GENERAL MUNICIPAL MONEY MARKET FUND INC
N-30D, 1997-08-01
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GENERAL MUNICIPAL MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to report the performance of General Municipal Money
Market Fund, Inc. for its six-month reporting period ended May 31, 1997 as
shown in the following table:
<TABLE>
<CAPTION>

                                                                                                   ANNUALIZED
                                                                   ANNUALIZED YIELD             EFFECTIVE YIELD*
                                                                  ___________________         _____________________
           <S>                                                          <C>                          <C>
           Class A Shares.........................                      3.01%                        3.05%
           Class B Shares.........................                      2.81%                        2.85%
</TABLE>




Money Market Overview
    Despite the predictions of many analysts who believed growth was slowing
at last, the U.S. economy remained upward bound throughout the period. In
fact, after posting a 3.8% gain during the fourth quarter of 1996, real Gross
Domestic Product (GDP) reached a zenith of 5.6% during the first three months
of 1997, a level not attained in a decade. Most recently, the widely watched
index of the National Association of Purchasing Management jumped to 57.1% in
May from 54.2% in April. The apparent pickup in manufacturing overshadowed
two Commerce Department reports that had pointed to a second-quarter slowdown
in national economic activity. Those April reports showed consumer spending
edging up just 0.1% _ the smallest increase since last September _ and personal
income posting a similarly small gain of only 0.1%.
    Alongside the news of surprisingly strong economic growth came another
surprise: inflation remained very low. The latest supporting evidence was a
drop in producer prices for April. At the same time, April's unemployment
rate hit 4.9%, the lowest level in 23 years. The Employment Cost Index also
showed minimal price pressure registering just 0.6% for the first quarter of
1997, a reduction from its 0.8% rise during the last quarter of 1996. Prior
to the release of these rather reassuring statistics, the Federal Reserve
Board (Fed) had increased overnight bank lending rates one quarter of a
percentage point at its March 25 Federal Open Market Committee meeting. While
many expected this to be the first in a series of moves, the Fed left rates
alone in May, leaving market participants guessing about what will happen
when the Fed meets again in July.
Market Environment/Portfolio
    Each year, as summer approaches, the short-term municipal market
experiences volatility that is reflective of the changing patterns of supply
and demand conditions during the period. These market "technicals" require
adjustments to portfolio strategy in anticipation of conditions such as: an
increase in available securities due to fund redemptions (April tax season),
a dearth of supply of high quality issues (end of June), and substantial new
money market issuance (mid-July financings). Our portfolio adjustments
attempt to structure your Fund in such a way as to take advantage of these
changing conditions in an effort to enhance your Fund's return while
maintaining our commitment to high quality holdings.
    In response to the expected changes in both cash flow and supply
conditions, we began preparations for extending your Fund's average maturity
in early June. By creating a calendar of upcoming new issues and by
subjecting each new issue to rigorous in-house credit review, we were
positioned to take advantage of those notes which we believe would be
attractive holdings for your Fund. We expect to continue to purchase notes
selectively through the summer months in an attempt to maximize your Fund's
current yield. As we endeavor to accomplish this, we will continue to commit
to those issues which meet our high quality investment guidelines and which
provide the appropriate level of liquidity for your Fund's needs.
Additionally, we will monitor those conditions which affect our marketplace
and adjust our investment policy where necessary to pursue competitive
returns.

    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 appreciate greatly your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Very truly yours,

                          [Richard J. Moynihan signature logo]

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
June 17, 1997
New York, N.Y.

* Annualized effective yield takes into account the effect of compounding and
is based upon dividends declared daily and reinvested monthly.
<TABLE>
<CAPTION>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                       MAY 31, 1997 (UNAUDITED)

