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

                         GENEERAL 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:        November 30


Date of reporting period:       May 31, 2003






                                  FORM N-CSR


ITEM 1. REPORTS TO STOCKHOLDERS.

      General Money
      Market Fund, Inc.

      SEMIANNUAL REPORT May 31, 2003


YOU, YOUR ADVISORY AND
DREYFUS
A MELLON FINANCIAL COMPANY(SM)

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

                            10   Statement of Assets and Liabilities

                            11   Statement of Operations

                            12   Statement of Changes in Net Assets

                            13   Financial Highlights

                            16   Notes to Financial Statements

                                 FOR MORE INFORMATION
- ---------------------------------------------------------------------------

                                 Back Cover

                                                                       The Fund

                                                General Money Market Fund, Inc.

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This  semiannual report for General Money Market Fund, Inc. covers the six-month
period from December 1, 2002, through May 31, 2003. 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.

We  have recently seen some signs of stability in the financial markets. Perhaps
most  important,  the  war  in  Iraq  wound down quickly, without disrupting oil
supplies  or  major  incidents of terrorism. While the U.S. economy has remained
weak,  growth  has  been positive overall. Many stock market indices have posted
encouraging gains since the start of 2003, suggesting greater investor optimism,
although  it  is  uncertain  whether such gains will continue. At the same time,
yields  of  U.S.  Treasury  securities  and money market instruments continue to
hover  near  historical  lows, and inflationary pressures have remained subdued

What are the implications for your investments? An accommodative monetary policy
and  a  stimulative fiscal policy suggest that money market yields should remain
relatively  low  for  the foreseeable future, even if the economy begins to gain
strength.  We  currently  see  opportunities for potentially higher returns from
longer-term  assets  in  the  stock  and  bond  markets,  but  selectivity among
individual  securities  should  remain a key factor. However, no one can say for
certain  what  direction the markets will take over time. Your financial advisor
can  help  you  to  ensure  that  your portfolio reflects your investment needs,
long-term goals and attitudes toward risk.

Thank you for your continued confidence and support.

Sincerely,

/s/Stephen E. Canter

Stephen E. Canter
Chairman and Chief Executive Officer
The Dreyfus Corporation
June 16, 2003



DISCUSSION OF FUND PERFORMANCE

Bernard W. Kiernan, Jr., Portfolio Manager

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

During  the  six-month  period  ended May 31, 2003, the fund produced annualized
yields of 0.72% for Class A shares, 0.48% for Class B shares and 0.44% for Class
X  shares.  Taking  into  account  the effects of compounding, the fund produced
annualized  effective  yields  of  0.72%  for  Class A shares, 0.48% for Class B
shares and 0.45% 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 in December 2002, the U.S. economy appeared to
be  gathering  momentum  in  the wake of the Federal Reserve Board's (the "Fed")
November  interest-rate  reduction  of  50 basis points, which drove the federal
funds  rate  down  to just 1.25%. Retail sales came in higher than most analysts
had  expected,  and  the  stock  market  began  to  rally. In addition, consumer
confidence  improved  during  December.  Nonetheless,  the  fourth quarter's GDP
growth rate came in at an estimated annualized rate of just 1.4%.

                                                             The Fund


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

During the first quarter of 2003, the economy sent mixed signals, and hopes of a
more  robust  economic  rebound  faded. Home sales rose in January, but consumer
confidence  fell  to  new  lows.  Manufacturing  expanded in January but fell in
February. For its part, the Fed kept the federal funds rate unchanged at 1.25%.

In  March, the outbreak of hostilities in Iraq clouded the economic picture. The
Fed  indicated  at  the time that uncertainty regarding the war with Iraq was so
great  that  it  could not adequately assess the economic risks. Nonetheless, as
the   conflict   progressed,  the  market's  focus  appeared  to  shift  toward
expectations  of  a  quick resolution to the war, causing money market yields to
rise at the longer end of the curve.

