General Government Securities Money Market Funds NCSR 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 811-3456

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)

	Mark N. Jacobs, 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:	05/31/04

SSL-DOCS2 70134233v1

		FORM N-CSR

Item 1.	Reports to Stockholders.

General Government

Securities Money

Market Fund

SEMIANNUAL REPORT May 31, 2004

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	Letter from the Chairman
3	Discussion of Fund Performance
6	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

General Government Securities

Money Market Fund

The Fund

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This semiannual report for General Government Securities Money Market Fund covers the six-month period from December 1, 2003, through May 31, 2004. Inside, you’ll find valuable information about how the fund was managed during the reporting period, including a discussion with the fund’s portfolio manager, Bernard W. Kiernan, Jr.

Positive economic data continued to accumulate during the reporting period, as consumers, flush with extra cash from their 2003 federal tax refunds and mortgage refinancings,continued to spend.At the same time, corporations have become more willing to hire new workers and invest in new projects and equipment.As a result, yields of longer-dated money market securities began to rise in the spring of 2004, as investors increasingly anticipated that the Federal Reserve Board might soon begin raising rates in an attempt to forestall potential inflationary pressures.

No matter where interest rates go from here, however, we continue to believe that the objectives of liquidity and stability make money market funds a valuable component of many investors’ portfolios. Indeed, despite recently encouraging economic news, concerns regarding the war on terrorism, instability in Iraq and higher energy prices have caused heightened volatility in the stock and bond markets.As always, we encourage you to speak regularly with your financial advisor, who may be in the best position to suggest ways to position your portfolio for the opportunities and challenges of today’s financial markets.

Thank you for your continued confidence and support.

Sincerely,

Stephen E. Canter

Chairman and Chief Executive Officer

The Dreyfus Corporation

June 15, 2004

DISCUSSION OF FUND PERFORMANCE

Bernard W. Kiernan, Jr., Portfolio Manager

How did General Government Securities Money Market Fund perform during the period?

Over the six-month period ended May 31, 2004, the fund produced annualized yields of 0.32% for Class A shares and 0.15% for Class B shares.Taking into account the effects of compounding, the fund also produced annualized effective yields of 0.32% for Class A shares and 0.15% for Class B shares for the same period.¹

What is 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 solely in securities issued or guaranteed by the U.S. government or its agencies or instrumentalities, and repurchase agreements collateralized by these securities.

What other factors influenced the fund’s performance?

When the reporting period began, the economy was exhibiting signs of renewed economic strength. Even before it was revealed that the U.S. gross domestic product (“GDP”) had expanded at a robust 8.2% annual rate during the third quarter of 2003, concerns that rising inflation and a ballooning federal budget deficit might lead to higher interest rates had already sparked a sharp decline in bond prices. Despite these concerns and their impact on longer-term fixed-income securities, money market yields remained anchored by the 1% federal funds rate.

Economic indicators toward the end of 2003 showed an encouraging increase in jobs and a decrease in the unemployment rate to 6.0%. Orders for durable goods rose more strongly, suggesting that business investment was finally contributing in a meaningful way to the recovery, and consumer confidence advanced to its highest level in more than a year.

The Fund

DISCUSSION OF FUND PERFORMANCE (continued)

As was widely expected, the Federal Reserve Board (the “Fed”) held the overnight federal funds rate steady at 1%, during its meeting in early December, and reiterated its commitment to keeping borrowing rates low. By the end of 2003, new data further confirmed that an economic recovery was well underway, while a drop in the consumer price index (“CPI”) suggested that inflation remained under control. The U.S. Commerce Department later estimated that the GDP grew at a 4.1% annualized rate during the fourth quarter of 2003.

While the Fed continued to maintain its accommodative monetary policy at its meeting in late January 2004, it noted that U.S. economic output was expanding briskly. However, the number of new jobs created by the recovering economy continued to disappoint. In addition, the CPI in February indicated that the core rate of inflation rose only 0.1%, reinforcing the perception that the Fed still had a great deal of flexibility in the conduct of monetary policy, potentially enabling it to keep interest rates low for an extended period. It was later revealed that U.S. economic growth rose relatively modestly during the first quarter of 2004, expanding at a 4.4% annualized rate.

In early April, however, the U.S. Department of Labor announced that the domestic economy had added 308,000 jobs in March. As the month progressed, higher energy and commodity prices appeared, fueling concerns that long-dormant inflationary pressures might have begun to resurface.As a result, the money-market yield curve began to steepen as yields rose at the longer end of the maturity spectrum.

