DREYFUS MUNICIPAL MONEY MARKET FUND INC
N-30D, 1995-07-31
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LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this annual report for the Dreyfus
Municipal Money Market Fund. For the period ended May 31, 1995, the yield
provided by your Fund was 2.94%. After taking into account the effect of
compounding, the effective yield was 2.98%.*  Dividends of approximately
$.029 per share paid during the period were exempt from Federal income tax.**
    Federal Reserve Board action since our last letter was limited to just
one 50 basis point tightening move, which represented a decrease in magnitude
from previous actions. The fact that the increase was smaller reflected, in
part, the belief that some slowing in the economy had occurred. However, as
some economic indicators had continued to conflict with that sentiment, the
argument for a moderate hike appeared to be in order.  More recent events
suggest the Fed may ease soon and, in large part, market levels now reflect
those expectations.
    While market fundamentals do affect the short-term municipal market, the
overriding influence continues to be market technicals (i.e. supply/demand).
Since the rates on those securities in the portfolio which provide the
highest degree of liquidity (1-day and 7-day demand notes) are adjusted on a
daily or weekly basis, your Fund's yield reflects these rapid adjustments and
fluctuates accordingly. Currently, rates on such securities provide an
attractive return, trading at better than 75% of the taxable overnight
repurchase rate. We anticipate that these yields will drop significantly in
the coming weeks as many holdings in municipal money market funds mature at
the end of June. However, if previous summer technicals are repeated, we
expect the situation to reverse in late July and August as issuers return to
the market with their summer financings.
    In the wake of the Orange County, California bankruptcy filing in
December, we continue to devote our resources to locating those credits which
achieve our high internal standards and which provide your Fund with
attractive returns.  We have included a current Statement of Investments and
recent financial statements for your review and look forward to serving your
investment needs in the future.
                              Very truly yours,
                          .
                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
June 16, 1995
New York, N.Y.
*  Effective yield is based upon dividends declared daily and reinvested
monthly.
**Some income may be subject to the Federal Alternative Minimum Tax (AMT) for
certain shareholders.
<TABLE>
<CAPTION>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                                             MAY 31, 1995
                                                                                                        PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                           AMOUNT           VALUE
                                                                                                   --------------   --------------
<S>                                                                                                <C>              <C>
ALABAMA-4.8%
Alabama Industrial Development Authority, SWDR, VRDN (Pine City Fiber Co.
Project)
    4.30% (LOC; Barclays Bank) (a,b)........................................                       $  39,000,000    $  39,000,000
Birmingham Medical Clinic Board, Revenue, VRDN (University of Alabama)
    4.35% (LOC; Morgan Guaranty Trust Co.) (a,b)............................                           5,000,000        5,000,000
ALASKA-1.3%
Valdez, Marine Terminal Revenue, Refunding, CP (Arco Transportation Project)
    4.20%, Series C, 7/21/95................................................                          11,800,000       11,800,000
CALIFORNIA-4.1%
California School Cash Reserve Program Authority (Pooled Project)
    4.50%, Series A, 7/5/95.................................................                          15,000,000       15,010,088
Los Angeles County Metropolitan Transportation Authority, Sales Tax Revenue,
    Refunding, VRDN
    3.90%, Series A (Insured; MBIA and SBPA; Industrial Bank of Japan) (a)..                          13,000,000       13,000,000
Los Angeles Unified School District, TRAN 4.50%, 7/10/95....................                          10,000,000       10,009,276
COLORADO-2.8%
Colorado Student Obligation Bond Authority, Student Loan Revenue, VRDN
    4.15%, Series A (LOC; Student Loan Marketing Association) (a,b).........                          12,200,000       12,200,000
Denver Urban Renewal Authority, Tax Increment Revenue (Downtown Denver
Renewal)
    4.75%, Series A, 8/24/95 (Collateralized in; U.S. Treasury Bills).......                            14,115,000     14,115,000
CONNECTICUT-2.8%
Connecticut Housing Financing Authority, Housing Mortgage Financing Program:
    4.40%, Series E, 11/15/95 (Escrowed in; U.S. Government Securities).....                            13,200,000    13,200,000
    4.50%, Series E2, 11/15/95 (Escrowed in; U.S. Government Securities)....                            12,400,000    12,400,000
DELAWARE-9.9%
Delaware Economic Development Authority, Revenue, VRDN
    (Hospital Billing and Collection Service Ltd. Project):
      4.10%, Series A (Insured; MBIA) (a)...................................                            25,000,000     25,000,000
      4.10%, Series B (Insured; MBIA) (a)...................................                            25,000,000     25,000,000
      4.10%, Series C (Insured; MBIA) (a)...................................                            41,400,000     41,400,000
DISTRICT OF COLUMBIA-1.8%
District of Columbia, VRDN (General Fund Recovery):
    4.75%, Series B (LOC; Union Bank of Switzerland) (a,b)..................                             5,100,000      5,100,000
    4.75%, Series B-3 (LOC; Union Bank of Switzerland) (a,b)................                            11,700,000     11,700,000
FLORIDA-1.3%
Sarasota County Health Facility Authority, HR, VRDN (Aces Venice Hospital
Project)
    4.65% (LOC; Krediet Bank) (a,b).........................................                            12,500,000     12,500,000
GEORGIA-1.4%
Athens-Clarke County Industrial Development Authority, IDR, VRDN
    (Nakanishi Manufacturing Corp. Project) 4.40% (LOC; Sumitomo Bank) (a,b)                             6,000,000      6,000,000
Rockdale County Development Authority, Industrial Revenue, VRDN
    (Liochem Inc. Project) 4.70% (LOC; Sanwa Bank) (a,b)....................                             7,000,000      7,000,000




DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                                 MAY 31, 1995
                                                                                                          PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                        AMOUNT          VALUE
                                                                                                     -------------- --------------

HAWAII-1.1%
Honolulu City and County, Multi-Family Revenue, VRDN (Royal Kunia Gardens)
    4.40%, Series B (LOC; Bank of Tokyo) (a,b)..............................                        $    9,900,000   $  9,900,000
ILLINOIS-3.3%
Illinois Development Finance Authority, PCR, VRDN (Illinois Power Co.)
    4.15%, Series C (LOC; Mitsubishi Bank) (a,b)............................                            10,400,000     10,400,000
Illinois Health Facilities Authority, Revenue, VRDN (Revolving Fund Pooled
Financing)
    4.20%, Series C (LOC; First National Bank of Chicago) (a,b).............                            16,250,000     16,250,000
Southwestern Development Authority, SWDR, VRDN (Shell Oil Co. Wood River
Project)
    4.45% (Corp Guaranty; Shell Oil Co.) (a)................................                             4,400,000      4,400,000
INDIANA-1.6%
Fort Wayne Hospital Authority, HR, VRDN (Parkview Memorial Hospital)
    4.25%, Series B (LOC; Fuji Bank) (a,b)..................................                             4,500,000      4,500,000
City of Petersburg, SWDR, VRDN (Indianapolis Power and Light Co. Project)
    4.10%, Series A (Corp. Guaranty; Indianapolis Power and Light Co.) (a)..                            10,000,000     10,000,000
IOWA-4.0%
Iowa Finance Authority, SWDR, VRDN (Cedar River Paper Co. Project)
    4.45%, Series A (LOC; Swiss Bank Corp.) (a,b)...........................                            37,100,000     37,100,000
KANSAS-4.0%
Butler County, Solid Waste Disposal and Cogeneration Revenue, VRDN
    (Texaco Refining and Marketing Project) 4.50%, Series B (LOC; Bank of Tokyo) (a,b)                  25,500,000     25,500,000
Topeka, MFHR, VRDN (Topeka Retirement Center Limited)
    4.275% (LOC; Krediet Bank) (a,b)........................................                             6,970,000      6,970,000
Wichita, PCR, Refunding, VRDN (CIC Industries Inc. Project)
    4.70% (LOC; The Bank of New York) (a,b).................................                             5,000,000      5,000,000
KENTUCKY-2.3%
City of Carroll, Collateralized Solid Waste Disposal Facilities Revenue, VRDN
    (Utility Co. Project) 4.45%, Series A (a)...............................                            17,000,000     17,000,000
Daviess County, Solid Waste Disposal Facility Revenue, VRDN (Scott Paper Co.
Project)
    4.45%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b)..................                             4,500,000      4,500,000
LOUISIANA-4.9%
Louisiana Public Facility Authority, School Board Advance Funding
    4.60%, 8/31/95 (GIC; American International Group)......................                            12,050,000     12,061,559
New Orleans Aviation Board, Revenue, VRDN (Passenger Facility Charge Project)
    4.45% (LOC: Banque Paribas and Canadian Imperial Bank of Commerce) (a,b)                            10,000,000     10,000,000
West Baton Rouge Parish Industrial District No. 3, Revenue, VRDN
    (Dow Chemical Co. Project) 4.50% (Corp. Guaranty; Dow Chemical Co.) (a).                            23,600,000     23,600,000
MAINE-1.6%
Orrington, RRR, VRDN (Penobscott Energy Recovery Co. Project)
    5.025%, Series B (LOC: Bank of Nova Scotia, Bankers Trust, Canadian
Imperial Bank of Commerce, Long-Term Credit Bank of Japan, and Toronto Dominian Bank) (a,b)             14,520,000     14,520,000

