

Composition of Net Assets ($):
Paid-in capital		412,449,258
Accumulated net realized gain (loss) on investments		11,783

Net Assets ($)		412,461,041

Net Asset Value Per Share
	Class A	Class B

Net Assets ($)	11,367,148	401,093,893
Shares Outstanding	11,366,593	401,082,665

Net Asset Value Per Share ($)	1.00	1.00

See notes to financial statements.

STATEMENT OF OPERATIONS

Six Months Ended May 31, 2008 (Unaudited)

Investment Income ($):
Interest Income		4,181,715
Expenses:
Management fee—Note 2(a)		835,907
Shareholder servicing costs—Note 2(c)		498,343
Distribution, service and prospectus fees—Note 2(b)		335,690
Registration fees		67,019
Professional fees		22,544
Custodian fees—Note 2(c)		17,440
Directors’ fees and expenses—Note 2(d)		8,744
Shareholders’ reports		6,013
Miscellaneous		7,626
Total Expenses		1,799,326
Less—reduction in service plan fees and shareholder
servicing costs due to undertaking—Note 2(b,c)		(135,419)
Less—reduction in fees due to earnings credits—Note 1(b)		(4,382)
Net Expenses		1,659,525
Investment Income—Net		2,522,190

Net Realized Gain (Loss) on Investments—Note 1(b) ($)		9,673
Net Increase in Net Assets Resulting from Operations		2,531,863

See notes to financial statements.

The Fund 9

STATEMENT OF CHANGES IN NET ASSETS

	Six Months Ended
	May 31, 2008	Year Ended
	(Unaudited)	November 30, 2007

Operations ($):
Investment income—net	2,522,190	3,298,384
Net realized gain (loss) on investments	9,673	6,980
Net Increase (Decrease) in Net Assets
Resulting from Operations	2,531,863	3,305,364

Dividends to Shareholders from ($):
Investment income—net:
Class A Shares	(51,195)	(36,106)
Class B Shares	(2,470,995)	(3,262,278)
Total Dividends	(2,522,190)	(3,298,384)

Capital Stock Transactions ($1.00 per share):
Net proceeds from shares sold:
Class A Shares	21,645,784	2,773,695
Class B Shares	742,430,042	427,529,203
Dividends reinvested:
Class A Shares	50,714	34,745
Class B Shares	2,469,590	3,242,581
Cost of shares redeemed:
Class A Shares	(11,349,736)	(4,032,593)
Class B Shares	(573,093,378)	(274,782,385)
Increase (Decrease) in Net Assets
from Capital Stock Transactions	182,153,016	154,765,246
Total Increase (Decrease) in Net Assets	182,162,689	154,772,226

Net Assets ($):
Beginning of Period	230,298,352	75,526,126
End of Period	412,461,041	230,298,352

See notes to financial statements.

FINANCIAL HIGHLIGHTS

	Six Months Ended
	May 31, 2008		Year Ended November 30,

Class A Shares	(Unaudited)	2007	2006	2005	2004	2003

Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.010	.039	.038	.020	.004	.004
Distributions:
Dividends from
investment income—net	(.010)	(.039)	(.038)	(.020)	(.004)	(.004)
Net asset value, end of period	1.00	1.00	1.00	1.00	1.00	1.00

Total Return (%)	1.91^a	4.01	3.84	2.00	.42	.39

Ratios/Supplemental Data (%):
Ratio of total expenses
to average net assets	.79^a	1.09	1.05	1.03	.93	.85
Ratio of net expenses
to average net assets	.78^a	.80	.80	.80	.80	.80
Ratio of net investment income
to average net assets	1.39^a	3.88	3.69	2.08	.34	.38

Net Assets, end of period
($ x 1,000)	11,367	1,020	2,244	5,375	4,848	26,315

^aAnnualized.

See notes to financial statements.

The Fund 11

FINANCIAL HIGHLIGHTS (continued)

	Six Months Ended
	May 31, 2008		Year Ended November 30,

Class B Shares	(Unaudited)	2007	2006	2005	2004	2003

Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.008	.037	.036	.018	.003	.002
Distributions:
Dividends from
investment income—net	(.008)	(.037)	(.036)	(.018)	(.003)	(.002)
Net asset value, end of period	1.00	1.00	1.00	1.00	1.00	1.00

Total Return (%)	1.68^a	3.80	3.64	1.80	.28	.24

Ratios/Supplemental Data (%):
Ratio of total expenses
to average net assets	1.08^a	1.20	1.20	1.27	1.15	1.12
Ratio of net expenses
to average net assets	1.00^a	1.00	.99	1.00	.92	.94
Ratio of net investment income
to average net assets	1.51^a	3.60	3.64	1.88	.26	.24

Net Assets, end of period
($ x 1,000)	401,094	229,278	73,282	50,027	29,806	30,537

^aAnnualized.