At its May meeting, the Fed left interest rates unchanged. However, unlike previous pronouncements, the Fed no longer indicated that it could be “patient” before raising rates, stating instead that future rate hikes were likely to be “measured.” Soon after the Fed meeting, non-farm payroll data showing a second consecutive month of strong gains triggered a significant change in investor expectations, which shifted

from the belief that interest rates were unlikely to rise in 2004 to anticipation that the Fed might begin to tighten monetary policy by 25 to 50 basis points as early as June.

What is the fund’s current strategy?

In light of expectations of higher short-term interest rates, we have adopted a more defensive posture, allowing the fund’s weighted average maturity to fall toward a range we consider neutral. Accordingly, we generally have limited new investments to U.S. government securities with maturities of three months or less. This strategy is designed to give us flexibility to take advantage of higher yields should they arise. Of course, we are prepared to adjust our strategy as market conditions evolve.

June 15, 2004

1 Annualized effective yield is based upon dividends declared daily and reinvested monthly. Past performance is no guarantee of future results.Yields fluctuate.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.Yields provided for the fund’s Class B shares reflect the absorption of 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 a yield of 0.08% and an effective yield of 0.08%.

The Fund

STATEMENT OF INVESTMENTS
May 31, 2004 (Unaudited)





	Annualized
	Yield on
	Date of	Principal
U.S. Government Agencies—99.7%	Purchase (%)	Amount ($)	Value ($)

Federal Farm Credit Banks, Consolidated
Systemwide Floating Rate Notes
6/2/2004	1.03 ^a	45,000,000	45,000,012
11/23/2005	1.06 ^a	110,000,000	110,008,877
Federal Farm Credit Banks,
Notes
12/15/2004	1.27	30,000,000	30,412,072
Federal Home Loan Banks,
Discount Notes
6/4/2004	1.17	18,462,000	18,460,217
6/16/2004	1.00	100,000,000	99,958,542
7/21/2004	1.00	73,000,000	72,898,611
7/30/2004	1.00	7,750,000	7,737,299
Federal Home Loan Banks,
Floating Rate Notes
7/30/2004	1.01 ^a	150,000,000	150,000,000
12/2/2004	1.02 ^a	100,000,000	100,005,362
Federal Home Loan Banks,
Notes
6/1/2004	.88	102,506,000	102,506,000
8/13/2004	1.18	5.000,000	5,010,421
3/11/2005	1.42	75,000,000	75,000,000
4/29/2005	1.34	50,000,000	50,000,000
Federal Home Loan Mortgage Corporation,
Discount Notes
6/16/2004	1.11	75,716,000	75,681,139
8/12/2004	1.18	21,000,000	20,950,860
Federal Home Loan Mortgage Corporation,
Notes
7/15/2004	1.24	35,699,000	35,848,238
Federal National Mortgage Association,
Discount Notes
8/20/2004	1.27	17,794,000	17,744,177

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

Federal National Mortgage Association,
Floating Rate Notes
10/7/2004			1.03	^a	100,000,000	99,989,480
1/10/2005			1.03	^a	100,000,000	99,969,457
3/10/2005			1.02	^a	50,000,000	50,000,000
Federal National Mortgage Association,
Notes
9/15/2004			1.21		41,940,000	42,209,270
4/19/2005			1.27		50,000,000	50,000,000
Total U.S. Government Agencies
(cost $	1,359,390,034)					1,359,390,034


Total Investments (cost $		1,359,390,034)			99.7%	1,359,390,034
Cash and Receivables (Net)					.3%	4,297,926
Net Assets					100.0%	1,363,687,960

a Variable interest rate—subject to periodic change.

See notes to financial statements.

The Fund

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2004 (Unaudited)






		Cost	Value

Assets ($):
Investments in securities—See Statement of Investments		1,359,390,034	1,359,390,034
Cash			2,187,854
Interest receivable			3,029,204
Prepaid expenses and other assets			103,283
			1,364,710,375

Liabilities ($):
Due to The Dreyfus Corporation and affiliates—Note 2(a)			952,768
Payable for shares of Common Stock redeemed			4,072
Accrued expenses			65,575
			1,022,415

Net Assets (	$)		1,363,687,960

Composition of Net Assets ($):
Paid-in capital			1,363,796,463
Accumulated net realized gain (loss) on investments			(108,503)

Net Assets (	$)		1,363,687,960



Net Asset Value Per Share
		Class A	Class B

Net Assets ($)		516,722,565	846,965,395
Shares Outstanding		516,823,872	846,972,591

Net Asset Value Per Share ($)		1.00	1.00

See notes to financial statements.