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                                 MAY 31, 1995
                                                                                                        PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                      AMOUNT           VALUE
                                                                                                   --------------    --------------

MARYLAND-.6%
Baltimore County, Housing Mortgage Revenue, Refunding, VRDN (Spring Hill)
    4% (LOC; Sumitomo Bank) (a,b)...........................................                        $  5,750,000     $  5,750,000
MASSACHUSETTS-1.4%
Massachusetts Health and Education Facilities Authority, Revenue
    (Boston Univeristy) 4.10%, Series H, 6/6/95 (LOC; First Chicago Corp.) (b)                        13,000,000       13,000,000
MICHIGAN-6.3%
Kent Hospital Finance Authority, Hospital Facility Revenue, VRDN
    (Butterworth Hospital) 4.20%, Series A (LOC; Sanwa Bank) (a,b)..........                           9,100,000        9,100,000
Michigan Hospital Finance Authority, Revenue, VRDN
    (Hospital Equipment Loan Program) 3.95% (LOC; Comerica Bank) (a,b)......                           3,800,000        3,800,000
Michigan Housing Development Authority, Rental Housing Revenue, VRDN
    4.10%, Series C (LOC: Credit Suisse) (a,b)..............................                          17,000,000       17,000,000
Michigan Strategic Fund, SWDR, VRDN (Grayling Generating Project)
    4.30% (LOC; Barclays Bank) (a,b)........................................                           8,000,000        8,000,000
Midland County Economic Development Corp., Economic Development
    Limited Obigation Revenue, VRDN (Dow Chemical Co. Project)
    4.60%, Series A (Corp. Guaranty; Dow Chemical Co.) (a)..................                          21,000,000       21,000,000
MONTANA-2.3%
Montana Board of Investment, RRR, VRDN (Colstrip Project)
    4.70% (LOC; Fuji Bank) (a,b)............................................                          21,050,000       21,050,000
NEBRASKA-1.5%
Nebraska Higher Education Loan Program Inc., Revenue, VRDN
    (Multiple Mode-Student Loan) 3.90%, Series A (Insured; MBIA) (a)........                          12,995,000       12,995,000
Nebraska Investment Finance Authority, HR, VRDN (Multiple Mode Depreciation
Assets)
    4.10%, Series A (Insured; FGIC) (a).....................................                           1,360,000        1,360,000
NEW JERSEY-.5%
New Jersey Housing and Mortgage Finance Agency, Revenue, Statewide Mortgage
    4.20%, 9/29/95 (LOC; Bayerische Landesbank) (b).........................                           5,095,000        5,095,000
NEW YORK-2.3%
New York State Energy, Research and Development Authority, PCR, VRDN
    (Niagara Mohawk Power Co. Project)
    4.40%, Series A (LOC; Toronto-Dominion Bank) (a,b)......................                           8,500,000        8,500,000
Suffolk County, TAN 4.50%, Series II, 9/14/95...............................                          13,000,000       13,015,065
NORTH CAROLINA-.4%
North Carolina Medical Care Community, HR, VRDN
    (Pooled Equipment Financing Project) 4.10% (Insured; MBIA) (a)..........                           3,400,000        3,400,000
OHIO-1.8%
Ohio Water Development Authority, PCR (Edison Project)
    4.25%, 9/1/95 (LOC; Barclays Bank) (b)..................................                           5,000,000        5,000,000
University of Cincinnati, General Receipt, BAN 4.75%, 8/30/95...............                          12,000,000       12,019,934