After  the war began to wind down in April, investors' attention returned to the
problems  underlying  the weak U.S. economy. The manufacturing sector contracted
in  April,  and  the  unemployment rate rose to 6%, suggesting lingering caution
among  businesses  reluctant  to  resume  hiring  and  production.  In addition,
uncertainty remained as to the prospects for continued spending among consumers,
as  revised estimates of U.S. economic growth for the first quarter of 2003 came
in at a relatively disappointing 1.9%.

In  May, the economy showed signs of gradual improvement. A key purchasing index
rose  significantly  over  the  previous  month's  levels,  suggesting that the
manufacturing  sector  may  be  improving  and  the  worst may be over. Consumer
confidence  rebounded  to  its  highest levels in almost a year, indicating that
consumers  were becoming increasingly optimistic after reining in their spending
during the Iraq war. These encouraging signs were supported by other potentially
constructive  factors,  including  gains  in  the  stock  market, low inflation,
declining  oil  prices,  gains in productivity and pending tax cuts. However, at
its  meeting  in early May, the Fed adopted a relatively cautious stance, citing
disappointing  numbers related to employment and production. The Fed also stated
that economic risks were "weighted toward weakness for the foreseeable future."


What is the fund's current strategy?

Despite  the  encouraging  signs  that  arose  during  May,  we  remain cautious
regarding  the  prospects for a quick pickup in economic growth. We believe that
more  solid  evidence  is  required to support a sustainable rebound in economic
activity among consumers and businesses. In fact, by the reporting period's end,
market  expectations  had begun to build that the Fed was likely to cut interest
rates further if the economy did not expand more robustly by its meeting in late
June.  These  expectations  have  recently  been reflected by lower yields among
money market securities.

Because  the  current money market yield curve is relatively flat, we have begun
to allow the fund's weighted average maturity to shorten gradually. Accordingly,
the  fund  ended  the  reporting  period  with  a weighted average maturity that
remained  longer  than  its  peer group average, but less so than it had been in
previous    months.

June 16, 2003

(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
THE U.S. GOVERNMENT. 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 AND CLASS X YIELDS
WOULD HAVE BEEN LOWER.

                                                             The Fund

STATEMENT OF INVESTMENTS




May 31, 2003 (Unaudited)

STATEMENT OF INVESTMENTS

                                                                                              Principal
NEGOTIABLE BANK CERTIFICATES OF DEPOSIT--50.6%                                                Amount ($)                Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

ABN-AMRO Bank N.V. (London)

                                                                                                               
   1.26%--1.65%, 6/30/2003--9/22/2003                                                       150,000,000              150,028,789

Alliance & Leicester PLC (London)

   1.30%--1.65%, 7/15/2003--11/12/2003                                                      250,000,000              250,001,735

BNP Paribas (Yankee)

   1.20%, 5/19/2004                                                                         100,000,000               99,995,156

Bank of Scotland (Yankee)

   2.57%, 7/1/2003                                                                          100,000,000               99,998,379

Barclays Bank PLC (London)

   1.70%, 6/26/2003                                                                         100,000,000              100,037,962

Canadian Imperial Bank of Commerce (Yankee)

   1.28%, 6/23/2003                                                                          50,000,000  (a)          49,998,639

Credit Agricole Indosuez S.A. (Yankee)

   1.30%--1.31%, 10/22/2003--3/15/2004                                                      250,000,000  (a)         249,982,168

Credit Lyonnais N.A. Inc. (London)

   1.32%, 7/17/2003                                                                         100,000,000              100,001,269

Credit Lyonnais N.A. Inc. (Yankee)

   1.28%, 6/24/2003--7/23/2003                                                              250,000,000              249,999,523

First Tennessee Bank N.A.

