General Money Market Fund N-CSR Certified annual shareholder report (management investment company)

	UNITED STATES
	SECURITIES AND EXCHANGE COMMISSION
	Washington, D.C. 20549
	FORM N-CSR
CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT
	INVESTMENT COMPANIES
Investment Company Act file number 811-3207
	GENERAL MONEY MARKET FUND, 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 Money

Market Fund, Inc.

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
9	Statement of Assets and Liabilities
10	Statement of Operations
11	Statement of Changes in Net Assets
12	Financial Highlights
15	Notes to Financial Statements
FOR MORE INFORMATION
Back Cover

   General Money

Market Fund, Inc.

The Fund

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This semiannual report for General Money Market Fund, Inc. 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

2

DISCUSSION OF FUND PERFORMANCE

Bernard W. Kiernan, Jr., Portfolio Manager

How did General Money Market Fund, Inc. perform during the period?

Over the six-month period ended May 31, 2004, the fund produced annualized yields of 0.37% 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 0.37% 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. To pursue this goal, the fund invests in a diversified portfolio of high-quality, short-term debt securities.These include securities issued or guaranteed by the U.S. government or its agencies or instrumentalities, certificates of deposit, short-term securities issued by domestic or foreign banks, repurchase agreements, asset-backed securities, domestic and dollar-denominated foreign commercial paper and dollar-denominated obligations issued or guaranteed by foreign governments. Normally, the fund invests at least 25% of its net assets in domestic or dollar-denominated foreign bank obligations.

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.

The Fund

3

DISCUSSION OF FUND PERFORMANCE (continued)

Economic indicators in the fall 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.

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. It was later revealed that U.S. economic growth rose only modestly, expanding at a 4.4% annualized rate during the first quarter of 2004.

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.

4

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 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 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 money market instruments 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 0.12% and an effective yield of 0.12%, and the fund’s Class X shares would have produced a yield of –0.02% and an effective yield of –0.02%.

The Fund

5

STATEMENT OF INVESTMENTS
May 31, 2004 (Unaudited)
	Principal
Negotiable Bank Certificates of Deposit—49.2%	Amount ($)		Value ($)
Alliance & Leicester PLC (London)
1.13%, 12/22/2004	125,000,000		125,000,000
Alliance & Leicester PLC (Yankee)
1.15%, 6/17/2004	150,000,000		150,000,000
Banco Bilbao Vizcaya Argentaria (Yankee)
1.20%, 8/20/2004	100,000,000		100,000,000
Chase Manhattan Bank USA (Yankee)
1.05%, 11/8/2004	233,000,000	a	233,000,000
Credit Agricole Indosuez S.A. (Yankee)
1.07%, 4/26/2005	250,000,000	a	249,954,616
Credit Lyonnais N.A. (Yankee)
1.06%, 10/14/2004	60,000,000	a	59,997,216
DnB NOR Bank ASA (London)
1.15%, 7/8/2004	40,000,000		40,000,204
First Tennessee Bank N.A.
1.04%, 6/10/2004	200,000,000		200,000,000
HBOS Treasury Services PLC (London)
1.13%, 7/23/2004	100,000,000		100,001,436
HSBC Bank USA
1.56%, 4/22/2005	150,000,000		150,000,000
Landesbank Hessen-Thueringen Girozentrale (London)
1.20%-1.26%, 10/6/2004-12/30/2004	325,000,000		325,037,977
Norddeutsche Landesbank Girozentrale (London)
1.47%, 5/6/2005	200,000,000		200,009,268
Norddeutsche Landesbank Girozentrale (Yankee)
1.20%, 8/27/2004	100,000,000		99,997,615
Royal Bank Of Scotland PLC (London)
1.05%-1.10%, 7/16/2004-8/9/2004	200,000,000		200,000,623
Societe Generale N.A. Inc (Yankee)
1.04%, 6/17/2004	200,000,000		200,000,000
UniCredito Italiano SpA (Yankee)
1.09%, 7/23/2004	300,000,000		300,002,160
WestLB AG (Yankee)
1.15%, 6/15/2004	125,000,000		125,000,000
Wilmington Trust Co.
1.15%-1.16%, 6/16/2004-7/7/2004	175,000,000		175,000,000
Total Negotiable Bank Certificates of Deposit
(cost $3,033,001,115)			3,033,001,115