                                                                                                   Principal
Tax Exempt Investments_100.0%                                                                       Amount          Value
                                                                                                 _____________    ___________
Alaska_3.5%
Alaska Housing Finance Corporation, VRDN
<S>                                                                                                 <C>            <C>
  3.90%, Series A (Liquidity Facility: Credit Suisse and Westdeutsche Landesbank) (a)            $  15,200,000. $  15,200,000
Arizona_7.6%
Arizona Educational Loan Marketing Corporation, Educational Loan Revenue, VRDN
  4%, Series A (BPA; Fuji Bank and Insured; MBIA) (a).......................                        10,675,000     10,675,000
Glendale Industrial Development Authority, HR, VRDN
  (West Valley Camelback) 3.90% (LOC; Northwest Corp.) (a,b)................                         8,300,000      8,300,000
Pima County Industrial Development Authority, Industrial Revenue, VRDN
  (Tuscon Electric) 3.90% (LOC; Barclays Bank) (a,b)........................                        14,100,000     14,100,000
California_7.3%
State of California, VRDN 3.80%, Series C-3 (SBPA; Bank of America) (a).....                         8,000,000      8,000,000
California Higher Education Loan Authority, Student Loan Revenue, Refunding
  3.95%, Series A, 5/1/98 (LOC; National Westminster Bank) (b)..............                        10,000,000     10,000,000
California Housing Finance Agency, Home Mortgage Revenue
  4%, Series J, 7/24/97 (Insured; FGIC).....................................                         5,600,000      5,600,000
California School Cash Reserve Program Authority, Revenue
  4.75%, Series A, 7/2/97 (Insured; MBIA)...................................                         8,000,000      8,005,886
Connecticut_8.2%
State of Connecticut Development Authority, VRDN (Connecticut Light and Power Co. Project)
  3.80%, Series A (LOC; Deutsche Bank) (a,b)................................                        28,700,000     28,700,000
State of Connecticut Special Assessment Unemployment Compensation Advance Fund, Revenue
  (Connecticut Unemployment) 3.90%, 7/1/97 (Insured and Liquidity; FGIC)....                         7,000,000      7,000,000
Delaware_.1%
Delaware Economic Development Authority, IDR, VRDN (Orient Chemical Corp. Project)
  4.225% (LOC; Sumitomo Bank) (a,b).........................................                           480,000        480,000
Florida_4.4%
Brevard County School Board, RAN 4.25%, 5/8/98..............................                        10,000,000     10,031,391
Broward County School District, Revenue Anticipation Renewal Notes 4.50%, 4/22/98                    8,900,000      8,945,744
Georgia_4.1%
Burke County Development Authority, PCR, Refunding (Oglethorpe Power Corp.):
  3.60%, Series A, 12/1/97 (Insured; AMBAC).................................                         5,000,000      5,000,000
  VRDN 3.85%, Series A (BPA; Credit Locale de France and Insured; FGIC) (a).                         7,900,000      7,900,000
Savannah Economic Development Authority, Exempt Facility Revenue, VRDN
  (Home Depot Project) 3.95% (LOC; Trust Co. Bank) (a,b)....................                         5,000,000      5,000,000
Hawaii_2.0%
Honolulu City and County, MFHR, VRDN (Halekua Gardens Project)
  4.10%, Series A (LOC; Bank of Tokyo-Mitsubishi) (a,b).....................                         8,471,000      8,471,000
Illinois_4.1%
Illinois Health Facilities Authority, Revenue, VRDN
  (Rehab Institute of Chicago) 3.90% (LOC; Bank of America) (a,b)...........                         13,500,000    13,500,000