STATEMENT OF OPERATIONS
Six Months Ended May 31, 2004 (Unaudited)







Investment Income ($):
Interest Income	8,378,309
Expenses:
Management fee—Note 2(a)	3,773,181
Shareholder servicing costs—Note 2(c)	1,654,217
Distribution, service and prospectus fees—Note 2(b)	1,521,650
Registration fees	68,521
Custodian fees	51,188
Professional fees	20,323
Directors’ fees and expenses—Note 2(d)	18,535
Shareholders’ reports	9,742
Miscellaneous	17,689
Total Expenses	7,135,046
Less—reduction in shareholder servicing costs
due to undertaking—Note 2(c)	(345,784)
Net Expenses	6,789,262
Investment Income—Net	1,589,047

Realized and Unrealized Gain (Loss) on Investments—Note 1(b) ($)	(20,639)
Net Increase in Net Assets Resulting from Operations	1,568,408

See notes to financial statements.

The Fund

STATEMENT OF CHANGES IN NET ASSETS

	Six Months Ended
	May 31, 2004	Year Ended
	(Unaudited)	November 30, 2003

Operations ($):
Investment income-net	1,589,047	6,313,026
Net realized gain (loss) on investments	(20,639)	(13,107)
Net Increase (Decrease) in Net Assets
Resulting from Operations	1,568,408	6,299,919

Dividends to Shareholders from ($):
Investment income-net:
Class A shares	(861,974)	(3,236,754)
Class B shares	(727,073)	(3,076,272)
Total Dividends	(1,589,047)	(6,313,026)

Capital Stock Transactions ($1.00 per share):
Net proceeds from shares sold:
Class A shares	2,525,623,986	4,700,029,832
Class B shares	1,363,361,725	2,477,298,303
Dividends reinvested:
Class A shares	854,492	3,173,385
Class B shares	633,087	2,641,589
Cost of shares redeemed:
Class A shares	(2,575,607,033)	(4,799,318,073)
Class B shares	(1,450,055,145)	(2,561,173,141)
Increase (Decrease) in Net Assets from
Capital Stock Transactions	(135,188,888)	(177,348,105)
Total Increase (Decrease) in Net Assets	(135,209,527)	(177,361,212)

Net Assets ($):
Beginning of Period	1,498,897,487	1,676,258,699
End of Period	1,363,687,960	1,498,897,487

See notes to financial statements.

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, 2004		Year Ended November 30,

Class A Shares	(Unaudited)	2003	2002	2001	2000	1999

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	.002	.005	.014	.040	.054	.043
Distributions:
Dividends from investment
income—net	(.002)	(.005)	(.014)	(.040)	(.054)	(.043)
Net asset value, end of period	1.00	1.00	1.00	1.00	1.00	1.00

Total Return (%)	.32^a	.52	1.38	4.05	5.54	4.42

Ratios/Supplemental Data (%):
Ratio of expenses to
average net assets	.79^a	.77	.77	.77	.76	.76
Ratio of net investment income
to average net assets	.32^a	.52	1.38	3.85	5.40	4.35

Net Assets, end of period
($ X 1,000)	516,723	565,857	661,976	804,956	574,630	610,511

a Annualized.

See notes to financial statements.

The Fund

FINANCIAL HIGHLIGHTS (continued)

	Six Months	Ended
	May 31, 2004			Year Ended November 30,

Class B Shares	(Unaudited)		2003	2002	2001	2000	1999

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		.001	.003	.011	.037	.052	.041
Distributions:
Dividends from investment
income—net		(.001)	(.003)	(.011)	(.037)	(.052)	(.041)
Net asset value, end of period		1.00	1.00	1.00	1.00	1.00	1.00

Total Return (%)		.16^a	.29	1.14	3.81	5.29	4.17

Ratios/Supplemental Data (%):
Ratio of expenses to
average net assets		.96^a	1.00	1.00	1.00	1.00	1.00
Ratio of net investment income
to average net assets		.15^a	.29	1.13	3.60	5.15	4.09
Decrease reflected in above
expense ratios due to
undertakings by
The Dreyfus Corporation		.07^a	.03	.03	.04	.03	.03

Net Assets, end of period
($ X 1,000)	846,965		933,041	1,014,283	826,720	552,238	659,185

a Annualized.

See notes to financial statements.

NOTES TO FINANCIAL STATEMENTS (Unaudited)

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”) serves as the fund’s investment adviser.The Manager is a wholly-owned subsidiary of Mellon Financial Corporation (“Mellon Financial”).

