DREYFUS MUNICIPAL MONEY MARKET FUND INC
N-30D, 1996-07-30
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DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on the Dreyfus Municipal
Money Market Fund, Inc. For its annual reporting period ended May 31, 1996,
your Fund produced an annualized yield of 3.10%. For investors in the highest
Federal income tax bracket, this equates to a taxable equivalent yield of
5.13%. Income dividends of approximately $.031 per share were paid during the
period. Reinvesting these dividends and calculating the effect of compounding
resulted in an annualized effective yield of 3.15%.* These dividends were
exempt from Federal personal income taxes, although some income may be
subject to the Federal Alternative Minimum Tax (AMT) for certain
shareholders.
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 annualized Gross Domestic Product grew at a moderate 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 May 31, 1996 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 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 the six
months ended this May 31, the direction would mirror closely the impact of
supply and demand conditions on municipal money market yields. 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 followed by 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 Fund'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. This enabled us to wait out a lower yield environment in
anticipation of higher rates.

    The 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 that 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 appreciate greatly 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.

*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
<TABLE>


DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                                         MAY 31, 1996
                                                                                                    PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                         AMOUNT           VALUE
                                                                                                       _______        _______
<S>                                                                                              <C>             <C>
ALABAMA-4.6%
Alabama Industrial Development Authority, SWDR, VRDN (Pine City Fiber Co.
Project)
    3.75% (LOC; Barclays Bank) (a,b)........................................                     $  39,000,000   $ 39,000,000
Phenix City Industrial Development Board, VRDN (Mead Coated Board Project)
    4% (LOC; Sumitomo Bank) (a,b)...........................................                         4,800,000      4,800,000
ALASKA-1.5%
Valdez, Marine Terminal Revenue, Refunding, CP (Arco Transportation Project)
    3.40%, Series C, 6/14/96................................................                        14,100,000     14,100,000
CALIFORNIA-2.4%
California Higher Education Loan Authority Inc., Student Loan Revenue, VRDN
    3.70% (LOC; Student Loan Marketing Association) (a,b)...................                         9,000,000      9,000,000
South Coast Local Education Agencies and Partnerships, TRAN
    5%, 8/14/96.............................................................                        14,560,000     14,572,604
COLORADO-.8%
Denver Urban Renewal Authority, Tax Increment Revenue (Downtown Denver Renewal)
    3.625%, Series A, 8/8/96 (Collateralized in; U.S. Treasury Bills).......                         7,440,000      7,440,000
CONNECTICUT-.7%
Mashantucket Western Pequot Tribe, CP
    3.60%, Series 1996, 7/11/96 (LOC; Bank of America) (b)..................                         7,000,000      7,000,000
DELAWARE-7.8%
Delaware Economic Development Authority, Revenue, VRDN
    (Hospital Billing and Collection Service Limited Project):
      3.60%, Series A (Insured; MBIA and Liquidity Facility; Morgan Stanley) (a)                    25,000,000     25,000,000
      3.60%, Series B (Insured; MBIA and Liquidity Facility; Morgan Stanley) (a)                    14,000,000     14,000,000
      3.60%, Series C (Insured; MBIA and Liquidity Facility; Morgan Stanley) (a)                    36,400,000     36,400,000
DISTRICT OF COLUMBIA-3.7%
District of Columbia, VRDN (General Fund Recovery):
    3.95%, Series B-1 (LOC; Union Bank of Switzerland) (a,b)................                        10,000,000     10,000,000
    3.95%, Series B-3 (LOC; Landesbank Hessen) (a,b)........................                        26,000,000     26,000,000
FLORIDA-3.1%
Hillsborough County Industrial Development Authority, VRDN (Tampa Electric Co. Project)
    4% (Corp. Guaranty; Tampa Electric Co.) (a).............................                         5,000,000      5,000,000
Pasco County Industrial Development Authority, Revenue, VRDN
    (Woodhaven Partners Limited Project) 3.60% (LOC; Krediet Bank) (a,b)....                         8,800,000      8,800,000
Sunshine State Governmental Financing Commission, Revenue, CP
    3.30%, Series B, 6/13/96 (Liquidity Facility; State Board of Administration of Florida)         16,390,000     16,390,000
GEORGIA-2.4%
Athens-Clarke County Industrial Development Authority, IDR, VRDN
    (Nakanishi Manufacturing Corp. Project) 3.875% (LOC; Sumitomo Bank) (a,b)                        6,000,000      6,000,000