   1.22%, 8/6/2003                                                                          125,000,000              125,000,000

HBOS Treasury Services PLC (London)

   1.24%--1.38%, 6/16/2003--7/3/2003                                                        200,000,000              199,997,814

ING Bank N.V. (London)

   1.65%, 9/22/2003                                                                          50,000,000               50,028,355

Landesbank Hessen-Thueringen Girozentrale (London)

   1.28%, 11/26/2003                                                                        200,000,000              200,004,897

Marshall & Ilsley Bank Milwaukee, WI (Yankee)

   1.30%, 3/17/2004                                                                         200,000,000  (a)         199,968,052

Natexis Banques Populaires (Yankee)

   1.26%, 10/17/2003                                                                        200,000,000              199,996,191

Nordea Bank Finland PLC (Yankee)

   1.32%, 1/12/2004                                                                         100,000,000  (a)          99,996,892

Societe Generale (Yankee)

   1.31%, 3/8/2004                                                                          250,000,000  (a)         249,971,494

Swedbank (Yankee)

   1.30%, 9/26/2003                                                                          50,000,000  (a)          49,998,396

Swedbank (Yankee)

   2.60%, 7/7/2003                                                                          100,000,000               99,999,028

Toronto-Dominion Bank (Yankee)

   1.42%--2.56%, 7/1/2003--8/12/2003                                                        135,000,000              135,021,274


                                                                                              Principal
NEGOTIABLE BANK CERTIFICATES OF DEPOSIT (CONTINUED)                                           Amount ($)                Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

Unicredito Italiano Spa (London)

   1.28%--1.64%, 7/23/2003--10/6/2003                                                       200,000,000              200,002,602

Wachovia Bank & Trust Co.

   1.30%, 10/20/2003                                                                        200,000,000  (a)         200,000,000

Westdeutsche Landesbank Girozentrale (Yankee)

   1.28%--2.60%, 6/3/2003--11/25/2003                                                       350,000,000              349,999,271

Wilmington Trust Co.

   1.23%, 8/27/2003                                                                         100,000,000              100,000,000

TOTAL NEGOTIABLE BANK CERTIFICATES OF DEPOSIT

   (cost $3,810,027,886)                                                                                           3,810,027,886
- ------------------------------------------------------------------------------------------------------------------------------------

COMMERCIAL PAPER--16.6%
- ------------------------------------------------------------------------------------------------------------------------------------

Altria Group Inc.

   1.30%, 6/3/2003                                                                           70,000,000               69,994,944

Amstel Funding Corp.

   1.29%, 7/31/2003                                                                         100,000,000  (b)          99,786,667

Bank of America Corp.

   1.23%, 7/10/2003                                                                          50,000,000               49,933,375

Depfa Bank PLC

   1.23%, 7/7/2003                                                                           13,000,000               12,984,010

Eurohypo AG

   1.30%, 8/13/2003                                                                         100,000,000               99,737,403

General Electric Co.

   1.28%, 6/27/2003                                                                         100,000,000               99,908,278

General Electric Capital Corp.

   1.20%, 8/27/2003                                                                         300,000,000              299,130,000

General Electric Capital Services Inc.

   1.30%, 10/29/2003--11/3/2003                                                             175,000,000              174,045,938

Hamburgische Landesbank Girozentrale

   1.29%, 10/9/2003--10/10/2003                                                             200,000,000              199,072,000

ING (U.S.) Funding LLC

   1.35%, 6/2/2003                                                                           50,000,000               49,998,125

Morgan Stanley & Co. Inc.

   1.39%, 12/9/2003                                                                         100,000,000              100,000,000

TOTAL COMMERCIAL PAPER

   (cost $1,254,590,740)                                                                                           1,254,590,740

                                                                                                     The Fund



STATEMENT OF INVESTMENTS (Unaudited) (CONTINUED)

                                                                                              Principal
CORPORATE NOTES--12.1%                                                                        Amount ($)                Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

American Honda Finance Corp.

   1.30%, 7/22/2003                                                                         125,000,000  (a)         125,000,000

CC USA Inc.

   1.33%, 7/15/2003                                                                         190,000,000  (a,b)       190,000,000

Merrill Lynch & Co. Inc.

   1.27%, 4/16/2004                                                                         150,000,000  (a)         150,000,000

Paradigm Funding LLC

   1.27%, 10/1/2003                                                                         200,000,000  (a,b)       200,000,000

Sigma Finance Inc.