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                      MAY 31, 1997 (UNAUDITED)
                                                                                                    Principal
Tax Exempt Investments (continued)                                                                   Amount          Value
                                                                                                    ___________   ___________
Illinois (continued)
Southwestern Development Authority, Environmental Improvement Revenue, VRDN
  (Shell Oil Co.-Wood River) 4.20% (Corp. Guaranty; Shell Oil Co.) (a)......                    $    4,050,000   $  4,050,000
Kentucky_.6%
Boone County, IDR, VRDN (Curtin Matheson Scientific Project)
  4.05% (LOC; Toronto-Dominion Bank) (a,b)..................................                         2,500,000      2,500,000
Louisiana_2.9%
West Baton Rouge Parish Industrial District Number 3, Revenue, VRDN
  (Dow Chemical Co. Project) 4.30% (Corp. Guaranty; Dow Chemical Co.) (a)...                        12,500,000     12,500,000
Michigan_3.6%
Macomb Township Economic Development Corporation, LOR, VRDN (ACR Industries Project)
  4% (LOC; Comerica Bank) (a,b).............................................                           600,000        600,000
Michigan Housing Development Authority, Rental Housing Revenue, Refunding, VRDN
  3.90%, Series C (LOC; Credit Suisse) (a,b)................................                         11,000,000    11,000,000
Michigan Strategic Fund, SWDR, VRDN (Grayling Generating Project)
  3.95% (LOC; Barclays Bank) (a,b)..........................................                         3,800,000      3,800,000
Missouri_2.3%
Missouri Health and Educational Facilities Authority, Health Facilities Revenue, VRDN
  (Deaconess Long Term Care) 3.95%, Series A (LOC; Bank One) (a,b)..........                         10,000,000    10,000,000
Nevada_1.2%
Washoe County, Water Facilities Revenue, VRDN (Sierra Pacific Power Co. Project)
  4.20% (LOC; Union Bank of Switzerland) (a,b)..............................                         5,400,000      5,400,000
New York_7.7%
New York City Housing Development Corporation, Special Obligation Revenue, VRDN
  (East 96th Street Project) 3.80%, Series A (LOC; Bank of Tokyo-Mitsubishi) (a,b)                  10,000,000     10,000,000
New York State Housing Finance Agency, Housing Revenue, VRDN (Normandie Court II)
  3.85%, Series A (LOC; Fleet Bank) (a,b)...................................                         4,200,000      4,200,000
Suffolk County, TAN 4%, Series I, 8/14/97 (LOC: Canadian Imperial Bank of Commerce,
  National Westminster Bank and Westdeutsche Landesbank) (b)................                         5,000,000      5,005,047
Triborough Bridge and Tunnel Authority, Special Obligation, VRDN
  3.85% (Insured and Liquidity; FGIC) (a)...................................                        14,000,000     14,000,000
Ohio_8.1%
Cincinnati City School District, Notes 4.37%, 9/18/97.......................                         7,830,000      7,838,300
Columbus, Sewer Revenue, Refunding, VRDN 3.80% (a)..........................                         7,400,000      7,400,000
Ohio Air Quality Development Authority, PCR, CP (Cleveland Electric)
  3.70%, Series B, 7/15/97 (Insured and Liquidity; FGIC)....................                        14,725,000     14,725,000
Ohio Housing Finance Agency, Mortgage Revenue
  3.65%, Series A-2, 3/2/98 (LOC; AIG Funding, Inc.) (b)....................                         5,000,000      5,000,000
Pennsylvania_4.9%
Allegheney County Hospital Development Authority, Revenue, VRDN (Health Center Presbyterian)
  3.90%, Series B (BPA; PNC Bank and Insured; MBIA) (a).....................                         6,100,000      6,100,000

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                   MAY 31, 1997 (UNAUDITED)
                                                                                                   Principal
Tax Exempt Investments (continued)                                                                   Amount          Value
                                                                                                    __________     __________
Pennsylvania (continued)
Schuylkill County Industrial Development Authority, RRR, VRDN (Northeastern Power Project)
  4.10%, Series B (LOC; Sumitomo Bank) (a,b)................................                     $  15,000,000    $15,000,000
Rhode Island_1.1%
Rhode Island Housing and Mortgage Financing Corporation, Homeownership Opportunity,
  Revenue 3.70%, Series 22-B, 12/2/97 (Insured; FGIC).......................                         4,900,000      4,900,000
Tennessee_2.8%
Morristown Industrial Development Board, IDR, VRDN (Camvac International Inc. Project)
  4.325% (LOC; Bankers Trust) (a,b).........................................                         3,000,000      3,000,000
Sevier County Public Building Authority, Local Government Public Improvement, VRDN:
  3.87%, Series A-2 (BPA; Kredietbank and Insured; AMBAC) (a)...............                         4,700,000      4,700,000
  3.87%, Series A-3 (BPA; Kredietbank and Insured; AMBAC) (a)...............                         4,500,000      4,500,000
Texas_19.5%
Brazos River Authority, PCR, Refunding, VRDN (Texas Utilities Electric Co.):
  4.10%, Series A (BPA; The Bank of New York and Insured; MBIA) (a).........                        13,500,000     13,500,000
  4.20%, Series C (BPA; The Bank of New York and Insured; MBIA) (a).........                        14,245,000     14,245,000
Brazos River Harbor Naval District, Harbor Revenue, VRDN:
  (BASF Corp. Project) 4.10% (Corp. Guaranty; BASF Corp.) (a)...............                         5,000,000      5,000,000
  (Dow Chemical Co. Project) 4.30%, Series A (Corp. Guaranty; Dow Chemical Co.) (a)                 12,800,000     12,800,000
Dallas County, Permanent Improvement
  3.75%, Series C, 6/17/97 (BPA; Union Bank of Switzerland).................                         4,640,000      4,640,000
Greater East Texas Higher Education Authority Inc., Student Loan Revenue
  4.15%, Series B, 9/1/97 (LOC; Student Loan Marketing Association) (a,b)...                         5,000,000      5,000,000
Panhandle-Plains Higher Education Authority, Student Loan Revenue, Refunding, VRDN
  3.95%, Series A (LOC; Student Loan Marketing Association) (a,b)...........                        12,700,000     12,700,000
State of Texas, TRAN 4.75%, 8/29/97.........................................                         8,000,000      8,015,003
Texas A & M University, University Financing Systems Revenues, CP
  3.45%, Series B, 7/24/97 (Guaranteed by; Texas A & M University Systems)..                         8,700,000      8,700,000
Virginia_1.9%
Pendleton County, IDR, VRDN (Greer Steel Project) 4.10% (LOC; PNC Bank) (a,b)                        3,415,000      3,415,000
Richmond Redevelopment and Housing Authority, MFHR (Richmeade LP Project)
  4.50%, 6/26/97............................................................                         4,800,000      4,800,000
West Virginia_.9%
Marion County, Community Solid Waste Disposal Facility Revenue, VRDN
  (Granttown Project) 3.95%, Series B (LOC; National Westminster Bank) (a,b)                         3,800,000      3,800,000
U.S. Related_1.2%
Government Development Bank of Puerto Rico, CP 3.30%, 6/13/97...............                         5,000,000      5,000,000
                                                                                                                _____________
TOTAL INVESTMENTS (cost $432,742,371).......................................                                    $432,742,371
                                                                                                               ==============