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                                 MAY 31, 1995
                                                                                                        PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                      AMOUNT           VALUE
                                                                                                   --------------   --------------

PENNSYLVANIA-1.8%
Columbia County Industrial Development Authority, IDR, VRDN (Kleerdex Co.
Project)
    4.45% (LOC; Bank of Tokyo) (a,b)........................................                       $   4,800,000   $    4,800,000
Pennsylvania Higher Education Assistance Agency, Student Loan Revenue, VRDN
    4.20%, Series A (LOC; Student Loan Marketing Association) (a,b).........                          12,100,000       12,100,000
SOUTH CAROLINA-.9%
York County, Industrial Revenue, VRDN (Textron Project) 5.63% (LOC; Bankers Trust) (a,b)               7,500,000        7,500,000
TENNESSEE-1.2%
Franklin, IDB, Multi-Family Revenue, VRDN (Landings Project)
    3.65%, Series C (LOC; Citibank) (a,b)...................................                            10,700,000     10,700,000
TEXAS-15.9%
Greater East Texas Higher Education Authority Inc., Student Loan Revenue:
    4.50%, Series B, 7/1/95 (LOC; Student Loan Marketing Association) (b)...                             9,000,000      9,000,000
    VRDN:
      Refunding, 4%, Series A (LOC; Student Loan Marketing Association) (a, b)                          10,000,000     10,000,000
      4.35%, Series B (LOC; Student Loan Marketing Association) (a, b)......                            24,000,000     24,000,000
Gulf Coast Waste Disposal Authority, VRDN (Amoco Oil Co. Project):
    PCR 4.45% (Corp. Guaranty; Amoco Credit Corp.) (a)......................                            32,700,000     32,700,000
    SWDR, Refunding 4.45% (Corp: Guaranty; Amoco Credit Corp.) (a)..........                             6,000,000      6,000,000
Harris County Health Facilities Development Corp., HR, VRDN
    (Memorial Hospital Systems Project) 4.80% (LOC; Societe Generale) (a,b).                            15,900,000     15,900,000
North Texas Higher Education Authority Inc., Student Loan Revenue, VRDN
    4.30% (LOC; Fuji Bank) (a,b)............................................                            19,800,000     19,800,000
San Antonio, Electric and Gas Revenue, CP 4.15%, Series A, 7/24/95
    (LOC: Bank of Tokyo, Credit Suisse, Mitsubishi Bank, Sanwa Bank, Sumitomo
    Bank, Texas Commerce Bank, Toronto Dominion Bank and Union Bank of Switzerland) (b)                 10,500,000     10,500,000
State of Texas, TRAN 5%, 8/31/95............................................                            20,000,000     20,040,345
UTAH-4.6%
Intermountain Power Agency, Power Supply Revenue, CP
    4.05%, Series E, 6/8/95 (LOC; Industrial Bank of Japan) (b).............                            30,300,000     30,300,000
Utah Board of Regents, Student Loan Revenue, Refunding, VRDN
    4.20%, Series A (LOC; Student Loan Marketing Association) (a,b).........                            12,500,000     12,500,000
VIRGINIA-1.9%
Charles City and County Industrial Development Authority, Exempt Facility
Revenue,
    VRDN (Chambers Development Inc. Project)
    4.40% (LOC; North Carolina National Bank) (a,b).........................                             9,000,000      9,000,000
Richmond Industrial Development Authority, Revenue, VRDN
    (Cogentrix of Richmond Project) 4.60%, Series A (LOC; Banque Paribas) (a,b)                          9,000,000      9,000,000
WASHINGTON-.9%
Seattle, Municipality Metropolitan Sewer Revenue, BAN 3.50%, 7/1/95.........                             8,655,000      8,648,877

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                                 MAY 31, 1995
                                                                                                          PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                        AMOUNT           VALUE
                                                                                                     --------------  -------------

