GENERAL MUNICIPAL MONEY MARKET FUND INC
N-30D, 1996-07-29
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GENERAL MUNICIPAL MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on the General Municipal
Money Market Fund, Inc. For its semi-annual reporting period ended May 31,
1996, your Fund's Class A shares produced an annualized yield of 3.01% and
Class B shares produced an annualized yield of 2.69%. For investors in the
highest Federal income tax bracket, this equates to a taxable equivalent
yield of 4.98% for Class A shares and 4.45% for Class B shares.* Income
dividends of approximately $.015 per share were paid during the period for
Class A shares and approximately $.013 for Class B shares. Assuming the
reinvestment of these dividends and accounting for the effect of compounding,
annualized effective yields of 3.05% and 2.72% were achieved for Class A
shares and Class B shares, respectively.** These dividends were exempt from
Federal personal income taxes.***
THE ECONOMY
    Recent economic reports show that the economy continues to recover from
its year-end 1995 pause. Spurred by a surge in consumer and business
spending, the economy grew at a moderate rate of 2.3% during the first
quarter of this year. The Index of Leading Economic Indicators, a major
forecasting index, extended its string of increases for the third consecutive
month in April, the first such three-month advance since late 1993. Despite a
sharp jump in energy prices, inflation remained in check. For the 12 months
ended in May, consumer prices rose 2.9%.
    Despite the relatively benign level of inflation, the economy's expansion
has sparked concerns that the Federal Reserve Board could raise short-term
interest rates. So far, the Fed has refrained from tightening monetary
policy, apparently interpreting economic data to mean that the economy
remains on a path of moderate growth unaccompanied by a surge in inflation.
There is now a greater consensus that the Fed will tighten eventually in
order to prevent unacceptable levels of price inflation from coming on the
heels of economic growth.
MARKET/PORTFOLIO ENVIRONMENT
    If one were to trace the trend in short-term municipal rates over this
most recent semi-annual period, the direction would mirror closely the
changes in supply and demand conditions. The six-month cycle would reflect:
higher rates at year-end due to December outflows, a precipitous drop in
yields throughout January as cash returned to the market, price
weakness/higher rates in April as investors tapped their money market funds
to pay income taxes, and yield stability in May as market activity settled
into a trading range. These technical influences continue to be the overriding
factor affecting municipal money rates.
    These conditions, coupled with policies of the Federal Reserve Board,
provide the framework for our investment strategy - both on a day-to-day
basis and looking ahead over a one-year horizon. During the first few months
of 1996, as a result of uncertainty surrounding potential tax reform,
variable rate demand notes (which represent a significant portion of your
Portfolio's investments) benefited from unusually high yields. While the
concerns were only temporary, they translated, for a time, into a more
attractive after-tax rate of return than was available on taxable instruments
with similar maturities. During this period, the purchase of attractively
yielding commercial paper in the 90-day range also allowed us to capture
returns similar to those on one-year issues without a significant extension
of average maturity - enabling us to wait out a lower yield environment in
anticipation of higher rates.

    Opportunity to commit to longer note issues has appeared in recent weeks
and should continue to be available during the summer months as issuers
return to the market with midyear financings. We expect to take advantage of
these buying opportunities as we monitor potential Fed activity and any other
significant changes in the municipal money market. All new investments will
continue to meet the high credit quality standards which we require and to
provide a significant level of liquidity, commensurate with the needs of your
Fund.
    Included in this report is a series of detailed statements about your
Fund's holdings and its financial condition. We hope they are informative.
Please know that we greatly appreciate your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Sincerely,
                          [Richard J. Moynihan signature logo]
                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
June 14, 1996
New York, N.Y.