   1.34%--1.36%, 6/2/2003--7/1/2003                                                         150,000,000  (a,b)       150,000,000

Societe Generale

   1.31%, 2/18/2004                                                                         100,000,000  (a)          99,990,754

TOTAL CORPORATE NOTES

   (cost $914,990,754)                                                                                               914,990,754
- ------------------------------------------------------------------------------------------------------------------------------------

PROMISSORY NOTES--3.3%
- ------------------------------------------------------------------------------------------------------------------------------------

Goldman Sachs Group Inc.

  1.41%--2.14%, 7/11/2003--1/21/2004

   (cost $245,000,000)                                                                      245,000,000  (c)         245,000,000
- ------------------------------------------------------------------------------------------------------------------------------------

SHORT-TERM BANK NOTES--8.6%
- ------------------------------------------------------------------------------------------------------------------------------------

Bank One N.A.

   1.30%, 8/15/2003--1/12/2004                                                              200,000,000  (a)         199,990,752

National City Bank

   1.29%--1.31%, 8/22/2003--2/23/2004                                                       350,000,000  (a)         350,003,498

Swedbank

   1.28%, 9/10/2003                                                                         100,000,000  (a)          99,991,668

TOTAL SHORT-TERM BANK NOTES

   (cost $649,985,918)                                                                                               649,985,918
- ------------------------------------------------------------------------------------------------------------------------------------

U.S. GOVERNMENT AGENCIES--.7%
- ------------------------------------------------------------------------------------------------------------------------------------

Federal Home Loan Banks, Notes

  1.24%, 6/22/2004

   (cost $50,000,000)                                                                        50,000,000               50,000,000


                                                                                              Principal
TIME DEPOSITS--8.5%                                                                           Amount ($)                Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

ABN-AMRO Bank (Grand Cayman)

   1.28%, 6/2/2003                                                                          150,000,000              150,000,000

Dexia Bank (Grand Cayman)

   1.28%, 6/2/2003                                                                          150,000,000              150,000,000

Fifth Third Bank (Grand Cayman)

   1.28%, 6/2/2003                                                                          100,000,000              100,000,000

Fleet National Bank (Grand Cayman)

   1.34%, 6/2/2003                                                                          200,000,000              200,000,000

State Street Bank & Trust Co. (Grand Cayman)

   1.21%, 6/2/2003                                                                           42,000,000               42,000,000

TOTAL TIME DEPOSITS

   (cost $642,000,000)                                                                                               642,000,000
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $7,566,595,298)                                                           100.4%           7,566,595,298

LIABILITIES, LESS CASH AND RECEIVABLES                                                              (.4%)            (29,494,776)

NET ASSETS                                                                                        100.0%           7,537,100,522




(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, 2003, THESE
SECURITIES AMOUNTED TO $639,786,667 OR 8.5% 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 7/16/02 TO 2/25/03 AT A COST OF $245,000,000. AT MAY 31,
2003, THE AGGREGATE VALUE OF THESE SECURITIES WAS $245,000,000 OR 3.3% OF NET
ASSETS AND ARE VALUED AT AMORTIZED COST.

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2003 (Unaudited)

                                                             Cost         Value
- --------------------------------------------------------------------------------

ASSETS ($):

Investments in securities--See Statement of
Investments                                        7,566,595,298  7,566,595,298

Cash                                                                      6,510

Interest receivable                                                  29,222,766

Prepaid expenses                                                        166,520

                                                                  7,595,991,094
- --------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                         6,044,783

Payable for investment securities purchased                          50,000,000

Payable for shares of Common Stock redeemed                           2,593,883

Accrued expenses                                                        251,906

                                                                     58,890,572
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                    7,537,100,522
- --------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                   7,537,102,150

Accumulated net realized gain (loss) on investments                      (1,628)
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                    7,537,100,522

NET ASSET VALUE PER SHARE





                                                                              Class A                Class B            Class X
- ------------------------------------------------------------------------------------------------------------------------------------

                                                                                                            
Net Assets ($)                                                          1,404,454,098          6,132,487,914            158,510

Shares Outstanding                                                      1,404,490,425          6,132,453,211            158,514
- ------------------------------------------------------------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                                                    1.00                   1.00               1.00

SEE NOTES TO FINANCIAL STATEMENTS.