6

		Principal
Commercial Paper—15.0%		Amount ($)		Value ($)
Alliance & Leicester PLC
1.16%, 6/10/2004		50,000,000		49,985,625
Amstel Funding Corp.
1.31%, 9/14/2004-9/17/2004		174,217,000	b	173,547,019
General Electric Capital Corp.
1.10%, 10/5/2004		200,000,000		199,237,000
General Electric Capital Services Inc.
1.03%, 6/7/2004-6/8/2004		300,000,000		299,944,208
UBS Finance Delaware LLC
1.02%, 6/1/2004		200,000,000		200,000,000
Total Commercial Paper
(cost $	922,713,852)			922,713,852
Corporate Notes—12.5%
Paradigm Funding LLC
1.06%, 8/20/2004		210,000,000	a,b	210,000,800
Sigma Finance Inc.
1.07%-1.08%, 1/27/2005-3/22/2005		262,000,000	a,b	261,982,810
Swedbank
1.05%, 10/1/2004		300,000,000	a	299,971,718
Total Corporate Notes
(cost $	771,955,328)			771,955,328
Promissory Notes—3.3%
Goldman Sachs Group Inc.
1.36%-1.53%, 11/8/2004-12/16/2004
(cost $	200,000,000)	200,000,000	c	200,000,000
Short-Term Bank Notes—8.9%
BNP Paribas
1.06%, 6/16/2004		250,000,000	a	249,997,934
Bank of America N.A.
1.05%, 3/15/2005		150,000,000	a	150,000,000
WestLB AG
1.07%, 6/7/2004		150,000,000	a	149,999,504
Total Short Term Bank Notes
(cost $	549,997,438)			549,997,438

The Fund

7

S T A T E M E N T O F I N V E S T M E N T S ( U n a u d i t e d ) (continued)

			Principal
U.S. Government Agencies—10.6%			Amount ($)	Value ($)
Federal Home Loan Banks, Floating Rate Notes
1.06%, 8/4/2005			200,000,000	199,882,042
Federal Home Loan Banks, Notes
1.34%-1.42%, 3/11/2005-4/29/2005			250,000,000	250,000,000
Federal Home Loan Mortgage Corp., Notes
1.50%, 12/24/2004			200,000,000	200,000,000
Total U.S. Government Agencies
(cost $	649,882,042)			649,882,042
Time Deposits—.6%
KBC Bank N.V. (Grand Cayman)
1.02%, 6/1/2004
(cost $	40,000,000)		40,000,000	40,000,000
Total Investments (cost $		6,167,549,775)	100.1%	6,167,549,775
Liabilities, Less Cash and Receivables			(.1%)	(8,222,459)
Net Assets			100.0%	6,159,327,316

a Variable interest rate—subject to periodic change.

b	Securities exempt from registration under Rule 144A of the Securities Act of 1933.These securities may be resold in transactions exempt from registration, normally to qualified institutional buyers.At May 31, 2004, these securities amounted to $645,530,629 or 10.5% of net assets.
c	These notes were acquired for investment, and not with the intent to distribute or sell. Securities restricted as to public resale. These securities were acquired from 1/21/2004 to 5/11/2004 at a cost of $200,000,000.At May 31, 2004, the aggregate value of these securities was $200,000,000, representing 3.3% of net assets and are valued at amortized cost.

See notes to financial statements.

8

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2004 (Unaudited)
			Cost	Value
Assets ($):
Investments in securities—See Statement of Investments			6,167,549,775	6,167,549,775
Cash				4,897,329
Interest receivable				13,789,684
Prepaid expenses				380,960
				6,186,617,748
Liabilities ($):
Due to The Dreyfus Corporation and affiliates—Note 2(a)				5,084,970
Payable for investment securities purchased				22,014,213
Payable for shares of Common Stock redeemed				27,519
Accrued expenses				163,730
				27,290,432
Net Assets (	$)			6,159,327,316
Composition of Net Assets ($):
Paid-in capital				6,159,341,432
Accumulated net realized gain (loss) on investments				(14,116)
Net Assets (	$)			6,159,327,316
Net Asset Value Per Share
		Class A	Class B	Class X
Net Assets ($)		1,126,699,096	5,032,530,499	97,721
Shares Outstanding		1,126,737,702	5,032,506,004	97,726
Net Asset Value Per Share ($)		1.00	1.00	1.00
See notes to financial statements.