*  The taxable equivalent yield quoted is for investors in the highest
Federal tax bracket of 39.6%.
**Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
***A portion of the Fund's income may be treated as a preference item for
some investors for the purposes of the Federal Alternative Minimum Tax (AMT).
Income may be subject to state and local taxes.
<TABLE>


GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                             MAY 31, 1996 (UNAUDITED)
                                                                                               PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                    AMOUNT                 VALUE
                                                                                             _______________       _______________
<S>                                                                                               <C>             <C>
ARIZONA-10.2%
Arizona Educational Loan Marketing Corporation, Educational Loan Revenue, VRDN
    3.75%, Series A (BPA; Fuji Bank and Insured; MBIA) (a)..................                      $  10,675,000    $  10,675,000
Glendale Industrial Development Authority, HR, VRDN (West Valley Camelback)
    3.60% (LOC; Northwest Corp.) (a,b)......................................                          8,500,000        8,500,000
Pima County Industrial Development Authority, Industrial Revenue, VRDN
    (Tucson Electric) 3.65% (LOC; Barclays Bank) (a,b)......................                         14,100,000       14,100,000
DELAWARE-.5%
Delaware Economic Development Authority, IDR, VRDN (Orient Chemical Corp. Project)
    3.875% (LOC; Sumitomo Bank) (a,b).......................................                          1,480,000        1,480,000
DISTRICT OF COLUMBIA-4.9%
District of Columbia, General Fund Recovery, VRDN:
    3.95%, Series B-2 (LOC; Westdeutsche Landesbank) (a,b)..................                          9,000,000        9,000,000
    3.95%, Series B-3 (LOC; Landesbank Hessen-Thuringen) (a,b)..............                          7,000,000        7,000,000
FLORIDA-1.2%
Pinellas County Health Facilities Authority, Revenue, Refunding, VRDN
    (Pooled Hospital Loan Program) 3.70% (LOC; Chemical Bank) (a,b).........                          4,000,000        4,000,000
GEORGIA-7.5%
Burke County Development Authority, PCR, VRDN (Oglethorpe Power Corp.)
    3.50%, Series A (BPA; Credit Locale de France and Insured; FGIC) (a)....                          9,400,000        9,400,000
Fulton County, TAN 4%, 12/31/96.............................................                         10,000,000       10,025,524
Savannah Economic Development Authority, Exempt Facility Revenue, VRDN
    (Home Depot Project) 3.70% (LOC; Trust Co. Bank) (a,b)..................                          5,000,000        5,000,000
HAWAII-2.7%
Honolulu City and County, MFHR, VRDN (Halekua Gardens Project)
    4%, Series A (LOC; Bank of Tokyo) (a,b).................................                          8,687,000        8,687,000
ILLINOIS-1.7%
Illinois Health Facilities Authority, Revenue, VRDN (Resurrection Health Care Systems)
    3.75% (LOC: Comerica Bank, First Chicago Bank,
    Lasalle National Bank and National Bank of Detroit) (a,b)...............                          3,700,000        3,700,000
Illinois Housing Development Authority, Homeowner Mortgage Revenue
    3.65%, Series E-1, 9/3/96 (LOC; Morgan Stanley and Co.) (b).............                          1,770,000        1,770,000
INDIANA-3.6%
Indiana Bond Bank, Notes (Reassessment Assistance Project)
    4.125%, Series A, 1/30/97...............................................                          4,990,000        5,002,027
City of Indianapolis, Local Public Improvement Bond Bank Notes:
    3.70%, Series E, 7/11/96................................................                          3,500,000        3,503,000
    3.70%, Series F, 7/11/96................................................                          3,250,000        3,252,786