Dreyfus Service 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 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, 2004, sub-accounting service fees amounted to $241,690 for Class B shares and are included in the shareholder servicing cost. 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

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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 fund’s Board of Directors to represent the fair value of the fund’s investments.

(b) Securities transactions and investment income: Securities transactions are recorded on a trade date basis. Interest income, adjusted for amortization of discount and premium on investment, is earned from settlement date and recognized on the accrual basis. Realized gain and loss from securities transactions are recorded on the identified cost basis. Cost of investments represents amortized cost. Under the terms of the custody agreement, the fund received net earnings credits of $4,023 during the period ended May 31, 2004, based on available cash balances left on deposit. Income earned under this arrangement is included in interest income.

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

(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.

The fund has an unused capital loss carryover of $93,109 available for federal income tax purposes to be applied against future net securities profits, if any, realized subsequent to November 30, 2003. If not

The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

applied, $21,009 of the carryover expires in fiscal 2005, $17,123 expires in fiscal 2007, $41,869 expires in fiscal 2008 and $13,108 expires in fiscal 2011.

The tax character of distributions paid to shareholders during the fiscal year ended November 30, 2003 was all ordinary income.The tax character of current year distributions will be determined at the end of the current fiscal year.

At May 31,2004,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 1% 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, 2004, there was no expense reimbursement pursuant to the Agreement.

The components of Due to The Dreyfus Corporation and affiliates in the Statement of Assets and Liabilities consists of: management fees $560,804, Rule 12b-1 distribution fees $224,487, shareholder services plan fees $206,287 and transfer agency per account fees $12,630, which are offset against an expense reimbursement currently in effect in the amount of $51,440.

(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 costs of preparing, printing and distributing prospectuses and statements of additional information and implementing and oper-

ating the Plan, such aggregate amount not to exceed in any fiscal year of the fund the greater of $100,000 or .005 of 1% 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 1% 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 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, 2004, Class A shares were charged $547,132 pursuant to the Plan.

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 1% 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 1% of the value of the average daily net assets of Class B. During the period ended May 31, 2004, Class B shares were charged $974,518 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 1% of

The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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 1% 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, 2003 through May 31, 2004, to reduce the expenses of Class B shares to the extent that, 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. In addition, the Manager may at times, limit certain money market fund expenses in an effort to enhance yields of a fund, or a particular class of a fund, as applicable, because of low interest rates. The Manager limited fund expenses on the fund (Class B) to maintain a minimum yield of 15 basis points. Such expense limitations are voluntary, temporary and may be revised or terminated at anytime. During the period ended May 31,2004,Class B shares were charged,$1,208,448 pursuant to the Class B Shareholder Services Plan, of which $345,784 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, 2004, the fund was charged $27,002 pursuant to the transfer agency agreement.

(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—Legal Matters:

Two class actions (which have been consolidated) have been filed against Mellon Financial and Mellon Bank, N.A., and Dreyfus and Founders Asset Management LLC (the “Investment Advisers”), and the directors of all or substantially all of the Dreyfus funds, alleging that the Investment Advisers improperly used assets of the Dreyfus funds, in the form of directed brokerage commissions and 12b-1 fees, to pay brokers to promote sales of Dreyfus funds,and that the use of fund assets to make these payments was not properly disclosed to investors.The complaints further allege that the directors breached their fiduciary duties to fund shareholders under the Investment Company Act of 1940 and at common law. The complaints seek unspecified compensatory and punitive damages, rescission of the funds’ contracts with the Investment Advisers, an accounting of all fees paid, and an award of attorneys’ fees and litigation expenses. Dreyfus and the Dreyfus funds believe the allegations to be totally without merit and will defend the actions vigorously.

Additional lawsuits arising out of these circumstances and presenting similar allegations and requests for relief may be filed against the defendants in the future. Neither Dreyfus nor the Dreyfus funds believe that any of the pending actions will have a material adverse effect on the Dreyfus funds or Dreyfus’ ability to perform its contracts with the Dreyfus funds.

The Fund

NOTES

For More Information

General Government Securities

Money Market Fund

200 Park Avenue

New York, NY 10166

Manager

The Dreyfus Corporation

200 Park Avenue

New York, NY 10166

Custodian

The Bank of New York

One Wall Street

New York, NY 10286

Transfer Agent &

Dividend Disbursing Agent

Dreyfus Transfer, Inc.