See notes to financial statements.

NOTES TO FINANCIAL STATEMENTS (Unaudited)

NOTE 1—Significant Accounting Policies:

General Treasury Prime Money Market Fund, (the “fund”) is a separate diversified series of General Government Securities Money Market Funds, Inc. (the “Company”), which is registered under the Investment Company Act of 1940, as amended (the “Act”), as an open-end management investment company and operates as a series company, currently offering two series, including the fund. The fund’s investment objective is to provide investors with as high a level of current income as is consistent with the preservation of capital and the maintenance of liquidity.The Dreyfus Corporation (the “Manager” or “Dreyfus”), a wholly-owned subsidiary of The Bank of New York Mellon Corporation (“BNY Mellon”), serves as the fund’s investment adviser.

MBSC Securities Corporation (the “Distributor”), a wholly-owned subsidiary of the Manager, is the distributor of the fund’s shares. The fund is authorized to issue 3 billion shares of $.001 par value Common Stock.The fund currently offers two classes of shares: Class A (1 billion shares authorized) and Class B (2 billion shares authorized). Class A and Class B shares are identical except for the services offered to and the expenses borne by each class, the allocation of certain transfer agency costs and certain voting rights. Class A shares are subject to a Service Plan adopted pursuant to Rule 12b-1 under the Act, Class B shares are subject to a Distribution Plan adopted pursuant to Rule 12b-1 under the Act and Class A and Class B shares are subject to a Shareholder Services Plan. In addition, Class B shares are charged directly for sub-accounting services provided by Service Agents (a securities dealer, financial institution or other industry professional) at an annual rate of .05% of the value of the average daily net assets of Class B shares. During the period ended May 31, 2008, sub-accounting service fees amounted to $81,749 for Class B shares and are included in shareholder servicing costs. Income, expenses (other than expenses attributable to a specific class), and realized and unrealized gains or losses on investments are allocated to each class of shares based on its relative net assets.

The Fund 13

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

The Financial Accounting Standards Board (FASB) released Statement of Financial Accounting Standards No. 157 “Fair Value Measurements” (“FAS 157”). FAS 157 establishes an authoritative definition of fair value, sets out a framework for measuring fair value, and requires additional disclosures about fair-value measurements. The application of FAS 157 is required for fiscal years beginning after November 15, 2007 and interim periods within those fiscal years.

Various inputs are used in determining the value of the fund’s investments relating to FAS 157.

These inputs are summarized in the three broad levels listed below.

Level 1—quoted prices in active markets for identical securities.

Level 2—other significant observable inputs (including quoted prices for similar securities, interest rates, prepayment speeds, credit risk, etc.)

Level 3—significant unobservable inputs (including fund’s own assumptions in determining the fair value of investments).

The following is a summary of the inputs used as of May 31, 2008 in valuing the fund’s investments carried at fair value:

		Investments in
Valuation Inputs		Securities ($)

Level 1—Quoted Prices		0
Level 2—Other Significant Observable Inputs		413,052,191
Level 3—Significant Unobservable Inputs		0
Total		413,052,191

(b) Securities transactions and investment income: Securities transactions are recorded on a trade date basis. Interest income, adjusted for accretion of discount and amortization of premium on investments, is earned from settlement date and is recognized on the accrual basis. Realized gains and losses from securities transactions are recorded on the identified cost basis. Cost of investments represents amortized cost.

In March 2008, the FASB released Statement of Financial Accounting Standards No. 161 “Disclosures about Derivative Instruments and

The Fund 15

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

Hedging Activities” (“FAS 161”). FAS 161 requires qualitative disclosures about objectives and strategies for using derivatives, quantitative disclosures about fair value amounts of gains and losses on derivative instruments and disclosures about credit-risk-related contingent features in derivative agreements.The application of FAS 161 is required for fiscal years beginning after November 15, 2008 and interim periods within those fiscal years. At this time, management is evaluating the implications of FAS 161 and its impact on the financial statements and the accompanying notes has not yet been determined.

whether the tax positions are “more-likely-than-not” of being sustained by the applicable tax authority.Tax positions not deemed to meet the more likely-than-not threshold would be recorded as a tax expense in the current year.The adoption of FIN 48 had no impact on the operations of the fund for the period ended May 31, 2008.

As of and during the period ended May 31, 2008, the fund did not have any liabilities for any unrecognized tax benefits. The fund recognizes interest and penalties, if any, related to unrecognized tax benefits as income tax expense in the Statement of Operations. During the period, the fund did not incur any interest or penalties.