</TABLE>

<TABLE>
<CAPTION>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.

Summary of Abbreviations
<S>           <C>                                                <C>    <C>
AMBAC         American Municipal Bond Assurance Corporation      MFHR     Multi-Family Housing Revenue
BPA           Bond Purchase Agreement                            PCR      Pollution Control Revenue
CP            Commercial Paper                                   RAN      Revenue Anticipation Notes
FGIC          Financial Guaranty Insurance Company               RRR      Resource Recovery Revenue
HR            Hospital Revenue                                   SBPA     Standby Bond Purchase Agreement
IDR           Industrial Development Revenue                     SWDR     Solid Waste Disposal Revenue
LOC           Letter of Credit                                   TAN      Tax Anticipation Notes
LOR           Limited Obligation Revenue                         TRAN     Tax and Revenue Anticipation Notes
MBIA          Municipal Bond Investors Assurance                 VRDN     Variable Rate Demand Notes
                 Insurance Corporation
</TABLE>
<TABLE>
<CAPTION>

Summary of Combined Ratings (Unaudited)
Fitch (c)              or          Moody's             or         Standard & Poor's          Percentage of Value
____                               ____________                   ________________          ______________________
<S>                                <S>                            <S>                               <S>
F1+/F1                             VMIG1/MIG1, P1 (d)             SP1+/SP1, A1+/A1 (d)              93.3%
AAA/AA (e)                         Aaa/Aa, A1 (e)                 AAA/AA (e)                         3.1
Not Rated (f)                      Not Rated (f)                  Not Rated (f)                      3.6
                                                                                                   ________
                                                                                                   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, 1997, 43.3% 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 and Standard &
    Poor's have been determined by the Manager to be of comparable quality to
    those rated securities in which the Fund may invest.





SEE NOTES TO FINANCIAL STATEMENTS.
<TABLE>
<CAPTION>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                 MAY 31, 1997 (UNAUDITED)
                                                                                              Cost                  Value
                                                                                           _____________        _____________
<S>                              <C>                                                       <C>                  <C>
ASSETS:                          Investments in securities_See Statement of Investments    $432,742,371         $432,742,371
                                 Cash.......................................                                       1,063,025
                                 Interest receivable........................                                       2,830,044
                                 Prepaid expenses...........................                                          90,759
                                                                                                                _____________
                                                                                                                 436,726,199
                                                                                                                _____________
LIABILITIES:                     Due to The Dreyfus Corporation and affiliates                                       189,600
                                 Due to Distributor.........................                                           6,164
                                 Accrued expenses...........................                                         137,854
                                                                                                                _____________
                                                                                                                     333,618
                                                                                                                _____________
NET ASSETS..................................................................                                    $436,392,581
                                                                                                               ==============
REPRESENTED BY:                  Paid-in capital............................                                    $436,383,201
                                 Accumulated net realized gain (loss) on investments                                   9,380
                                                                                                                _____________
NET ASSETS..................................................................                                    $436,392,581
                                                                                                               ==============

                                                NET ASSET VALUE PER SHARE
                                                _________________________
                                                                                           Class A                 Class B
                                                                                        _____________           _____________
Net Assets..................................................................            $240,814,068            $195,578,513
Shares Outstanding..........................................................             241,094,395             195,570,081
NET ASSET VALUE PER SHARE...................................................                   $1.00                   $1.00
                                                                                               ======                 =======
</TABLE>