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                           MAY 31, 1996
                                                                                                    PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                     AMOUNT         VALUE
                                                                                                       _______       _______
GEORGIA (CONTINUED)
Savannah Economic Development Authority, Revenue Exempt Facilities, VRDN
    (Home Depot Project) 3.75%, Series A (Corp. Guaranty; Home Depot) (a)...                     $  17,000,000   $ 17,000,000
HAWAII-1.0%
Honolulu City and County, Multi-Family Revenue, VRDN (Royal Kunia Gardens)
    4.05%, Series B (LOC; Bank of Tokyo) (a,b)..............................                         9,675,000      9,675,000
ILLINOIS-4.1%
Illinois Development Finance Authority, PCR, VRDN (Illinois Power Co.)
    3.75%, Series C (LOC: Bank of Tokyo and Mitsubishi Bank) (a,b)..........                         10,400,000    10,400,000
Illinois Health Facilities Authority, Revenue, VRDN (Revolving Fund Pooled
Financing)
    3.65%, Series C (LOC; First National Bank of Chicago) (a,b).............                        16,250,000     16,250,000
Illinois Housing Development Authority, Revenue (Homeownership Mortgage)
    3.70%, Series E-2, 9/3/96 (LOC; Morgan Stanley) (b).....................                         8,440,000      8,440,000
Southwestern Development Authority, SWDR, VRDN (Shell Oil Co. Wood River
Project)
    3.90% (Corp Guaranty; Shell Oil Co.) (a)................................                         4,400,000      4,400,000
INDIANA-7.3%
Indiana Bond Bank:
    Advance Fundings Notes 4.25%, Series A-2, 1/9/97........................                        30,000,000     30,132,229
    Reassessment Assistance Project Notes 4.125%, Series A, 1/30/97.........                        17,590,000     17,632,395
Indiana Development Finance Authority, SWDR, CP (Pure Air on the Lake
Project)
    4%, Series A, 7/15/96 (LOC; Fuji Bank) (b)..............................                        12,750,000     12,750,000
City of Petersburg, SWDR, VRDN (Indianapolis Power and Light Co. Project)
    3.65%, Series A (Corp. Guaranty; Indianapolis Power and Light Co.) (a)..                        10,000,000     10,000,000
IOWA-1.3%
Iowa Finance Authority, SWDR, VRDN (Cedar River Paper Co. Project)
    3.75%, Series A (LOC; Swiss Bank Corp.) (a,b)...........................                        13,000,000     13,000,000
KANSAS-1.2%
Topeka, MFHR, VRDN (Topeka Retirement Center Limited)
    3.60% (LOC; Krediet Bank) (a,b).........................................                         6,970,000      6,970,000
Wichita, PCR, Refunding, VRDN (CIC Industries Inc. Project)
    4.075% (LOC; The Bank of New York) (a,b)................................                         5,000,000      5,000,000
KENTUCKY-3.6%
Daviess County, Solid Waste Disposal Facility, Revenue, VRDN (Scott Paper Co.
Project)
    3.90%, Series A (Corp. Guaranty; Kimberly Clark Corp.) (a)..............                        34,500,000     34,500,000
LOUISIANA-.9%
New Orleans Aviation Board, Revenue, VRDN (Passenger Facility Charge Project)
    3.85% (LOC: Banque Paribas and Canadian Imperial Bank of Commerce) (a,b)                         9,000,000      9,000,000