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                   MAY 31, 1996 (UNAUDITED)
                                                                                                   PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                  AMOUNT               VALUE
                                                                                                _______________   _______________
IOWA-1.2%
Iowa Finance Authority, SWDR, VRDN (Cedar River Paper Co. Project)
    3.75% (LOC; Swiss Bank Corp.) (a,b).....................................                     $    4,000,000    $   4,000,000
KENTUCKY-2.3%
Boone County, IDR, VRDN (Curtin Matheson Scientific)
    3.90% (LOC; Barclays Bank) (a,b)........................................                          2,500,000        2,500,000
Carroll County, Solid Waste Disposal Facilities Revenue, VRDN
    (Kentucky Utilities Co. Project) 3.90%, Series A (a)....................                          5,000,000        5,000,000
LOUISIANA-7.2%
Ascension Parish, Revenue, VRDN (BASF Corp. Project)
    3.75% (Corp. Guaranty; BASF Corp.) (a)..................................                          4,500,000        4,500,000
Plaquemines Parish, Environmental Revenue, Refunding, VRDN
    (British Petroleum Exploration and Oil) 4% (Corp. Guaranty; British Petroleum) (a)                6,400,000        6,400,000
West Baton Rouge Parish Industrial District Number 3, Revenue, VRDN
    (Dow Chemical Co. Project) 4.05% (Corp. Guaranty; Dow Chemical Co.) (a).                         12,500,000       12,500,000
MICHIGAN-13.0%
Macomb Township Economic Development Corporation, LOR, VRDN
    (ACR Industries Project) 3.75% (LOC; Comerica Bank) (a,b)...............                            700,000          700,000
State of Michigan, GO Notes 4%, 9/30/96.....................................                         19,600,000       19,652,835
Michigan Housing Development Authority, Rental Housing Revenue, Refunding, VRDN
    3.65%, Series C (LOC; Credit Suisse) (a,b)..............................                          7,000,000        7,000,000
Michigan Strategic Fund, VRDN:
    LOR, Refunding (Consumers Power Co. Project)
      3.60%, Series A (LOC; Canadian Imperial Bank of Commerce) (a,b).......                         11,500,000       11,500,000
    SWDR (Grayling Generating Project) 3.75% (LOC; Barclays Bank) (a,b).....                          3,800,000        3,800,000
MINNESOTA-2.5%
Minnesota Housing Finance Agency, SFMR:
    3.25%, Series M, 12/12/96 (LOC; Societe Generale) (b)...................                          5,900,000        5,900,000
    3.60%, Series O, 12/12/96 (LOC; Societe Generale) (b)...................                          2,200,000        2,200,000
MISSOURI-2.4%
Missouri Housing Development Commission, SFMR (Homeowner Loan)
    4%, Series B, 7/1/96 (Insured; FGIC)....................................                          8,000,000        8,000,000
NEW JERSEY-9.5%
New Jersey Sports and Exposition Authority, VRDN (State Contract)
    3.50% (LOC; Industrial Bank of Japan and Insured; MBIA) (a,b)...........                         10,000,000       10,000,000
New Jersey Transportation Trust Fund Authority, CP
    3.80%, 6/14/96 (Liquidity Agreement; Union Bank of Switzerland).........                         10,000,000       10,000,000