The Fund

9

STATEMENT OF OPERATIONS
Six Months Ended May 31, 2004 (Unaudited)
Investment Income ($):
Interest Income	39,493,417
Expenses:
Management fee—Note 2(a)	17,205,671
Shareholder servicing costs—Note 2(c)	9,049,891
Distribution, service and prospectus fees—Note 2(b)	6,950,285
Registration fees	181,622
Custodian fees	125,596
Directors' fees and expenses—Note 2(d)	78,344
Shareholders' reports	24,894
Professional fees	21,558
Miscellaneous	66,729
Total Expenses	33,704,590
Less—reduction in shareholder servicing costs
due to undertaking—Note 2(c)	(740,937)
Net Expenses	32,963,653
Investment Income—Net	6,529,764
Net Realized Gain (Loss) on Investments—Note 1(b) ($)	41
Net Increase in Net Assets Resulting from Operations	6,529,805
See notes to financial statements.

10

STATEMENT OF CHANGES IN NET ASSETS

	Six Months Ended
	May 31, 2004	Year Ended
	(Unaudited)	November 30, 2003
Operations ($):
Investment income—net	6,529,764	27,689,737
Net realized gain (loss) on investments	41	(10,418)
Net Increase (Decrease) in Net Assets
Resulting from Operations	6,529,805	27,679,319
Dividends to Shareholders from ($):
Investment income—net:
Class A Shares	(2,244,119)	(8,018,360)
Class B Shares	(4,285,559)	(19,670,906)
Class X Shares	(86)	(471)
Total Dividends	(6,529,764)	(27,689,737)
Capital Stock Transactions ($1.00 per share):
Net proceeds from shares sold:
Class A Shares	4,107,585,343	7,231,363,649
Class B Shares	7,652,131,458	14,956,398,812
Class X Shares	-	78,645
Dividends reinvested:
Class A Shares	2,212,179	7,901,889
Class B Shares	3,991,000	18,419,010
Class X Shares	25	246
Cost of shares redeemed:
Class A Shares	(4,261,054,140)	(7,517,672,820)
Class B Shares	(8,257,248,811)	(14,800,138,189)
Class X Shares	(30,000)	(110,443)
Increase (Decrease) in Net Assets from
Capital Stock Transactions	(752,412,946)	(103,759,201)
Total Increase (Decrease) in Net Assets	(752,412,905)	(103,769,619)
Net Assets ($):
Beginning of Period	6,911,740,221	7,015,509,840
End of Period	6,159,327,316	6,911,740,221
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, 2004		Year Ended November 30,
Class A Shares	(Unaudited)	2003	2002	2001	2000	1999
Per Share Data ($):
Net asset value,
beginning of period	1.00	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net	.002	.006	.014	.041	.056	.044
Distributions:
Dividends from
investment income—net	(.002)	(.006)	(.014)	(.041)	(.056)	(.044)
Net asset value,
end of period	1.00	1.00	1.00	1.00	1.00	1.00
Total Return (%)	.36a	.56	1.43	4.21	5.77	4.53
Ratios/
Supplemental Data (%):
Ratio of expenses to
average net assets	.78a	.77	.77	.79	.78	.78
Ratio of net investment
income to average
net assets	.37a	.57	1.42	4.03	5.64	4.44
Net Assets, end of period
($x 1,000)	1,126,699	1,277,956	1,556,365	1,379,758	982,685	863,981

a Annualized.

See notes to financial statements.