WEST VIRGINIA-.9%
Marion County, Commission Solid Waste Disposal Facility Revenue, VRDN
    (Granttown Project) 4.30%, Series B (LOC; National Westminster Bank) (a,b)                      $    8,000,000  $   8,000,000
WISCONSIN-1.8%
City of Ashwaubenon, IDR, VRDN (Bemis Corp. Project)
    5.85% (LOC; Northwest Bank of Minneapolis) (a,b)........................                             3,000,000      3,000,000
Milwaukee Housing Authority, MFHR, VRDN (Yankee Hill Apartments)
    3.65% (LOC; Citibank) (a,b).............................................                            14,000,000     14,000,000
                                                                                                                    --------------
TOTAL INVESTMENTS (cost $928,668,351).......................................                                         $928,710,144
                                                                                                                    ==============
</TABLE>
<TABLE>
<CAPTION>
SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <C>     <C>
BAN           Bond Anticipation Notes                            MFHR    Multi-Family Housing Revenue
CP            Commercial Paper                                   PCR     Pollution Control Revenue
FGIC          Financial Guaranty Insurance Company               RRR     Resources Recovery Revenue
GIC           Guaranteed Investment Contract                     SBPA    Standby Bond Purchase Agreement
HR            Hospital Revenue                                   SWDR    Solid Waste Disposal Revenue
IDB           Industrial Development Board                       TAN     Tax Anticipation Notes
IDR           Industrial Development Revenue                     TRAN    Tax and Revenue Anticipation Notes
LOC           Letter of Credit                                   VRDN    Variable Rate Demand Notes
MBIA          Municipal Bond Investors Assurance
</TABLE>

<TABLE>
<CAPTION>

SUMMARY OF COMBINED RATINGS (UNAUDITED)
FITCH (C)              OR          MOODY'S             OR         STANDARD & POOR'S            PERCENTAGE OF VALUE
- ---------                          ---------                      --------------------        -----------------------
<S>                                <C>                            <C>                                 <C>
F1+/F1                             VMIG1/MIG1, P1 (d)             SP1+/SP1, A1+/A1 (d)                 97.9%
Not Rated (e)                      Not Rated (e)                  Not Rated (e)                         2.1
                                                                                                    --------
                                                                                                      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, 1995, 59.4% of the Fund's
    net assets are backed by letters of credit issued by domestic banks,
    foreign banks, brokerage firms, corporations and government agencies.
(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) 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 notes to financial statements.
<TABLE>
<CAPTION>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                                  MAY 31, 1995
<S>                                                                                                  <C>            <C>
ASSETS:
    Investments in securities, at value
      (cost $928,668,351)-see statement.....................................                                         $928,710,144
    Interest receivable.....................................................                                            7,260,761
    Prepaid expenses........................................................                                              111,996
                                                                                                                    --------------
                                                                                                                      936,082,901
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                         $   418,867
    Due to Custodian........................................................                           2,041,276
    Accrued expenses and other liabilities..................................                             312,049        2,772,192
                                                                                                     ------------    -------------
NET ASSETS  ................................................................                                         $933,310,709
                                                                                                                    ==============
REPRESENTED BY:
    Paid-in capital.........................................................                                         $935,113,042
    Accumulated undistributed investment income-net.........................                                              133,931
    Accumulated net realized (loss) on investments..........................                                           (1,978,057)
    Accumulated gross unrealized appreciation on investments................                                               41,793
                                                                                                                    --------------
NET ASSETS at value applicable to 935,113,042 shares outstanding
    (5 billion shares of $.01 par value Common Stock authorized)............                                         $933,310,709
                                                                                                                    ==============
NET ASSET VALUE, offering and redemption price per share
    ($933,310,709 / 935,113,042 shares).....................................                                                $1.00
                                                                                                                           =======