STATEMENT OF OPERATIONS

Six Months Ended May 31, 2003 (Unaudited)

- --------------------------------------------------------------------------------

INVESTMENT INCOME ($):

INTEREST INCOME                                                     54,728,389

EXPENSES:

Management fee--Note 2(a)                                           18,435,467

Shareholder servicing costs--Note 2(c)                               9,478,904

Distribution fees, service fees and prospectus--Note 2(b)            7,402,866

Custodian fees                                                         144,040

Registration fees                                                      112,260

Directors' fees and expenses--Note 2(d)                                 94,296

Professional fees                                                       29,488

Prospectus and shareholders' reports                                    15,905

Miscellaneous                                                           38,394

TOTAL EXPENSES                                                      35,751,620

Less--reduction in shareholder servicing costs
  due to undertaking--Note 2(c)                                       (228,341)

NET EXPENSES                                                        35,523,279

INVESTMENT INCOME--NET                                              19,205,110
- --------------------------------------------------------------------------------

NET REALIZED GAIN (LOSS) ON INVESTMENTS--NOTE 1(B) ($)                   2,111

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                19,207,221

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

STATEMENT OF CHANGES IN NET ASSETS

                                         Six Months Ended
                                             May 31, 2003            Year Ended
                                               (Unaudited)    November 30, 2002
- --------------------------------------------------------------------------------

OPERATIONS ($):

Investment income--net                         19,205,110            84,953,550

Net realized gain (loss) on investments             2,111               120,459

NET INCREASE (DECREASE) IN NET ASSETS
   RESULTING FROM OPERATIONS                   19,207,221            85,074,009
- --------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A Shares                                 (5,210,948)          (21,557,165)

Class B Shares                                (13,993,811)          (63,394,048)

Class X Shares                                       (351)               (2,337)

TOTAL DIVIDENDS                               (19,205,110)          (84,953,550)
- --------------------------------------------------------------------------------

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

Net proceeds from shares sold:

Class A Shares                              3,509,118,880         7,659,411,969

Class B Shares                              7,240,368,188        14,614,130,063

Class X Shares                                         --                12,830

Dividends reinvested:

Class A Shares                                  5,150,187            21,033,870

Class B Shares                                 13,099,037            56,427,944

Class X Shares                                        181                 1,383

Cost of shares redeemed:

Class A Shares                             (3,666,180,244)       (7,503,864,979)

Class B Shares                             (6,579,966,738)      (13,925,485,108)

Class X Shares                                       (920)             (146,242)

INCREASE (DECREASE) IN NET ASSETS FROM
   CAPITAL STOCK TRANSACTIONS                 521,588,571           921,521,730

TOTAL INCREASE (DECREASE) IN NET ASSETS       521,590,682           921,642,189
- --------------------------------------------------------------------------------

NET ASSETS ($):

Beginning of Period                         7,015,509,840         6,093,867,651

END OF PERIOD                               7,537,100,522         7,015,509,840

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, 2003                                   Year Ended November 30,
                                                             -----------------------------------------------------------------------
CLASS A SHARES                             (Unaudited)            2002            2001            2000           1999          1998
- ------------------------------------------------------------------------------------------------------------------------------------

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                           .004             .014            .041            .056           .044          .049

Distributions:

Dividends from
   investment income--net                       (.004)           (.014)          (.041)          (.056)         (.044)        (.049)

Net asset value, end of period                   1.00             1.00            1.00            1.00           1.00          1.00
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL RETURN (%)                                  .72(a)          1.43            4.21            5.77           4.53          4.98
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses
   to average net assets                          .77(a)           .77             .79             .78            .78           .77

Ratio of net investment
   income to average
   net assets                                     .72(a)          1.42            4.03            5.64           4.44          4.88
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period
   ( $x 1,000)                              1,404,454        1,556,365       1,379,758         982,685        863,981       835,706

(A) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

FINANCIAL HIGHLIGHTS (CONTINUED)

                              Six Months Ended
                                  May 31, 2003                                   Year Ended November 30,
                                                      ------------------------------------------------------------------------------
CLASS B SHARES                      (Unaudited)            2002            2001            2000              1999             1998
- ------------------------------------------------------------------------------------------------------------------------------------