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                           MAY 31, 1996
                                                                                                    PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                     AMOUNT         VALUE
                                                                                                       _______       _______
MAINE-1.4%
Orrington, RRR, VRDN (Penobscott Energy Recovery Co. Project)
    3.75%, 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)                 $  13,010,000  $  13,010,000
MASSACHUSETTS-3.2%
Massachusetts Bay Transportation Authority, CP
    3.50%, Series C, 7/17/96 (LOC; WestDeutsche Landesbank) (b).............                        12,200,000     12,200,000
Massachusetts Multi-Family Housing Financing Agency, Refunding, VRDN
    (Harbor Point)
    3.55%, Series A (LOC; Republic National Bank of New York) (a,b).........                        18,300,000     18,300,000
MICHIGAN-9.1%
Michigan Hospital Finance Authority, Revenue, VRDN
    (Hospital Equipment Loan Program) 3.75% (LOC; Comerica Bank) (a,b)......                         1,600,000      1,600,000
Michigan Housing Development Authority, Rental Housing Revenue, Refunding,
VRDN
    3.65%, Series C (LOC; Credit Suisse) (a,b)..............................                        17,000,000     17,000,000
Michigan Municipal Bond Authority 4.50%, Series B, 7/3/96...................                        11,000,000     11,010,212
Michigan Strategic Fund, SWDR, VRDN (Grayling Generating Project)
    3.75% (LOC; Barclays Bank) (a,b)........................................                         8,000,000      8,000,000
Midland County Economic Development Corporation, Economic Development LOR
    Refunding, VRDN (Dow Chemical Co. Project)
    3.60%, Series B (Corp. Guaranty; Dow Chemical Co.) (a)..................                         7,000,000      7,000,000
State of Michigan, GO Notes 4%, 9/30/96.....................................                        43,000,000     43,119,253
NEBRASKA-1.5%
Nebraska Higher Education Loan Program Inc., Revenue, VRDN
    (Multiple Mode-Student Loan) 3.60%, Series A (Insured; MBIA and LOC;
    Student Loan Marketing Association) (a,b)...............................                        12,995,000     12,995,000
Nebraska Investment Finance Authority, HR, VRDN (Multiple Mode Depreciation
Assets)
    3.50%, Series A (Insured; FGIC and LOC; First National Bank Association) (a,b)                   1,360,000      1,360,000
NEVADA-2.1%
Clark County, IDR, Refunding, VRDN (Nevada Power Co. Project)
    3.80%, Series B (LOC; Societe Generale) (a,b)...........................                        20,000,000     20,000,000
NEW JERSEY-1.2%
New Jersey Turnpike Authority, Turnpike Revenue, Refunding, VRDN
    3.25%, Series D (Insured; FGIC and LOC; Societe Generale) (a,b).........                        11,600,000     11,600,000
NEW YORK-10.2%
New York City:
    CP 3.35%, Series H-5,
      8/15/96 (Insured; MBIA and Liquidity Facility; Landesbank Hessen).....                        25,000,000     25,000,000

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                          MAY 31, 1996
                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                     AMOUNT          VALUE
                                                                                                       _______       _______
NEW YORK (CONTINUED)
New York City (continued):
    RAN 4.75%, Series B, 6/28/96 (LOC: Bank of Nova Scotia, Canadian Imperial
Bank
      of Commerce, Chemical Bank, Citibank, Commerz Bank, Morgan Guaranty
      Trust Co. and Union Bank of Switzerland) (b)..........................                     $  15,000,000   $ 15,008,070
New York State Energy Research and Development Authority, PCR (LILCO Project)
    3.25%, Series A, 3/1/97 (LOC; Deutsche Bank) (b)........................                        10,000,000      9,977,989
New York State Housing Finance Agency, HR, VRDN (Normandie Court II)
    3.50%, Series A (LOC; Fleet Bank) (a,b).................................                        11,000,000     11,000,000
New York State Local Government Assistance Corporation, VRDN:
    3.45%, Series A (LOC: Credit Suisse, Swiss Bank Corp. and Union
      Bank of Switzerland) (a,b)............................................                        11,500,000     11,500,000
    3.45%, Series C (LOC; Landesbank Hessen) (a,b)..........................                         9,900,000      9,900,000
New York State Power Authority, CP 3.75%, 8/16/96 (Liquidity Facility: Bank
of America,
    The Bank of New York, Bank of Nova Scotia, Chemical Bank, Citibank,
    Industrial Bank of Japan, Mitsubishi Bank and Sanwa Bank)...............                        13,000,000     13,000,000
Port Authority of New York and New Jersey, Special Obligation Revenue, VRDN
    (Versatile Structure Obligation) 3.65%, Series 4 (LOC; Landesbank Hessen) (a,b)                  3,000,000      3,000,000
NORTH CAROLINA-.4%
North Carolina Medical Care Community, HR, VRDN (Pooled Equipment Financing
Project)
    3.90% (Insured; MBIA and LOC; Banque Paribas) (a,b).....................                         3,400,000      3,400,000
OHIO-3.8%
Greene County, Certificate of Indebteness 3.88%, 6/4/97.....................                        14,000,000     14,021,560
Ohio Water Development Authority, Pollution Control Facilities, PCR, CP
    (Duquesne Light) 3.60%, 7/9/96 (LOC; Toronto-Dominion Bank) (b).........                         9,850,000      9,850,000
University of Cincinnati, General Receipt, BAN
    4.25%, 8/28/96..........................................................                        13,000,000     13,007,511
PENNSYLVANIA-2.3%
Columbia County Industrial Development Authority, IDR, VRDN (Kleerdex Co.
Project)
    4.15% (LOC; Bank of Tokyo) (a,b)........................................                         4,800,000      4,800,000
Delaware Valley Regional Finance Authority, Local Government Revenue, VRDN
    3.65%, Series D (LOC; Marine Midland Bank) (a,b)........................                         5,000,000      5,000,000
Pennsylvania Higher Education Assistance Agency, Student Loan Revenue, VRDN
    3.65%, Series A (LOC; Student Loan Marketing Association) (a,b).........                        12,100,000     12,100,000
SOUTH CAROLINA-.8%
York County, Industrial Revenue, VRDN (Textron Project)
    5.156% (LOC; Bankers Trust) (a,b).......................................                         7,500,000      7,500,000