</TABLE>











See notes to financial statements.
<TABLE>
<CAPTION>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                                                    YEAR ENDED MAY 31, 1995
<S>                                                                                                 <C>               <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                          $38,760,431
    EXPENSES:
      Management fee-Note 2(a)..............................................                         $5,500,256
      Shareholder servicing costs-Note 2(b).................................                            957,339
      Custodian fees........................................................                            100,137
      Registration fees.....................................................                             51,460
      Professional fees.....................................................                             51,354
      Directors' fees and expenses--Note 2(c)...............................                             42,854
      Prospectus and shareholders' reports..................................                             33,130
      Miscellaneous.........................................................                             35,774
                                                                                                     ------------
          TOTAL EXPENSES....................................................                                            6,772,304
                                                                                                                     -------------
          INVESTMENT INCOME-NET.............................................                                           31,988,127
REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
    Net realized gain on investments-Note 1(b)..............................                       $     64,104
    Net unrealized appreciation on investments..............................                             34,481
                                                                                                     ------------
          NET REALIZED AND UNREALIZED GAIN ON INVESTMENTS...................                                               98,585
                                                                                                                     -------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                          $32,086,712
                                                                                                                     =============


</TABLE>












See notes to financial statements.
<TABLE>
<CAPTION>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                                       YEAR ENDED MAY 31,
                                                                                               -----------------------------------
                                                                                                      1994              1995
                                                                                               -----------------  ----------------
<S>                                                                                             <C>                <C>
OPERATIONS:
    Investment income-net..................................................                     $     25,779,255   $   31,988,127
    Net realized gain on investments.......................................                              508,174           64,104
    Net unrealized appreciation on investments for the year................                                6,158           34,481
                                                                                               -----------------  ----------------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS.................                           26,293,587       32,086,712
                                                                                               -----------------  ----------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net..................................................                          (25,779,255)     (31,988,127)
                                                                                                ----------------  ----------------
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold..........................................                        4,240,427,196    3,482,290,984
    Dividends reinvested...................................................                           18,349,521       22,043,236
    Cost of shares redeemed................................................                       (4,556,104,173)  (3,688,123,812)
                                                                                                ----------------  ----------------
      (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS.............                         (297,327,456)    (183,789,592)
                                                                                                ----------------  ----------------
          TOTAL (DECREASE) IN NET ASSETS...................................                         (296,813,124)    (183,691,007)
NET ASSETS:
    Beginning of year......................................................                        1,413,814,840    1,117,001,716
                                                                                                ----------------  ----------------
    End of year (including undistributed investment income-net:
      $133,931 in 1994 and in 1995)........................................                       $1,117,001,716    $ 933,310,709
                                                                                                ================  ================

</TABLE>









See notes to financial statements.

DREYFUS 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 year indicated. This information
has been derived from the Fund's financial statements.
<TABLE>
<CAPTION>


                                                                                         YEAR ENDED MAY 31,
                                                                 ---------------------------------------------------------------
PER SHARE DATA:                                                  1991           1992           1993          1994          1995
                                                                 ---------     ---------     ---------     --------    ---------
<S>                                                              <C>           <C>           <C>           <C>         <C>
    Net asset value, beginning of year...........                $  .9973      $  .9975      $  .9981      $  .9983    $  .9983
                                                                 ---------     ---------     ---------     ---------   ---------
    INVESTMENT OPERATIONS:
    Investment income-net........................                   .0492         .0341         .0221         .0198       .0294
    Net realized and unrealized gain (loss) on investments          .0002         .0005         .0002           --       (.0002)
                                                                 ---------     ---------     ---------     ---------   ---------
      TOTAL FROM INVESTMENT OPERATIONS...........                   .0494         .0346         .0223         .0198       .0292
                                                                 ---------     ---------     ---------     ---------   ---------
    DISTRIBUTIONS;
    Dividends from investment income-net.........                  (.0492)       (.0340)       (.0221)       (.0198)     (.0294)
                                                                 ---------     ---------     ---------     ---------   ---------
    Net asset value, end of year.................                $  .9975      $  .9981      $  .9983      $  .9983    $  .9981
                                                                 =========     =========     =========     =========   =========
TOTAL INVESTMENT RETURN..........................                  5.04%         3.46%         2.23%         2.00%       2.98%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......                   .59%          .62%          .62%          .62%        .62%
    Ratio of net investment income to average net assets           4.95%         3.41%         2.22%         1.98%       2.91%
    Net Assets, end of year (000's Omitted)......            $1,818,864    $1,498,772    $1,413,815    $1,117,002    $933,311




</TABLE>







See notes to financial statements.