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             .012            .039            .054              .042             .047

Distributions:

Dividends from
   investment
   income--net                           (.002)           (.012)          (.039)          (.054)            (.042)           (.047)

Net asset value,
   end of period                          1.00             1.00            1.00            1.00              1.00             1.00
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL RETURN (%)                           .48(a)          1.20            3.98            5.53              4.32             4.78
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL
   DATA (%):

Ratio of expenses
   to average net assets                  1.01(a)          1.00            1.00            1.00              1.00             1.00

Ratio of net investment
   income to average
   net assets                              .47(a)          1.19            3.81            5.41              4.24             4.66

Decrease reflected in
   above expense ratios
   due to undertakings
   by The Dreyfus
   Corporation                             .01(a)           .01             .03             .02               .03              .06
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets,
   end of period
   ($x 1,000)                        6,132,488        5,458,986       4,713,819       3,338,285         3,056,844        2,427,332

(A) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.


                                                             Six Months Ended
                                                                 May 31, 2003                     Year Ended November 30,
                                                                                      ----------------------------------------------
CLASS X SHARES                                                     (Unaudited)          2002        2001        2000         1999(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                                                   .002           .012        .039        .054         .021

Distributions:

Dividends from investment income--net                                   (.002)         (.012)      (.039)      (.054)       (.021)

Net asset value, end of period                                           1.00           1.00        1.00        1.00         1.00
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL RETURN (%)                                                          .44(b)        1.16        3.94        5.49         4.33(b)
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                  1.05(b)        1.05        1.05        1.05         1.05(b)

Ratio of net investment income
   to average net assets                                                  .44(b)        1.20        4.03        5.43         4.01(b)

Decrease reflected in above
   expense ratios due to undertakings
   by The Dreyfus Corporation                                             .07(b)         .14         .13         .06          .25(b)
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ( $x 1,000)                                     159            159         291         478          554

(A) FROM JUNE 1, 1999 (COMMENCEMENT OF INITIAL OFFERING) TO NOVEMBER 30, 1999.

(B) ANNUALIZED.




SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

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") serves as the
fund's  investment  adviser. The Manager is a wholly-owned subsidiary of Mellon
Bank, N.A., which is a wholly-owned subsidiary of Mellon Financial Corporation.

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  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.

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 accounting
principles generally accepted in the United States, which may require the use of
management  estimates  and  assumptions.  Actual results could differ from those
estimates.


(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.  Realized  gain  and  loss  from securities
transactions  are  recorded  on  the  identified  cost  basis.  Interest income,
adjusted for amortization of discount and premium on investments, is earned from
the  settlement  date  and  recognized on the accrual 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.

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
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.

                                                             The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

(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 $3,739 available for federal
income tax purposes to be applied against future net securities profits, if any,
realized  subsequent to November 30, 2002. If not applied, the carryover expires
in fiscal 2008.

The  tax  character of distributions paid to shareholders during the fiscal year
ended  November  30,  2002 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,  2003,  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
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,  2003,  there  was  no  expense
reimbursement pursuant to the Agreement.

(B)  Under the Service Plan with respect to Class A shares (the "Plan"), adopted
pursuant  to  Rule 12b-1 under the Act, Class A shares bear directly the 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
time  to  time  by  the fund's Board of Directors. If a holder of Class A shares
ceases  to be a client of a Service Agent, but continues to hold Class A shares,
the  Manager will be permitted to act as a Service Agent in respect of such fund
shareholders and receive payments under the Service Plan for Servicing. The fees
payable  for  Servicing  are payable without regard to actual expenses incurred.
During  the  period  ended  May 31, 2003, Class A shares were charged $1,457,531
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, 2003, Class B shares were charged $5,945,137 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