<TABLE>
<CAPTION>

SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                       SIX MONTHS ENDED MAY 31, 1997 (UNAUDITED)
INVESTMENT INCOME
<S>                              <C>                                                             <C>              <C>
INCOME                           Interest Income............................                                      $6,225,221
EXPENSES:                        Management fee_Note 2(a)...................                     $  837,645
                                 Shareholder servicing costs_Note 2(c)......                        222,648
                                 Registration fees..........................                        107,972
                                 Distribution fees (Class B)_Note 2(b)......                         84,561
                                 Professional fees..........................                         23,342
                                 Directors' fees and expenses_Note 2(d).....                         19,919
                                 Custodian fees.............................                         16,831
                                 Prospectus and shareholders' reports.......                            616
                                 Miscellaneous..............................                          5,741
                                                                                                ____________
                                       Total Expenses.......................                      1,319,275
                                 Less_reduction in shareholder servicing costs due to
                                     undertaking_Note 2(c)..................                        (126,842)
                                                                                                ____________
                                       Net Expenses.........................                       1,192,433
                                                                                                  ____________
INVESTMENT INCOME_NET.......................................................                       5,032,788
REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS_Note 1(b):
                                 Net realized gain (loss) on investments....                   $     28,460
                                 Net unrealized appreciation (depreciation) on investments           (8,845)
                                                                                                ____________
NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS......................                          19,615
                                                                                                ____________
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                      $5,052,403
                                                                                                 ===========




SEE NOTES TO FINANCIAL STATEMENTS.

</TABLE>
<TABLE>
<CAPTION>

GENERAL MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                   Six Months Ended
                                                                                      May 31, 1997              Year Ended
                                                                                      (Unaudited)            November 30, 1996
                                                                                  __________________        ___________________
OPERATIONS:
  <S>                                                                                   <C>                       <C>
  Investment income_net.........................................                     $  5,032,788              $  9,142,775
  Net realized gain (loss) on investments..........................                        28,460                    (6,076)
  Net unrealized appreciation (depreciation) on investments........                        (8,845)                   8,845
                                                                                  __________________        ___________________
      Net Increase (Decrease) in Net Assets Resulting from Operations                   5,052,403                 9,145,544
                                                                                  __________________        ___________________
DIVIDENDS TO SHAREHOLDERS FROM:
  Investment income_net:
    Class A shares.................................................                    (3,765,782)               (8,758,784)
    Class B shares.................................................                    (1,267,006)                 (383,991)
                                                                                  __________________        ___________________
      Total Dividends..............................................                    (5,032,788)               (9,142,775)
                                                                                  __________________        ___________________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
  Net proceeds from shares sold:
    Class A shares.................................................                   565,406,734             2,093,318,275
    Class B shares.................................................                   413,663,855                73,759,615
  Dividends reinvested:
    Class A shares.................................................                     3,613,409                 8,186,756
    Class B shares.................................................                     1,223,398                   265,333
  Cost of shares redeemed:
    Class A shares.................................................                  (585,078,877)           (2,139,025,002)
    Class B shares.................................................                  (236,808,374)              (59,557,960)
                                                                                  __________________        ___________________
      Increase (Decrease) in Net Assets from Capital Stock Transactions               162,020,145               (23,052,983)
                                                                                  __________________        ___________________
        Total Increase (Decrease) in Net Assets....................                   162,039,760               (23,050,214)
NET ASSETS:
  Beginning of Period..............................................                   274,352,821               297,403,035
                                                                                  __________________        ___________________
  End of Period...............................................                   $    436,392,581          $    274,352,821
                                                                                 ==================        ===================
</TABLE>



SEE NOTES TO FINANCIAL STATEMENTS.
<TABLE>
<CAPTION>

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.