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a diversified open-end management investment company. Dreyfus Service
Corporation, until August 24, 1994, acted as the exclusive distributor of the
Fund's shares, which are sold to the public without a sales charge. Dreyfus
Service Corporation is a wholly-owned subsidiary of The Dreyfus Corporation
("Manager"). Effective August 24, 1994, the Manager became a direct
subsidiary of Mellon Bank, N.A.
    On August 24, 1994, Premier Mutual Fund Services, Inc. (the
"Distributor") was engaged as the Fund's distributor. The Distributor,
located at One Exchange Place, Boston, Massachusetts 02109, is a wholly-owned
subsidiary of FDI Distribution Services, Inc., a provider of mutual fund
administration services, which in turn is a wholly-owned subsidiary of FDI
Holdings, Inc., the parent company of which is Boston Institutional Group,
Inc.
    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 $1,338,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to May 31, 1995. If not
applied, the carryover expires in fiscal 1996.
    At May 31, 1995, the cost of investments for Federal income tax purposes
was substantially the same as the cost for financial reporting purposes (see
the Statement of Investments).
NOTE 2-MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("Agreement") with the Manager,
the management fee is computed at the annual rate of 1/2 of 1% of the average
daily value of the Fund's net assets and is
DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
payable monthly. The Agreement provides for an expense reimbursement from the
Manager should the Fund's aggregate expenses, exclusive of taxes, interest on
borrowings, brokerage commissions and extraordinary expenses, exceed the
expense limitation of any state having jurisdiction over the Fund. The most
stringent state expense limitation applicable to the Fund presently requires
reimbursement of expenses in any full fiscal year that such expenses exceed 2
1/2% of the first $30 million, 2% of the next $70 million and 1 1/2% of the
excess over $100 million of the average value of the Fund's net assets in
accordance with California "blue sky" regulations. There was no expense
reimbursement for the year ended May 31, 1995.
    (B) Pursuant to the Fund's Shareholder Services Plan, the Fund reimburses
Dreyfus Service Corporation an amount not to exceed an annual rate of .25 of
1% of the value of the Fund's average daily net assets 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. During the year ended May
31, 1995, the Fund was charged an aggregate of $356,051 pursuant to the
Shareholder Services Plan.
    (C) Prior to August 24, 1994, certain officers and directors of the Fund
were "affiliated persons," as defined in the Act, of the Manager and/or
Dreyfus Service Corporation. Each director who is not an "affiliated person"
receives an annual fee of $4,500 and an attendance fee of $500 per meeting.
The Chairman of the Board receives an additional 25% of such compensation.


DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF DIRECTORS
DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
    We have audited the accompanying statement of assets and liabilities of
Dreyfus Municipal Money Market Fund, Inc., including the statement of
investments, as of May 31, 1995, and the related statement of operations for
the year then ended, the statement of changes in net assets for each of the
two years in the period then ended, and financial highlights for each of the
years indicated therein. These financial statements and financial highlights
are the responsibility of the Fund's management. Our responsibility is to
express an opinion on these financial statements and financial highlights
based on our audits.
    We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures
in the financial statements. Our procedures included confirmation of
securities owned as of May 31, 1995 by correspondence with the custodian. An
audit also includes assessing the accounting principles used and significant
estimates made by management, as well as evaluating the overall financial
statement presentation. We believe that our audits provide a reasonable basis
for our opinion.
    In our opinion, the financial statements and financial highlights
referred to above present fairly, in all material respects, the financial
position of Dreyfus Municipal Money Market Fund, Inc. at May 31, 1995, the
results of its operations for the year then ended, the changes in its net
assets for each of the two years in the period then ended, and the financial
highlights for each of the indicated years, in conformity with generally
accepted accounting principles.


                                    (Ernst & Young LLP  Signature Logo)
New York, New York
July 7, 1995

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
IMPORTANT TAX INFORMATION (UNAUDITED)
    In accordance with Federal tax law, the Fund hereby designates all the
dividends paid from investment income-net during the fiscal year ended May
31, 1995 as "exempt-interest dividends" (not generally subject to regular
Federal income tax).


















DREYFUS 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
The Shareholder Services Group, Inc.
P.O. Box 9671
Providence, RI 02940




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




Printed in U.S.A.                            910AR955
Municipal
Money Market
Fund, Inc.
Annual Report
May 31, 1995



(Dreyfus Logo)




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