Each of the tax years in the three-year period ended November 30, 2007, remains subject to examination by the Internal Revenue Service and state taxing authorities.

At May 31, 2008, the cost of investments for federal income tax purposes was substantially the same as the cost for financial reporting purposes (see the Statement of Investments).

NOTE 2—Management Fee and Other Transactions with Affiliates:

(a) Pursuant to a management agreement (“Agreement”) with the Manager, the management fee is computed at the annual rate of .50% of the value of the fund’s average daily net assets and is payable monthly. The Agreement provides that if in any full fiscal year the aggregate expenses of the fund, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed 1¹/₂% of the value of the fund’s average net assets, the fund may deduct from payments to be made to the Manager, or the Manager will bear, such excess expense. During the period ended May 31, 2008 there was no expense reimbursement pursuant to the Agreement.

The Fund 17

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

(b) Under the Service Plan with respect to Class A (the “Plan”), adopted pursuant to Rule 12b-1 under the Act, Class A shares bear directly the cost of preparing, printing and distributing prospectuses and statements of additional information and implementing and operating the Plan, such aggregate amount not to exceed in any full fiscal year of the fund, the greater of $100,000 or .005% of the average daily net assets of Class A. In addition, Class A shares pay the Distributor for distributing their shares, servicing shareholder accounts (“Servicing”) and advertising and marketing relating to Class A shares at an aggregate annual rate of .20% of the value of the average daily net assets of Class A.The Distributor may pay one or more Service Agents a fee in respect of Class A shares owned by shareholders with whom the Service Agent has a Servicing relationship or for whom the Service Agent is the dealer or holder of record.The schedule of such fees and the basis upon which such fees will be paid shall be determined from time to time by the Distributor. If a holder of Class A shares ceases to be a client of a Service Agent, but continues to hold Class A shares, the Distributor will be permitted to act as a Service Agent in respect of such fund shareholders and receive payments under the Plan for Servicing.The fees payable for Servicing are payable without regard to actual expenses incurred. During the period ended May 31, 2008, Class A shares were charged $7,396 pursuant to the Plan, of which $413 was reimbursed by the Manager, due to an undertaking. See Note 2(c).

Under the Distribution Plan with respect to Class B (“Class B Distribution Plan”) adopted pursuant to Rule 12b-1 under the Act, Class B shares bear directly the costs of preparing, printing and distributing prospectuses and statements of additional information and of implementing and operating the Class B Distribution Plan, such aggregate amount not to exceed in any fiscal year of the fund the greater of $100,000 or .005% of the average daily net assets of Class B. In addition, Class B shares reimburse the Distributor for payments made to third parties for distributing Class B shares at an annual rate not to

exceed .20% of the value of the average daily net assets of Class B. During the period ended May 31, 2008, Class B shares were charged $328,294 pursuant to the Class B Distribution Plan.

(c) Under the Shareholder Services Plan with respect to Class A (“Class A Shareholder Services Plan”), Class A shares reimburse the Distributor an amount not to exceed an annual rate of .25% of the value of the average daily net assets of Class A for certain allocated expenses of providing personal services and/or maintaining shareholder accounts.The services provided may include personal services relating to shareholder accounts, such as answering shareholder inquiries regarding Class A shares and providing reports and other information, and services related to the maintenance of shareholder accounts.The Manager had undertaken from December 1, 2007 through May 31, 2008, to reduce the expenses of Class A shares if the aggregate expenses of Class A shares, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed .80% of the value of the average daily net assets of Class A. Such expense limitations are voluntary, temporary and may be terminated at any time. During the period ended May 31, 2008, Class A shares were charged $75 pursuant to the Class A Shareholder Services Plan, all of which was reimbursed by the Manager.

Under the Shareholder Services Plan with respect to Class B (“Class B Shareholder Services Plan”), Class B shares pay the Distributor at an annual rate of .25% of the value of the average daily net assets of Class B shares for servicing shareholder accounts. The services provided may include personal services relating to shareholder accounts, such as answering shareholder inquiries regarding Class B shares and providing reports and other information, and services related to the maintenance of shareholder accounts.The Distributor may make payments to Service Agents in respect of these services.The Distributor determines the amounts to be paid to Service Agents.

The Fund 19

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

The Manager had undertaken from December 1, 2007 through May 31, 2008, to reduce the expenses of Class B shares, if the aggregate expenses of Class B shares, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed an annual rate of 1% of the value of the average daily net assets of Class B shares. Such expense limitations are voluntary, temporary and may be reused or terminated at any time. During the period ended May 31, 2008, Class B shares were charged $408,748 pursuant to the Class B Shareholder Services Plan, of which $134,931 was reimbursed by the Manager.

The fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the Manager, under a transfer agency agreement for providing personnel and facilities to perform transfer agency services for the fund. During the period ended May 31, 2008, the fund was charged $2,736 pursuant to the transfer agency agreement.

The fund compensates The Bank of New York under a custody agreement for providing custodial services for the fund. During the period ended May 31, 2008, the fund was charged $17,440 pursuant to the custody agreement.

During the period ended May 31, 2008, the fund was charged $2,820 for services performed by the Chief Compliance Officer.

The components of “Due to The Dreyfus Corporation and affiliates” in the Statement of Assets and Liabilities consist of: management fees $174,479, Rule 12b-1 distribution plan fees $69,921, shareholder services plan fees $102,326, custodian fees $8,597, chief compliance officer fees $2,350 and transfer agency per account fees $1,077, which are offset against an expense reimbursement currently in effect in the amount of $20,680.

(d) Each Board member also serves as a Board member of other funds within the Dreyfus complex. Annual retainer fees and attendance fees are allocated to each fund based on net assets.

NOTE 3—Subsequent Event:

The Fund 21

Item 2.		Code of Ethics.
		Not applicable.
Item 3.		Audit Committee Financial Expert.
		Not applicable.
Item 4.		Principal Accountant Fees and Services.
		Not applicable.
Item 5.		Audit Committee of Listed Registrants.
		Not applicable.
Item 6.		Investments.
(a)		Not applicable.
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 Companies and
		Affiliated Purchasers.
		Not applicable. [CLOSED END FUNDS ONLY]
Item 10.		Submission of Matters to a Vote of Security Holders.

The Registrant has a Nominating Committee (the "Committee"), which is responsible for selecting and nominating persons for election or appointment by the Registrant's Board as Board members. The Committee has adopted a Nominating Committee Charter (the "Charter"). Pursuant to the Charter, the Committee will consider recommendations for nominees from shareholders submitted to the Secretary of the Registrant, c/o The Dreyfus Corporation Legal Department, 200 Park Avenue, 8th Floor East, New York, New York 10166. A nomination submission must include information regarding the recommended nominee as specified in the Charter. This information includes all information relating to a recommended nominee that is required to be disclosed in solicitations or proxy statements for the election of Board members, as well as information sufficient to evaluate the factors to be considered by the Committee, including character and integrity, business and professional experience, and whether the person has the ability to apply sound and

independent business judgment and would act in the interests of the Registrant and its shareholders. Nomination submissions are required to be accompanied by a written consent of the individual to stand for election if nominated by the Board and to serve if elected by the shareholders, and such additional information must be provided regarding the recommended nominee as reasonably requested by the Committee.

Item 11.

Controls and Procedures.

(a) The Registrant's principal executive and principal financial officers have concluded, based on their evaluation of the Registrant's disclosure controls and procedures as of a date within 90 days of the filing date of this report, that the Registrant's disclosure controls and procedures are reasonably designed to ensure that information required to be disclosed by the Registrant on Form N-CSR is recorded, processed, summarized and reported within the required time periods and that information required to be disclosed by the Registrant in the reports that it files or submits on Form N-CSR is accumulated and communicated to the Registrant's management, including its principal executive and principal financial officers, as appropriate to allow timely decisions regarding required disclosure.

(b) There were no changes to the Registrant's internal control over financial reporting that occurred during the second fiscal quarter of the period covered by this report that have materially affected, or are reasonably likely to materially affect, the Registrant's internal control over financial reporting.

Item 12.

Exhibits.

(a)(1)		Not applicable.
(a)(2)		Certifications of principal executive and principal financial officers as required by Rule 30a-2(a)
under the Investment Company Act of 1940.
(a)(3)		Not applicable.
(b)		Certification of principal executive and principal financial officers 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.

General Government Securities Money Market Funds, Inc.

By:		/s/ J. David Officer
		J. David Officer,
		President

Date:		July 23, 2008

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/J. David Officer
		J. David Officer,
		President

Date:		July 23, 2008

By:		/s/ James Windels
		James Windels,
		Treasurer

Date:		July 23, 2008

EXHIBIT INDEX

(a)(2) Certifications of principal executive and principal financial officers as required by Rule 30a-2(a) under the Investment Company Act of 1940. (EX-99.CERT)

(b) Certification of principal executive and principal financial officers as required by Rule 30a-2(b) under the Investment Company Act of 1940. (EX-99.906CERT)

Portfolio Summary (Unaudited) ^†

U.S. Government Agencies

Repurchase Agreements