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                  MAY 31, 1996 (UNAUDITED)
                                                                                                   PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                  AMOUNT               VALUE
                                                                                                _______________   _______________
NEW JERSEY (CONTINUED)
New Jersey Turnpike Authority, Turnpike Revenue, Refunding, VRDN
    3.25%, Series D (LOC; Bankers Trust) (a,b)..............................                      $  11,000,000    $  11,000,000
NEW YORK-1.3%
New York State Housing Finance Agency, Housing Revenue, VRDN (Normandie Court II)
    3.50%, Series A (LOC; Fleet Bank) (a,b).................................                          4,200,000        4,200,000
OHIO-3.8%
Brecksville-Broadview Heights City School District, Notes 3.90%, 1/17/97....                          4,000,000        4,008,494
Greene County, Certificates of Indebtedness 4.25%, 7/18/96..................                          8,275,500        8,280,103
PENNSYLVANIA-1.7%
Delaware County Economic Development Authority, Solid Waste Disposal and
    Sewer Revenue, VRDN (CIBA-Geigy) 3.75% (LOC; Union Bank of Switzerland) (a,b)                     5,700,000        5,700,000
TENNESSEE-3.7%
Morristown Industrial Development Board, IDR, VRDN (Camvac International Inc. Project)
    4.075% (LOC; Bankers Trust) (a,b).......................................                          3,000,000        3,000,000
Sevier County Public Building Authority, Local Government Public Improvement, VRDN:
    3.50%, Series A-2 (BPA; Kredietbank and Insured; AMBAC) (a).............                          4,700,000        4,700,000
    3.50%, Series A-3 (BPA; Kredietbank and Insured; AMBAC) (a).............                          4,500,000        4,500,000
TEXAS-14.2%
Brazos River Authority, PCR, Refunding, VRDN (Utility Electric Co.)
    4%, Series C (LOC; Swiss Bank Corp.) (a,b)..............................                          4,000,000        4,000,000
Brazos River Harbor Naval District, Harbor Revenue, VRDN (Dow Chemical Co. Project)
    4.05%, Series A (Corp. Guaranty; Dow Chemical Co.) (a)..................                          9,700,000        9,700,000
Dallas County, Permanent Improvement
    3.90%, Series C, 6/15/96 (LOC; Union Bank of Switzerland) (b)...........                          5,000,000        5,000,000
Greater East Texas Higher Education Authority Inc., Student Loan Revenue, VRDN
    3.65%, Series B (LOC; Student Loan Marketing Association) (a,b).........                          7,500,000        7,500,000
Gulf Coast Waste Disposal Authority, SWDR, VRDN (Amoco Oil Co. Project)
    3.90% (Corp. Guaranty; Amoco Credit Corp.) (a)..........................                          7,700,000        7,700,000
Panhandle-Plains Higher Education Authority, Student Loan Revenue, Refunding, VRDN
    3.60%, Series A (LOC; Student Loan Marketing Association) (a,b).........                          7,700,000        7,700,000
San Antonio Housing Finance Corporation, MFHR, VRDN (Sunrise Apartments Project)
    3.65% (LOC; Swiss Bank Corp.) (a,b).....................................                          5,000,000        5,000,000
VIRGINIA-1.1%
Pendleton County, IDR, VRDN (Greer Steel Project)
    3.95% (LOC; Pittsburgh National Bank) (a,b).............................                          3,715,000        3,715,000
WASHINGTON-.9%
Washington State Housing Finance Commission (Single Family Program)
    4.10%, Series 95 1A-S, 6/1/96 (Insured; FGIC)...........................                          2,950,000        2,950,000

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                   MAY 31, 1996 (UNAUDITED)
                                                                                                    PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                   AMOUNT              VALUE
                                                                                                _______________   _______________
WEST VIRGINIA-1.2%
Marion County, Community Solid Waste Disposal Facility Revenue, VRDN
    (Granttown Project) 3.65%, Series B (LOC; National Westminster Bank) (a,b)                   $    4,000,000     $   4,000,000
WYOMING-1.7%
Lincoln County, PCR, VRDN (Exxon Project)
    3.60%, Series B (Corp. Guaranty; Exxon Corp.) (a).......................                          5,700,000         5,700,000
                                                                                                                    ______________
TOTAL INVESTMENTS (cost $327,101,769).......................................                                         $327,101,769
                                                                                                                    ==============
</TABLE>
<TABLE>

SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <C>         <C>
AMBAC         American Municipal Bond Assurance Corporation      MBIA        Municipal Bond Investors Assurance
BPA           Bond Purchase Agreement                                         Insurance Corporation
CP            Commercial Paper                                   MFHR        Multi-Family Housing Revenue
FGIC          Financial Guaranty Insurance Company               PCR         Pollution Control Revenue
GO            General Obligation                                 SFMR        Single Family Mortgage Revenue
HR            Hospital Revenue                                   SWDR        Solid Waste Disposal Revenue
IDR           Industrial Development Revenue                     TAN         Tax Anticipation Notes
LOC           Letter of Credit                                   VRDN        Variable Rate Demand Notes
LOR           Limited Obligation Revenue
</TABLE>
<TABLE>