200 Park Avenue

New York, NY 10166

Distributor

Dreyfus Service Corporation

200 Park Avenue

New York, NY 10166

To obtain information:

By telephone

Call 1-800-645-6561

By mail Write to:

The Dreyfus Family of Funds

144 Glenn Curtiss Boulevard

Uniondale, NY 11556-0144

By E-mail Send your request

to info@dreyfus.com

On the Internet Information

can be viewed online or

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0975SA0504

General

Treasury Prime

Money Market Fund

SEMIANNUAL REPORT May 31, 2004

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

Contents

THE FUND

2	Letter from the Chairman
3	Discussion of Fund Performance
6	Statement of Investments
7	Statement of Assets and Liabilities
8	Statement of Operations
9	Statement of Changes in Net Assets
10	Financial Highlights
13	Notes to Financial Statements
FOR MORE INFORMATION
Back Cover

General Treasury Prime

Money Market Fund

The Fund

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This semiannual report for General Treasury Prime Money Market Fund covers the six-month period from December 1, 2003, through May 31, 2004. Inside, you’ll find valuable information about how the fund was managed during the reporting period, including a discussion with the fund’s portfolio manager, Bernard W. Kiernan, Jr.

Positive economic data continued to accumulate during the reporting period, as consumers, flush with extra cash from their 2003 federal tax refunds and mortgage refinancings,continued to spend.At the same time, corporations have become more willing to hire new workers and invest in new projects and equipment.As a result, yields of longer-dated money market securities began to rise in the spring of 2004, as investors increas ingly anticipated that the Federal Reserve Board might soon begin raising rates in an attempt to forestall potential inflationary pressures.

No matter where interest rates go from here, however, we continue to believe that the objectives of liquidity and stability make money market funds a valuable component of many investors’ portfolios Indeed, despite recently encouraging economic news, concerns regarding the war on terrorism, instability in Iraq and higher energy prices have caused heightened volatility in the stock and bond markets As always, we encourage you to speak regularly with your financial advisor, who may be in the best position to suggest ways to position your portfolio for the opportunities and challenges of today’s financial markets

Thank you for your continued confidence and support.

Sincerely,

Stephen E. Canter

Chairman and Chief Executive Officer

The Dreyfus Corporation

June 15, 2004

DISCUSSION OF FUND PERFORMANCE

Bernard W. Kiernan, Jr., Portfolio Manager

How did General Treasury Prime Money Market Fund perform during the period?

Over the six-month period ended May 31, 2004, the fund produced annualized yields of 0.24% for Class A shares, 0.15% for Class B shares and 0.15% for Class X shares.Taking into account the effects of compounding, the fund also produced annualized effective yields of 0.24% for Class A shares, 0.15% for Class B shares and 0.15% for Class X shares for the same period.¹

What is 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.

What other factors influenced the fund’s performance?

The Fund

DISCUSSION OF FUND PERFORMANCE (continued)

As was widely expected, the Federal Reserve Board (the “Fed”) held the overnight federal funds rate steady at 1% during its meeting in early December, and reiterated its commitment to keeping borrowing rates low. By the end of 2003, new data further confirmed that an economic recovery was well underway, while a drop in the consumer price index (“CPI”) suggested that inflation remained under control. The U.S. Commerce Department later estimated that the GDP grew at a 4.1% annualized rate during the fourth quarter of 2003.

from the belief that interest rates were unlikely to rise in 2004 to anticipation that the Fed might begin to tighten monetary policy by 25 to 50 basis points as early as June.

What is the fund’s current strategy?

In light of expectations of higher short-term interest rates, we have adopted a more defensive posture, allowing the fund’s weighted average maturity to fall toward a range we consider neutral. Accordingly, we generally have limited new investments to U.S. Treasury securities with maturities of three months or less. This strategy is designed to give us flexibility to take advantage of higher yields should they arise. Of course, we are prepared to adjust our strategy as market conditions evolve.

June 15, 2004

1 Annualized effective yield is based upon dividends declared daily and reinvested monthly. Past performance is no guarantee of future results.Yields fluctuate.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.Yields provided for the fund’s Class B and Class X shares reflect the absorption of 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 a yield of 0.18% and an effective yield of 0.18%, and the fund’s Class X shares would have produced a yield of –0.12% and an effective yield of –0.12%.