                                                                 The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

annual  rate  of .25 of 1% of the value of the average daily net assets of Class
X.  During  the  period  ended  May  31,  2003, Class X shares were charged $198
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  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,  2003, Class A shares were charged $256,357
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, 2002 through May 31, 2003 that if
the  aggregate  expenses  of  Class  B  shares  of the fund, exclusive of taxes,
brokerage  fees, interest on borrowings and extraordinary expenses, exceed 1.01%
of  the  value  of  the  average  daily net assets of Class B, the Manager would
reimburse  the  expenses of the fund under the Class B Shareholder Services Plan
to  the  extent  of  any excess expense and up to the full fee payable under the
Class  B  Shareholder Services Plan. The Manager had undertaken from December 1,
2002  through  May  31,  2003,  that if the aggregate expenses of Class X shares

of  the  fund,  exclusive  of  taxes, brokerage fees, interest on borrowings and
extraordinary  expenses,  exceed  1.05%  of  the  value of the average daily net
assets  of  Class  X, the Manager would reimburse the expenses of the fund under
the Class X Shareholder Services Plan to the extent of any excess expense and up
to  the full fee payable under the Class X Shareholder Services Plan. During the
period  ended  May  31, 2003, Class B and Class X shares were charged $7,402,554
and  $198,  respectively,  pursuant  to  the Shareholder Services Plan, of which
$228,289 and $52, respectively, 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,  2003,  the  fund  was charged $209,907 pursuant to the transfer
agency agreement.

(D)  Each  Board  member also serves as a Board member of other funds within the
Dreyfus  complex  (collectively, the "Fund Group"). Each Board member who is not
an  "affiliated  person" as defined in the Act receives an annual fee of $50,000
and  an  attendance  fee  of  $6,500  for  each  in-person  meeting and $500 for
telephone  meetings.  These fees are allocated among the funds in the Fund Group
in  proportion  to  each  fund's relative net assets. The Chairman of the Board
receives  an additional 25% of such compensation. Subject to the fund's Emeritus
Program  Guidelines,  Emeritus  Board members, if any, receive 50% of the annual
retainer  fee  and  per  meeting  fee paid at the time the Board member achieves
emeritus status.

                                                             The Fund

                        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
                        100 Church 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

(c) 2003 Dreyfus Service Corporation                                  196SA0503




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. [RESERVED]

ITEM 6. [RESERVED]

ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END
        MANAGEMENT INVESTMENT COMPANIES.

                Not applicable.

ITEM 8. [RESERVED]

ITEM 9. CONTROLS AND PROCEDURES.

(a)   Based on an evaluation of the Disclosure Controls and Procedures (as
defined in Rule 30a-2(c) under the Investment Company Act of 1940, the
"Disclosure Controls") as of a date within 90 days prior to the filing date
(the "Filing Date") of this Form N-CSR (the "Report"), the Disclosure
Controls are effectively designed to ensure that information required to be
disclosed by the Registrant in the Report is recorded, processed, summarized
and reported by the Filing Date, including ensuring that information required
to be disclosed in the Report is accumulated and communicated to the
Registrant's management, including the Registrant's principal executive
officer and principal financial officer, as appropriate to allow timely
decisions regarding required disclosure.

(b)   There were no significant changes in the Registrant's internal controls
or in other factors that could significantly affect these controls subsequent
to the date of their evaluation, and there were no corrective actions with
regard to significant deficiencies and material weaknesses.

ITEM 10.  EXHIBITS.

(a)   Not applicable.

(b)(1)      Certifications of principal executive officer and principal
financial officer as required by Rule 30a-2 under the Investment Company Act
of 1940.





                                  SIGNATURES



Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the Registrant has duly caused this Report to
be signed on its behalf by the undersigned, thereunto duly authorized.

GENERAL MONEY MARKET FUND, INC.

By:   /S/ STEPHEN E. CANTER
         Stephen E. Canter
         President

Date:  July 30, 2003

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 30, 2003

By:   /S/ JAMES WINDELS
      James Windels
      Chief Financial Officer

Date:  July 30, 2003


                                EXHIBIT INDEX

            (b)(1)      Certifications of principal executive officer and
            principal financial officer as required by Rule 30a-2 under the
            Investment Company Act of 1940.

            (b)(2)      Certification of principal executive officer and
            principal financial officer as required by Section 906 of the
            Sarbanes-Oxley Act of 2002.