SUMMARY OF COMBINED RATINGS
<S>                                <C>                            <C>                                 <C>
FITCH (C)              OR          MOODY'S             OR         STANDARD & POOR'S                   PERCENTAGE OF VALUE
__________                         _________                      __________________                  ____________________
F1+/F1                             VMIG1/MIG1, P1 (d)             SP1+/SP1, A1+/A1 (d)                        93.9%
AAA/AA (e)                         Aaa/Aa, A1 (e)                 AAA/AA (e)                                   3.6
Not Rated (f)                      Not Rated (f)                  Not Rated (f)                                2.5
                                                                                                            ---------
                                                                                                             100.0%
                                                                                                            =========
</TABLE>

NOTES TO STATEMENT OF INVESTMENTS:
    (a)  Securities payable on demand. The interest rate, which is subject to
    change, is based upon bank prime rates or an index  of market interest
    rates.
    (b)  Secured by letters of credit. At May 31, 1996, 52.7% of the Fund's
    net assets are backed by letters of credit issued by domestic banks,
    foreign banks, government agencies and brokerage firms.
    (c)  Fitch currently provides creditworthiness information for a limited
    number of investments.
    (d)  P1 and A1 are the highest ratings assigned tax exempt commercial
    paper by Moody's and Standard & Poor's, respectively.
    (e)  Notes which are not F, MIG or SP rated are represented by bond
    ratings of the issuers.
    (f)  Securities which, while not rated by Fitch, Moody's or Standard &
    Poor's have been determined by the Fund's Board of Directors to be of
    comparable quality to those rated securities in which the Fund may
    invest.



See independent accountants' review report and notes to financial statements.
<TABLE>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                 MAY 31, 1996 (UNAUDITED)
<S>                                                                                                  <C>             <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                         $327,101,769
    Interest receivable.....................................................                                            2,259,892
    Due from Distributor....................................................                                                1,467
    Prepaid expenses........................................................                                              101,125
                                                                                                                    _____________
                                                                                                                      329,464,253
LIABILITIES:
    Due to The Dreyfus Corporation and subsidiaries.........................                         $   132,796
    Due to Custodian........................................................                           3,522,627
    Accrued expenses and other liabilities..................................                             59, 267        3,714,690
                                                                                                 _______________
NET ASSETS  ................................................................                                         $325,749,563
                                                                                                                    =============
REPRESENTED BY:
    Paid-in capital.........................................................                                         $325,762,563
    Accumulated net realized (loss) on investments..........................                                              (13,000)
                                                                                                                    _____________
NET ASSETS at value.........................................................                                         $325,749,563
                                                                                                                    =============
Shares of Common Stock Outstanding:
    Class A Shares
      (15 billion shares of $.01 par value shares authorized)...............                                          310,662,386
                                                                                                                    =============
    Class B Shares
      (1 billion shares of $.01 par value shares authorized)................                                           15,377,586
                                                                                                                    =============
NET ASSET VALUE per share:
    Class A Shares
      ($310,371,989 / 310,662,386 shares)...................................                                                $1.00
                                                                                                                    =============
    Class B Shares
      ($15,377,574 / 15,377,586 shares).....................................                                                $1.00
                                                                                                                    =============

</TABLE>

See independent accountants' review report and notes to financial statements.
<TABLE>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                            SIX MONTHS ENDED MAY 31, 1996 (UNAUDITED)
<S>                                                                                            <C>                  <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                        $5,563,754
    EXPENSES:
      Management fee-Note 2(a)..............................................                    $   761,220
      Shareholder servicing costs-Note 2(c).................................                         94,307
      Registration fees.....................................................                         69,709
      Directors' fees and expenses-Note 2(d)................................                         19,275
      Professional fees.....................................................                         17,563
      Custodian fees........................................................                         15,952
      Distribution fees (Class B shares)-Note 2(b)..........................                         11,115
      Prospectus and shareholders' reports..................................                          5,728
      Miscellaneous.........................................................                          6,056
                                                                                             ______________
            TOTAL EXPENSES..................................................                      1,000,925
      Less-reduction in shareholder servicing costs due to
          undertakings-Note 2(c)............................................                         14,061
                                                                                             ______________
            NET EXPENSES....................................................                                           986,864
                                                                                                                   ___________
INVESTMENT INCOME-NET.......................................................                                         4,576,890
NET REALIZED GAIN ON INVESTMENTS-Note 1(b)..................................                                             3,870
                                                                                                                   ___________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                        $4,580,760
                                                                                                                   ___________