The Fund

STATEMENT OF INVESTMENTS
May 31, 2004 (Unaudited)





			Annualized
			Yield on
			Date of	Principal
U.S. Treasury Bills—61.8%			Purchase (%)	Amount ($)	Value ($)

6/10/2004			.84	1,262,000	1,261,734
6/17/2004			.88	461,000	460,820
6/24/2004			.90	521,000	520,700
7/15/2004			.94	10,000,000	9,988,572
8/26/2004			.99	4,000,000	3,990,540
10/14/2004			1.05	5,000,000	4,980,500
Total U.S. Treasury Bills
(cost $	21,202,866)				21,202,866


U.S. Treasury Notes—41.1%

2.875%, 6/30/2004			.94	5,000,000	5,007,616
6%, 8/15/2004			1.25	9,000,000	9,088,370
Total U.S. Treasury Notes
(cost $	14,095,986)				14,095,986


Total Investments (cost $		35,298,852)		102.9%	35,298,852
Liabilities, Less Cash and Receivables				(2.9%)	(993,817)
Net Assets				100.0%	34,305,035

See notes to financial statements.

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2004 (Unaudited)





			Cost	Value

Assets ($):
Investments in securities—See Statement of Investments			35,298,852	35,298,852
Interest receivable				217,052
Prepaid expenses				689
				35,516,593

Liabilities ($):
Due to The Dreyfus Corporation and affiliates—Note 2(a)				25,023
Payable for shares of common stock redeemed				73
Cash overdraft due to custodian				1,163,845
Accrued expenses				22,617
				1,211,558

Net Assets (	$)			34,305,035

Composition of Net Assets ($):
Paid-in capital				34,304,533
Accumulated net realized gain (loss) on investments				502

Net Assets (	$)			34,305,035



Net Asset Value Per Share
		Class A	Class B	Class X

Net Assets ($)		6,273,138	28,019,397	12,500
Shares Outstanding		6,272,692	28,019,341	12,500

Net Asset Value Per Share ($)		1.00	1.00	1.00

See notes to financial statements.

The Fund

STATEMENT OF OPERATIONS
Six Months Ended May 31, 2004 (Unaudited)







Investment Income ($):
Interest Income	218,641
Expenses:
Management fee—Note 2(a)	107,262
Shareholder servicing costs—Note 2(c)	53,029
Distribution, service and prospectus fees—Note 2(b)	44,256
Professional fees	12,200
Custodian fees	4,289
Shareholders’ reports	2,969
Directors’ fees and expenses—Note 2(d)	829
Registration fees	350
Miscellaneous	3,011
Total Expenses	228,195
Less—reduction in service plan fees and shareholder
servicing costs due to undertaking—Note 2(b,c)	(45,820)
Net Expenses	182,375
Investment Income—Net	36,266

Net Realized Gain (Loss) on Investments—Note 1(b) ($)	1,155
Net Increase in Net Assets Resulting from Operations	37,421

See notes to financial statements.

STATEMENT OF CHANGES IN NET ASSETS

		Six Months Ended
		May 31, 2004	Year Ended
		(Unaudited)	November 30, 2003

Operations ($):
Investment income—net		36,266	180,155
Net realized gain (loss) on investments		1,155	(589)
Net Increase (Decrease) in Net Assets
Resulting from Operations		37,421	179,566

Dividends to Shareholders from ($):
Investment income—net:
Class A shares		(12,522)	(103,233)
Class B shares		(23,735)	(76,896)
Class X shares		(9)	(26)
Total Dividends		(36,266)	(180,155)

Capital Stock Transactions	(1.00 per share):
Net proceeds from shares sold:
Class A shares		15,709,109	48,879,828
Class B shares		70,013,593	154,799,623
Dividends reinvested:
Class A shares		11,894	101,992
Class B shares		23,708	76,896
Cost of shares redeemed:
Class A shares		(35,762,852)	(53,095,000)
Class B shares		(72,555,399)	(147,217,919)
Increase (Decrease) in Net Assets
from Capital Stock Transactions		(22,559,947)	3,545,420
Total Increase (Decrease) in Net Assets		(22,558,792)	3,544,831

Net Assets ($):
Beginning of Period		56,863,827	53,318,996
End of Period		34,305,035	56,863,827

See notes to financial statements.

The Fund

FINANCIAL HIGHLIGHTS

	Six Months Ended
	May 31, 2004	Year Ended November 30,

Class A Shares	(Unaudited)	2003	2002	2001	2000^a

Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.001	.004	.011	.034	.051
Distributions:
Dividends from investment income—net	(.001)	(.004)	(.011)	(.034)	(.051)
Net asset value, end of period	1.00	1.00	1.00	1.00	1.00

Total Return (%)	.24^b	.39	1.07	3.49	5.21

Ratios/Supplemental Data (%):
Ratio of expenses to average net assets	.80^b	.80	.78	.80	.80
Ratio of net investment income
to average net assets	.22^b	.38	1.13	3.25	5.49
Decrease reflected in above
expense ratios due to undertaking
by The Dreyfus Corporation	.06^b	.05	.00^c	.08	.43

Net Assets, end of period ($ X 1,000)	6,273	26,315	30,428	66,694	20,179

a From December 1, 1999 (commencement of operations) to November 30, 2000.

b	Annualized.
c	Amount represents less than .01%.