                                                                                        Class A Shares
                                           __________________________________________________________________________________
                                            Six Months Ended
                                               May 31, 1997                        Year Ended November 30,
                                                                _____________________________________________________________
PER SHARE DATA:                                (Unaudited)      1996          1995          1994          1993          1992
    <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............             .015          .029          .034          .023          .021         .027
                                                ______         _____        ______         ______       ______        ______
    Distributions:
    Dividends from investment income_net         (.015)        (.029)        (.034)        (.023)        (.021)        (.027)
                                                ______         _____        ______         ______       ______        ______
    Net asset value, end of period....          $ 1.00        $ 1.00        $ 1.00        $ 1.00        $ 1.00        $ 1.00
                                                ======        ======       ========       =======       =======      =======
TOTAL INVESTMENT RETURN...............          3.03%*         2.97%         3.41%         2.27%         2.10%         2.74%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets      .65%*          .66%          .66%          .64%          .63%          .64%
    Ratio of net investment income
      to average net assets...........          3.01%*         2.93%         3.35%         2.22%         2.08%         2.71%
    Net Assets, end of period
      (000's Omitted).................        $240,814      $256,862      $294,379      $294,711      $352,147      $397,912
    *Annualized.


SEE 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.

                                                                                            Class B Shares
                                                                      _____________________________________________________
                                                                       Six Months Ended
                                                                         May 31, 1997          Year Ended November 30,
                                                                                               _____________________________
PER SHARE DATA:                                                          (Unaudited)                1996            1995(1)
                                                                      _________________           _______           ______
    Net asset value, beginning of period..............                      $ 1.00                 $ 1.00          $ 1.00
                                                                           _______                 _______          ______
    Investment Operations:
    Investment income_net.............................                        .014                   .027            .020
                                                                           _______                 _______          ______
    Distributions:
    Dividends from investment income_net..............                       (.014)                 (.027)          (.020)
                                                                           _______                 _______          ______
    Net asset value, end of period....................                      $ 1.00                 $ 1.00          $ 1.00
                                                                           =======                 =======         =======
TOTAL INVESTMENT RETURN...............................                       2.83%(2)               2.70%           3.01%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets...........                        .89%(2)                .85%           1.10%(2)
    Ratio of net investment income
      to average net assets...........................                       3.00%(2)               2.65%           2.83%(2)
    Decrease reflected in above expense ratios
      due to undertakings by the Manager..............                        .32%(2)                .29%            .09%(2)
    Net Assets, end of period (000's Omitted).........                    $195,579                $17,491         $3,024
    (1)  From March 31, 1995 (commencement of initial offering) to November 30, 1995.
    (2)  Annualized.
</TABLE>


SEE 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") is the distributor
of the Fund's shares, which are sold to the public without a sales load. The
Fund is authorized to issue 16 billion shares of $.01 par value Common Stock.
The Fund is currently authorized to issue two classes of shares: Class A (15
billion shares authorized) and Class B (1 billion shares authorized). 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 per share of $1.00.
    The Fund's financial statements are prepared in accordance with generally
accepted accounting principles 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, 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. Cost of investments represents amortized cost.
    (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 $19,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1996. If not
applied, $2,800 of the carryover expires in fiscal 1998, $10,200 expires in
fiscal 2003 and $6,000 expires in fiscal 2004.
    As a result of the expiration of a prior year capital loss carryover,
$281,275 was reclassified from accumulated net realized loss to additional
paid-in capital.
    At May 31, 1997, 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 that if in any full fiscal year the aggregate expenses of the Fund,
exclusive of taxes, brokerage, interest on borrowings and extraordinary
expenses, exceed 1-1\2% of the average value of the Fund's net assets, the
Fund may deduct from payments to be made to the Manager, or the Manager will
bear such excess expense. There was no expense reimbursement for the period
ended May 31, 1997.
    (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 period ended May 31, 1997,
$84,561 was charged to the Fund pursuant to the Class B Distribution Plan.
    (C) Under the 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
period ended May 31, 1997, the Fund was charged an aggregate of $41,164
pursuant to the Class A Shareholder Services Plan.
    Under the 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 had undertaken from December 1, 1996 through May 30, 1997,
that if the aggregate expenses of Class B of the Fund, exclusive of taxes,
brokerage, interest on borrowings and extraordinary expenses, exceeded
specified annual percentages 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. The Manager has currently undertaken
from May 31, 1997 through June 30, 1997 that if the aggregate expenses of
Class B of the Fund, (exclusive of certain expenses as described above)
exceed .95 of 1% of 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 period ended May 31,
1997, $126,842 was charged to the Fund pursuant to the Class B Shareholder
Services Plan, of which all 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 $33,913 during the period ended May 31, 1997.
    (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.
[Dreyfus lion "d" logo]
Registration Mark
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.
P.O. Box 9671
Providence, RI 02940





Printed in U.S.A.                        918/697SA975
[Dreyfus logo]
Registration Mark

General Municipal
Money Market
Fund, Inc.
Semi-Annual
Report
May 31, 1997



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