</TABLE>

See independent accountants' review report and notes to financial statements.
<TABLE>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                        YEAR ENDED               SIX MONTHS ENDED
                                                                                        NOVEMBER 30,               MAY 31, 1996
                                                                                           1995                     (UNAUDITED)
                                                                                      _______________          __________________
<S>                                                                                   <C>                          <C>
OPERATIONS:
    Investment income-net.............................................                $  9,688,956                 $  4,576,890
    Net realized gain (loss) on investments...........................                     (10,219)                       3,870
                                                                                      ____________                 _____________
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........                   9,678,737                    4,580,760
                                                                                      ____________                 _____________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares..................................................                  (9,661,080)                   (4,428,661)
      Class B shares..................................................                     (27,876)                     (148,229)
                                                                                      ____________                 _____________
          TOTAL DIVIDENDS.............................................                  (9,688,956)                   (4,576,890)
                                                                                      ____________                 _____________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares..................................................               2,123,635,457                1,263,443,351
      Class B shares..................................................                  13,057,352                   40,497,233
    Dividends reinvested:
      Class A shares..................................................                   8,659,640                    4,149,986
      Class B shares..................................................                       2,503                       81,912
    Cost of shares redeemed:
      Class A shares..................................................              (2,132,616,921)              (1,251,604,051)
      Class B shares..................................................                 (10,035,642)                 (28,225,773)
                                                                                      ____________                 _____________

        INCREASE IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS....                       2,702,389                   28,342,658
                                                                                      ____________                 _____________
            TOTAL INCREASE IN NET ASSETS..............................                   2,692,170                   28,346,528
NET ASSETS:
    Beginning of period...............................................                 294,710,865                  297,403,035
                                                                                      ____________                 _____________
    End of period.....................................................              $  297,403,035               $    325,749,563
                                                                                      ============                 =============

</TABLE>

See independent accountants' review report and notes to financial statements.

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Common Stock outstanding, total investment return, ratios to average net
assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.
<TABLE>


                                                                                     CLASS A SHARES
                                                     __________________________________________________________________________
                                                                                                              SIX MONTHS ENDED
                                                                      YEAR ENDED NOVEMBER 30,                   MAY 31, 1996
                                                     ____________________________________________________
PER SHARE DATA:                                      1991        1992        1993        1994       1995         (UNAUDITED)
                                                     _______     _______     ______      ______     ______       _____________
<S>                                                  <C>         <C>        <C>         <C>         <C>             <C>
    Net asset value, beginning of period..           $ 1.00      $ 1.00     $ 1.00      $ 1.00      $ 1.00          $ 1.00
                                                     _______     _______     ______      ______     ______       _____________
    INVESTMENT OPERATIONS;
    Investment income-net.................             .043        .027       .021        .023        .034            .015
                                                     _______     _______     ______      _____     ______       _____________
    DISTRIBUTIONS;
    Dividends from investment income-net..            (.043)      (.027)     (.021)      (.023)      (.034)          (.015)
                                                     _______     _______     ______      ______     ______       _____________
    Net asset value, end of period........           $ 1.00      $ 1.00     $ 1.00      $ 1.00      $ 1.00          $ 1.00
                                                     =======     =======     ======      ======     ======       =============
TOTAL INVESTMENT RETURN...................             4.36%       2.74%      2.10%       2.27%       3.41%           3.03%*
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets             .62%        .64%       .63%        .64%        .66%            .64%*
    Ratio of net investment income to
      average net assets..................             4.30%       2.71%      2.08%       2.22%       3.35%           3.01%*
    Net Assets, end of period (000's Omitted)      $342,595    $397,912   $352,147    $294,711    $294,379        $310,372
    *Annualized.