See notes to financial statements.

	Six Months Ended
	May 31, 2004	Year Ended November 30,

Class B Shares	(Unaudited)	2003	2002	2001	2000^a

Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.001	.002	.009	.032	.049
Distributions:
Dividends from investment income—net	(.001)	(.002)	(.009)	(.032)	(.049)
Net asset value, end of period	1.00	1.00	1.00	1.00	1.00

Total Return (%)	.16^b	.24	.86	3.27	5.00

Ratios/Supplemental Data (%):
Ratio of expenses to average net assets	.87^b	.94	1.00	1.00	1.00
Ratio of net investment income
to average net assets	.15^b	.24	.84	2.94	5.14
Decrease reflected in above
expense ratios due to undertaking
by The Dreyfus Corporation	.27^b	.18	.08	.13	4.97

Net Assets, end of period ($ X 1,000)	28,019	30,537	22,878	11,987	5,385

a From December 1, 1999 (commencement of operations) to November 30, 2000.

b Annualized.

See notes to financial statements.

The Fund

FINANCIAL HIGHLIGHTS (continued)

	Six Months Ended
	May 31, 2004	Year Ended November 30,

Class X Shares	(Unaudited)	2003	2002	2001	2000^a

Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.001	.002	.008	.032	.048
Distributions:
Dividends from investment income—net	(.001)	(.002)	(.008)	(.032)	(.048)
Net asset value, end of period	1.00	1.00	1.00	1.00	1.00

Total Return (%)	.15^b	.21	.82	3.22	4.94

Ratios/Supplemental Data (%):
Ratio of expenses to average net assets	.87^b	.96	1.05	1.05	1.05
Ratio of net investment income
to average net assets	.15^b	.21	.74	3.03	4.55
Decrease reflected in above
expense ratios due to undertaking
by The Dreyfus Corporation	.43^b	.33	.42	3.24	20.13

Net Assets, end of period ($ X 1,000)	13	12	12	1	1

a From December 1, 1999 (commencement of operations) to November 30, 2000.

b Annualized.

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”) serves as the fund’s investment adviser.The Manager is a wholly-owned subsidiary of Mellon Financial Corporation (“Mellon Financial”).

Dreyfus Service 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 three classes of shares: Class A (1 billion shares authorized), Class B (1 billion shares authorized) and Class X (1 billion shares authorized). Class A, Class B and Class X shares are identical except for the services offered to and the expenses borne by each class and certain voting rights. Class A shares are subject to a Service Plan adopted pursuant to Rule 12b-1 under the Act, Class B and Class X shares are subject to a Distribution Plan adopted pursuant to Rule 12b-1 under the Act and Class A, Class B and Class X shares are subject to 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, 2004, sub-accounting service fees amounted to $7,884 for Class B shares and are included in the shareholder servicing cost.

The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

Investment, expenses (other than expenses attributable to a specific class), and realized and unrealized gains and losses on investments are allocated to each class of shares based on its relative assets.

(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 fund’s Board of Directors to represent the fair value of the fund’s investments.

identified cost basis. Cost of investments represents amortized cost. Under the terms of the custody agreement, the fund receives net earnings credits based on available cash balances left on deposit and includes such credits in interest income.

The fund has an unused capital loss carryover of $653 available for federal income tax purposes to be applied against future net securities profits, if any, realized subsequent to November 30, 2003. If not applied, $64 of the carryover expires in fiscal 2009 and $589 expires in fiscal 2011.

At May 31,2004,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).

The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

NOTE 2—Management Fee and Other Transactions with Affiliates:

The components of Due to The Dreyfus Corporation and affiliates in the Statement of Assets and Liabilities consists of: management fees $15,786, Rule 12b-1 distribution plan fees $6,325, shareholder services plan fees $9,577 and transfer agency per account fees $428, which are offset against an expense reimbursement currently in effect in the amount of $7,093.

(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 1% 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 1% 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, 2004, Class A shares were charged $11,700 pursuant to the Plan, of which $3,447 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 1% 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 1% of the value of the average daily net assets of Class B. During the period ended May 31, 2004, Class B shares were charged $32,540 pursuant to the Class B Distribution Plan, of which $2,722 was reimbursed by the Manager, due to undertaking. See Note 2(c).