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                           MAY 31, 1996
                                                                                                    PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                     AMOUNT         VALUE
                                                                                                       _______       _______
TENNESSEE-4.0%
Franklin, IDB, Multi-Family Revenue, VRDN (Landings Project)
    3.60%, Series C (LOC; Citibank) (a,b)...................................                     $  10,700,000   $ 10,700,000
Oak Ridge, IDB, Solid Waste Revenue, VRDN (M4 Environmental)
    3.75% (LOC; Sun Trust Bank) (a,b).......................................                        10,000,000     10,000,000
Sevier County Public Building Authority, Local Government Public Improvement, VRDN:
    3.50%, Series A-1 (Insured; AMBAC and SBPA; Krediet Bank) (a)...........                         7,500,000      7,500,000
    3.65%, Series B-1 (Insured; AMBAC and SBPA; Krediet Bank) (a)...........                         5,000,000      5,000,000
    3.65%, Series B-2 (Insured; AMBAC and SBPA; Krediet Bank) (a)...........                         5,000,000      5,000,000
TEXAS-5.2%
Brazos River Authority, PCR, Refunding, VRDN (Utility Electric Co.)
    4%, Series C (LOC; Swiss Bank Corp.) (a,b)..............................                         7,000,000      7,000,000
Greater East Texas Higher Education Authority Inc., Student Loan Revenue,
Refunding
    VRDN 3.55%, Series A (LOC; Student Loan Marketing Association) (a,b)....                        10,000,000     10,000,000
Pan-Handle Plains Higher Education Authority Inc., Student Loan Revenue, VRDN
    3.60% (LOC; Student Loan Marketing Association) (a,b)...................                        13,000,000     13,000,000
State of Texas Public Finance Authority, Revenue, CP
    3.40%, 7/18/96 (Liquidity Facility; State of Texas Treasurer)...........                        11,500,000     11,500,000
Texas A & M, University Revenues, University Financing Systems Revenue, CP
    3.65%, Series B, 7/11/96................................................                         8,700,000      8,700,000
UTAH-4.2%
Intermountain Power Agency, Power Supply Revenue, CP
    3.60%, Series E, 7/26/96 (LOC; Bank of America) (b).....................                        27,900,000     27,900,000
Utah Board of Regents, Student Loan Revenue, Refunding, VRDN
    3.65%, Series A (LOC; Student Loan Marketing Association) (a,b).........                        12,500,000     12,500,000
VIRGINIA-.9%
Charles City and County Industrial Development Authority, Exempt Facilities
Revenue
    VRDN (Chambers Project) 3.95% (LOC; North Carolina National Bank) (a,b).                         8,700,000      8,700,000
WEST VIRGINIA-.8%
Marion County Commission, Solid Waste Disposal Facility Revenue, VRDN
    (Granttown Project) 3.65% (LOC; National Westminster Bank) (a,b)........                         7,800,000      7,800,000
WASHINGTON-1.0%
Washington Housing Finance Commission (Single Family Program)
    3.80%, Series 1A-S, 6/2/97 (Insured; FGIC)..............................                        10,000,000     10,000,000
WISCONSIN-1.5%
Milwaukee Housing Authority, MFHR, VRDN (Yankee Hill Apartments)
    3.60% (LOC; Citibank) (a,b).............................................                        14,000,000     14,000,000
                                                                                                                     _______
TOTAL INVESTMENTS (cost $963,206,605).......................................                                     $963,211,823
                                                                                                                     =======
</TABLE>



DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
<TABLE>

SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <C>     <C>
AMBAC         American Municipal Bond Assurance Corporation      MBIA    Municipal Bond Investors Assurance
BAN           Bond Anticipation Notes                                         Insurance Corporation
CP            Commercial Paper                                   MFHR    Multi-Family Housing Revenue
FGIC          Financial Guaranty Insurance Company               PCR     Pollution Control Revenue
GO            General Obligation                                 RAN     Revenue Anticipation Notes
HR            Hospital Revenue                                   RRR     Resources Recovery Revenue
IDB           Industrial Development Board                       SBPA    Standby Bond Purchase Agreement
IDR           Industrial Development Revenue                     SWDR    Solid Waste Disposal Revenue
LOC           Letter of Credit                                   TRAN    Tax Revenue Anticipation Notes
LOR           Limited Obligation Revenue                         VRDN    Variable Rate Demand Notes

</TABLE>

SUMMARY OF COMBINED RATINGS (UNAUDITED)
<TABLE>
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)              95.3%
AAA/AA (e)                         Aaa/Aa (e)                     AAA/AA (e)                         3.3
Not Rated (f)                      Not Rated (f)                  Not Rated (f)                      1.4
                                                                                                   ____
                                                                                                   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, 57.1% of the Fund's
    net assets are backed by letters of credit issued by domestic banks,
    foreign banks, brokerage firms, 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)  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 notes to financial statements.
<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                           MAY 31, 1996
<S>                                                                                            <C>               <C>
ASSETS:
    Investments in securities, at value
      (cost $963,206,605)-see statement.....................................                                      $963,211,823
    Cash....................................................................                                         5,533,718
    Interest receivable.....................................................                                         6,438,939
    Prepaid expenses........................................................                                           123,878
                                                                                                                       _______
                                                                                                                   975,308,358
LIABILITIES:
    Due to The Dreyfus Corporation and subsidiaries.........................                   $     428,643
    Payable for investment securities purchased.............................                      24,021,560
    Accrued expenses and other liabilities..................................                         260,545        24,710,748
                                                                                                       ______          _______
NET ASSETS  ................................................................                                      $950,597,610
                                                                                                                       =======
REPRESENTED BY:
    Paid-in capital.........................................................                                      $950,255,940
    Accumulated undistributed investment income-net.........................                                           133,931
    Accumulated undistributed net realized gain on investments..............                                           202,521
    Accumulated gross unrealized appreciation on investments................                                             5,218
                                                                                                                       _______
NET ASSETS at value applicable to 952,233,997 shares outstanding
    (5 billion shares of $.01 par value Common Stock authorized)............                                      $950,597,610
                                                                                                                       =======
NET ASSET VALUE, offering and redemption price per share
    ($950,597,610 / 952,233,997 shares).....................................                                             $1.00
                                                                                                                       =======


</TABLE>








See notes to financial statements.
<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                                                YEAR ENDED MAY 31, 1996
<S>                                                                                             <C>                <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                       $38,737,873
    EXPENSES:
      Management fee-Note 2(a)..............................................                     $5,156,708
      Shareholder servicing costs-Note 2(b).................................                      1,104,262
      Custodian fees........................................................                         83,905
      Professional fees.....................................................                         83,170
      Registration fees.....................................................                         75,901
      Directors' fees and expenses_Note 2(c)...............................                          61,293
      Prospectus and shareholders' reports..................................                         36,630
      Miscellaneous.........................................................                         41,327
                                                                                                      _____
          TOTAL EXPENSES....................................................                                         6,643,196
                                                                                                                        ______
          INVESTMENT INCOME-NET.............................................                                        32,094,677
REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
    Net realized gain on investments-Note 1(b)..............................                    $   202,521
    Net unrealized (depreciation) on investments............................                        (36,575)
                                                                                                      _____
          NET REALIZED AND UNREALIZED GAIN ON INVESTMENTS...................                                           165,946
                                                                                                                        ______
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                       $32,260,623
                                                                                                                        ======