12

	Six Months	Ended
	May 31, 2004			Year Ended November 30,
Class B Shares	(Unaudited)		2003	2002	2001	2000	1999
Per Share Data ($):
Net asset value,
beginning of period		1.00	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net		.001	.003	.012	.039	.054	.042
Distributions:
Dividends from
investment income—net		(.001)	(.003)	(.012)	(.039)	(.054)	(.042)
Net asset value,
end of period		1.00	1.00	1.00	1.00	1.00	1.00
Total Return (%)		.16a	.33	1.20	3.98	5.53	4.32
Ratios/
Supplemental Data (%):
Ratio of expenses to
average net assets		1.00a	1.00	1.00	1.00	1.00	1.00
Ratio of net investment
income to average
net assets		.15a	.33	1.19	3.81	5.41	4.24
Decrease reflected in
above expense ratios
due to undertakings by
The Dreyfus Corporation		.03a	.01	.01	.03	.02	.03
Net Assets, end of period
($x 1,000)	5,032,530		5,633,657	5,458,986	4,713,819	3,338,285	3,056,844

a Annualized.

See notes to financial statements.

The Fund

13

FINANCIAL HIGHLIGHTS (continued)

	Six Months	Ended
	May 31, 2004			Year Ended November 30,
Class X Shares	(Unaudited)		2003	2002	2001	2000	1999a
Per Share Data ($):
Net asset value,
beginning of period		1.00	1.00	1.00	1.00	1.00	1.00
Investment Operations:
Investment income—net		.001	.003	.012	.039	.054	.021
Distributions:
Dividends from
investment income—net		(.001)	(.003)	(.012)	(.039)	(.054)	(.021)
Net asset value, end of period		1.00	1.00	1.00	1.00	1.00	1.00
Total Return (%)		.16b	.32	1.16	3.94	5.49	4.33b
Ratios/Supplemental Data (%):
Ratio of expenses to
average net assets		1.00b	1.02	1.05	1.05	1.05	1.05b
Ratio of net investment income
to average net assets		.16b	.34	1.20	4.03	5.43	4.01b
Decrease reflected in
above expense ratios
due to undertakings by
The Dreyfus Corporation		.17b	.10	.14	.13	.06	.25b
Net Assets, end of period
($x 1,000)		98	128	159	291	478	554

a From June 1, 1999 (commencement of initial offering) to November 30, 1999. b Annualized.

See notes to financial statements.

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NOTES TO FINANCIAL STATEMENTS (Unaudited)

NOTE 1—Significant Accounting Policies:

General Money Market Fund, Inc. (the “fund”) is registered under the Investment Company Act of 1940, as amended (the “Act”), as a diversified open-end management investment company.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.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, which are sold to the public without a sales charge.The fund is authorized to issue 25.5 billion shares of $.001 par value Common Stock. The fund currently offers three classes of shares: Class A (15 billion shares authorized), Class B (10 billion shares authorized) and Class X (500 million 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 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 $1,415,607 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.

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

15

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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 investments, is earned from the 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 receives net earnings credits based on available cash balances left on deposit and includes such credits in interest income.

The fund may enter into repurchase agreements with financial institutions deemed to be creditworthy by the 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

16

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 $14,157 available to be applied against future net securities profits, if any, realized subsequent to November 30, 2003. If not applied, $3,739 of the carryover expires in fiscal 2008 and $10,418 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).

The Fund

17

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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 1 ¹ / 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 $2,710,084, Rule 12b-1 distribution fees $1,084,038, shareholder services plan fees $1,342,791,custodian fees $333 and transfer agency per account fees $52,500, which are offset against an expense reimbursement currently in effect in the amount of $104,776.

(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 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

18

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 $1,231,796 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 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 $5,718,351 pursuant to the Class B Distribution Plan.

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 $138 pursuant to the Class X 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 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

The Fund

19

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

inquiries regarding Class A shares and providing reports and other information, and services related to the maintenance of shareholder accounts. During the period ended May 31, 2004, Class A shares were charged $210,824 pursuant to the Class A Shareholder Services Plan.

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 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 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. 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 anytime. During the period ended May 31, 2004, Class B and Class X shares were charged $7,078,034 and $137, respectively, pursuant to the Shareholder Services Plan, of which $740,845 and $92, respectively, were reimbursed by the Manager.

20

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 $204,652 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

21

For More Information

General Money

Market Fund, Inc.

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, New York 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

© 2004 Dreyfus Service Corporation

0196SA0504

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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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.

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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 MONEY MARKET FUND, 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:	/s/ Stephen E. Canter
	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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