</TABLE>

See independent accountants' review report and notes to financial statements.

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
FINANCIAL HIGHLIGHTS (CONTINUED)
    Contained below is per share operating performance data for a share of
Common Stock outstanding, total investment return, ratios to average net
assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.
<TABLE>


                                                                                                     CLASS B SHARES
                                                                               ___________________________________________________
                                                                                           YEAR ENDED            SIX MONTHS ENDED
                                                                                           NOVEMBER 30,            MAY 31, 1996
                                                                                             1995(1)                (UNAUDITED)
                                                                                    ______________________     ___________________
<S>                                                                                           <C>                    <C>
PER SHARE DATA:
    Net asset value, beginning of period..................................                    $  1.00                $  1.00
                                                                                              ___________            ___________
    INVESTMENT OPERATIONS;
    Investment income-net.................................................                       .020                   .014
                                                                                              ___________            ___________
    DISTRIBUTIONS;
    Dividends from investment income-net..................................                      (.020)                 (.014)
                                                                                              ___________            ___________
    Net asset value, end of period........................................                    $  1.00                $  1.00
                                                                                              ===========            ===========
TOTAL INVESTMENT RETURN...................................................                       3.01%(2)               2.71%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets...............................                       1.10%(2)                .87%(2)
    Ratio of net investment income to average net assets..................                       2.83%(2)               2.66%(2)
   Decrease reflected in above expense ratios due to
      undertakings by the Manager.........................................                        .09%(2)                .25%(2)
    Net Assets, end of period (000's Omitted).............................                     $3,024                $15,378
    (1)  From March 31, 1995 (commencement of initial offering) to November 30, 1995.
    (2)  Annualized.

</TABLE>



See independent accountants' review report and notes to financial statements.

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    General Municipal Money Market Fund, Inc. (the "Fund") is registered
under the Investment Company Act of 1940 ("Act") as a diversified open-end
management investment company. The Fund's investment objective is to maximize
current income exempt from Federal income tax to the extent consistent with
the preservation of capital and the maintenance of liquidity. The Dreyfus
Corporation ("Manager") serves as the Fund's investment adviser. The Manager
is a direct subsidiary of Mellon Bank, N.A.
    Premier Mutual Fund Services, Inc. (the "Distributor") acts as the
distributor of the Fund's shares, which are sold to the public without a
sales load. Class A shares and Class B shares are identical except as to the
services offered to and the expenses borne by each class and certain voting
rights. Class B shares are subject to a Distribution Plan adopted pursuant to
Rule 12b-1 under the Act and, in addition, Class B shares are charged
directly for sub-accounting services provided by service agents at an annual
rate of .05% of the value of the average daily net assets of Class B.
    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 of $1.00.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, 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 premiums and original issue discounts on investments, is
earned from settlement date and recognized on the accrual basis. Realized
gain and loss from securities transactions are recorded on the identified
cost basis.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends daily from investment income-net. Such dividends are paid monthly.
Dividends from net realized capital gain 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. 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, which can distribute tax exempt
dividends, by complying with the applicable provisions of the Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income and
excise taxes.
    The Fund has an unused capital loss carryover of approximately $13,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1995. If not
applied, $2,800 of the carryover expires in fiscal 1998 and $10,200 expires
in fiscal 2003.
    As a result of the expiration of a prior year capital loss carryover,
$277,409 was reclassified from accumulated net realized loss to additional
paid in capital.
    At May 31, 1996, 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).