Under the Distribution Plan with respect to Class X (“Class X Distribution Plan”) adopted pursuant to Rule 12b-1 under the Act, Class X shares pay the Distributor for distributing Class X shares at an annual rate of .25 of 1% of the value of the average daily net assets of Class X. During the period ended May 31, 2004, Class X shares were charged $16 pursuant to the Class X Distribution Plan, of which $11 was reimbursed by the Manager.

The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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 has undertaken from December 1, 2003 through May 31, 2004, that if the aggregate expenses of Class A shares, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed .80 of 1% of the value of the average daily net assets of Class A, the Manager would reimburse the expenses of the fund under the Class A Shareholder Services Plan, to the extent of any excess expense and up to the full fee payable under the Class A Shareholder Services Plan. During the period ended May 31, 2004, Class A shares were charged $99 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 and Class X (“Shareholder Services Plan”), Class B and Class X shares pay the Distributor at an annual rate of .25 of 1% of the value of the average daily net assets of Class B and Class X shares for servicing shareholder accounts.The services provided may include personal services relating to shareholder accounts, such as answering shareholder inquiries regarding Class B and Class X 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, 2003 through May 31, 2004, to reduce the expenses of Class B shares to the extent that, 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%.The Manager had undertaken from December 1, 2003 through May 31, 2004, to reduce the expenses of Class X shares to the extent that, if the aggregate expenses of Class X shares, exclusive of taxes, brokerage fees, interest on borrowings and extraordinary expenses, exceed an annual rate of 1.05%, of the value of the average daily net assets of Class X shares. In addition, the Manager may, at times, limit certain money market fund expenses in an effort to enhance yields of a fund, or a particular class of a fund, as applicable, because of low interest rates. The Manager limited fund expenses on the fund (Class B and Class X) to maintain a minimum yield of 15 basis points. Such expense limitations are voluntary, temporary and may be revised or terminated at any time. During the period ended May 31, 2004, Class B and Class X shares were charged $39,525 and $16, respectively, pursuant to the Shareholder Services Plan, all of which were 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, 2004, the fund was charged $1,178 pursuant to the transfer agency agreement.

(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—Legal Matters:

The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

form of directed brokerage commissions and 12b-1 fees, to pay brokers to promote sales of Dreyfus funds,and that the use of fund assets to make these payments was not properly disclosed to investors.The complaints further allege that the directors breached their fiduciary duties to fund shareholders under the Investment Company Act of 1940 and at common law. The complaints seek unspecified compensatory and punitive damages, rescission of the funds’ contracts with the Investment Advisers, an accounting of all fees paid, and an award of attorneys’ fees and litigation expenses. Dreyfus and the Dreyfus funds believe the allegations to be totally without merit and will defend the actions vigorously.

For More Information

General Treasury

Prime Money Market Fund

200 Park Avenue

New York, NY 10166

Manager

The Dreyfus Corporation

200 Park Avenue

New York, NY 10166

Custodian

The Bank of New York

One Wall Street

New York, NY 10286

Transfer Agent &

Dividend Disbursing Agent

Dreyfus Transfer, Inc.

200 Park Avenue

New York, NY 10166

Distributor

Dreyfus Service Corporation

200 Park Avenue

New York, NY 10166

To obtain information:

By telephone

Call 1-800-645-6561

By mail Write to:

The Dreyfus Family of Funds

144 Glenn Curtiss Boulevard

Uniondale, NY 11556-0144

By E-mail Send your request

to info@dreyfus.com

On the Internet Information

can be viewed online or

downloaded from:

http://www.dreyfus.com

0387SA0504

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.	[Reserved]

Item 7.	Disclosure of Proxy Voting Policies and Procedures for Closed-End Management
	Investment Companies.
	Not applicable.

Item 8.	Purchases of Equity Securities by Closed-End Management Investment Companies
	and Affiliated Purchasers.
	Not applicable.

Item 9.	Submission of Matters to a Vote of Security Holders.
	Not applicable.

Item 10.	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 Registrant's most recently ended fiscal half-year that have materially affected, or are reasonably likely to materially affect, the Registrant's internal control over financial reporting.

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SSL-DOCS2 70134233v1

Item 11. 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.

-3-

SSL-DOCS2 70134233v1

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/ Stephen E. Canter

	Stephen E. Canter
	President

Date:	July 28, 2004

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:
	Stephen E. Canter
	Chief Executive Officer

Date:	July 28, 2004

By:	/s/ James Windels

	James Windels
	Chief Financial Officer

Date:	July 28, 2004

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)

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SSL-DOCS2 70134233v1

General Government Securities Money Market Funds N-CSRCertified annual shareholder report (management investment company)