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
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 for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses, exceed 1-1/2% of the average value of the Fund's net
assets for any full fiscal year. There was no expense reimbursement for the
six months ended May 31, 1996.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, the Fund
directly bears the costs of preparing, printing and distributing prospectuses
and statements of additional information and of implementing and operating
the Class B Distribution Plan. In addition, the Fund reimburses the
Distributor for payments made to third parties for distributing the Fund's
Class B shares at an aggregate annual rate of .20 of 1% of the value of the
average daily net assets of Class B. During the six months ended May 31,
1996, $11,115 was charged to the Fund pursuant to the Class B Distribution
Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan, with respect to
Class A ("Class A Shareholder Services Plan"), the Fund reimburses Dreyfus
Service Corporation, a wholly-owned subsidiary of the Manager, an amount not
to exceed an annual rate of .25 of 1% of the value of the Fund's 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 the Fund and providing reports
and other information, and services related to the maintenance of shareholder
accounts. During the six months ended May 31, 1996, the Fund was charged an
aggregate of $27,772 pursuant to the Class A Shareholder Services Plan.
    Pursuant to the Fund's Shareholder Services Plan, with respect to Class B
("Class B Shareholder Services Plan"), the Fund pays the Distributor, at an
annual rate of .25 of 1% of the value of the average daily net assets of
Class B shares for servicing shareholder accounts. The services provided may
include personal services relating to shareholder accounts, such as answering
shareholder inquiries regarding the Fund and providing reports and other
information, and services related to the maintenance of shareholder accounts.
The Distributor may make payments to Service Agents (a securities dealer,
financial institution or other industry professional) in respect of their
services. The Distributor determines the amounts to be paid to Service
Agents.
    The Manager has undertaken through November 30, 1996, that if the
aggregate expenses of Class B of the Fund, (exclusive of certain expenses as
described above) exceed .85 of 1% the value of the average daily net assets
of Class B, the Manager will reimburse the expenses of the Fund under the
Class B Shareholder Services Plan relating to Class B to the extent of any
excess expense and up to the full fee payable under such Plan. During the six
months ended May 31, 1996, $14,061 was charged to the Fund pursuant to the
Class B Shareholder Services Plan, all of which was reimbursed by the
Manager.
    The Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of
the Manager, under a transfer agency agreement for providing personnel and
facilities to perform transfer agency services for the Fund. Such
compensation amounted to $31,967 during the six months ended May 31, 1996.
    (D) Each director who is not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $500
per meeting. The Chairman of the Board receives an additional 25% of such
compensation.

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL MUNICIPAL MONEY MARKET FUND, INC.
    We have reviewed the accompanying statement of assets and liabilities of
General Municipal Money Market Fund, Inc., including the statement of
investments, as of May 31, 1996, and the related statements of operations and
changes in net assets and financial highlights for the six month period ended
May 31, 1996. These financial statements and financial highlights are the
responsibility of the Fund's management.
    We conducted our review in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures
to financial data, and making inquiries of persons responsible for financial
and accounting matters. It is substantially less in scope than an audit
conducted in accordance with generally accepted auditing standards, which
will be performed for the full year with the objective of expressing an
opinion regarding the financial statements and financial highlights taken as
a whole. Accordingly, we do not express such an opinion.
    Based on our review, we are not aware of any material modifications that
should be made to the interim financial statements and financial highlights
referred to above for them to be in conformity with generally accepted
accounting principles.
    We have previously audited, in accordance with generally accepted
auditing standards, the statement of changes in net assets for the year ended
November 30, 1995 and financial highlights for each of the five years in the
period ended November 30, 1995 and in our report dated January 5, 1996, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.

                              [Ernst & Young LLP signature logo]

New York, New York
July 10, 1996

[Dreyfus lion "d" logo]
GENERAL MUNICIPAL
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
90 Washington Street
New York, NY 10286
TRANSFER AGENT &
DIVIDEND DISBURSING AGENT
Dreyfus Transfer, Inc.
One American Express Plaza
Providence, RI 02903


Further information is contained
in the Prospectus, which must
precede or accompany this report.


Printed in U.S.A.                        918/697SA965
[Dreyfus logo]
General Municipal
Money Market
Fund, Inc.
Semi-Annual
Report
May 31, 1996







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