</TABLE>










See notes to financial statements.
<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                               YEAR ENDED MAY 31,
                                                                                    ______________________________________
                                                                                            1995                    1996
                                                                                          _________                _________
<S>                                                                               <C>                      <C>
OPERATIONS:
    Investment income-net.............................................            $      31,988,127        $      32,094,677
    Net realized gain on investments..................................                       64,104                  202,521
    Net unrealized appreciation (depreciation) on investments for the year                   34,481                  (36,575)
                                                                                          _________                _________
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS............                   32,086,712               32,260,623
                                                                                          _________                _________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net.............................................                  (31,988,127)             (32,094,677)
                                                                                          _________                _________
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold.....................................                3,482,290,984            3,902,085,298
    Dividends reinvested..............................................                   22,043,236               20,778,711
    Cost of shares redeemed...........................................               (3,688,123,812)          (3,905,743,054)
                                                                                          _________                _________
      INCREASE (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS                (183,789,592)              17,120,955
                                                                                          _________                _________
          TOTAL INCREASE (DECREASE) IN NET ASSETS.....................                 (183,691,007)              17,286,901
NET ASSETS:
    Beginning of year.................................................                 1,117,001,716             933,310,709
                                                                                          _________                _________
    End of year (including undistributed investment income-net:
      $133,931 in 1995 and in 1996)...................................             $    933,310,709       $      950,597,610
                                                                                          =========                =========

</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>


                                                                                    YEAR ENDED MAY 31,
                                                                ______________________________________________________
PER SHARE DATA:                                                   1992        1993        1994        1995        1996
                                                                   ___         ___         ___         ___         ___
<S>                                                              <C>         <C>         <C>         <C>         <C>
    Net asset value, beginning of year...........                $1.00       $1.00       $1.00       $1.00       $1.00
                                                                   ___         ___         ___         ___         ___
    INVESTMENT OPERATIONS;
    Investment income-net........................                 .034        .022        .020        .029        .031
                                                                   ___         ___         ___         ___         ___
    DISTRIBUTIONS;
    Dividends from investment income-net.........                (.034)      (.022)      (.020)      (.029)      (.031)
                                                                   ___         ___         ___         ___         ___
    Net asset value, end of year.................                $1.00       $1.00       $1.00       $1.00       $1.00
                                                                   ===         ===         ===         ===         ===
TOTAL INVESTMENT RETURN..........................                 3.46%       2.23%       2.00%       2.98%       3.16%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......                  .62%        .62%        .62%        .62%        .64%
    Ratio of net investment income to
      average net assets.........................                 3.41%       2.22%        1.98%      2.91%       3.11%
    Net Assets, end of year (000's Omitted)......           $1,498,772  $1,413,815   $1,117,002   $933,311    $950,598

</TABLE>












See notes to financial statements.

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    Dreyfus 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 charge.
    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.
    As a result of the expiration of a prior year capital loss carryover,
$1,135,065 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).
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 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
DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
any full fiscal year that such expenses exceed 21\2% of the first $30
million, 2% of the next $70 million and 11\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, 1996.
    (B) Pursuant to the Fund's 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 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 year ended May 31, 1996, the Fund was charged an aggregate of
$626,310 pursuant to the Shareholder Services Plan.
    Effective December 1, 1995, 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 $141,384 for the period from
December 1, 1995 through May 31, 1996.
    (C) Each director who is not an "affiliated person" as defined in the Act
receives from the Fund 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 and the Director Emeritus receives 50% 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, 1996, 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, 1996 by correspondence with the custodian and
brokers. 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, 1996, 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 and Young LLP signature logo]

New York, New York
July 8, 1996
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, 1996 as "exempt-interest dividends" (not generally subject to regular
Federal income tax).


[Dreyfus lion "d" logo]
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
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.                            910AR965
[Dreyfus logo]
Municipal
Money Market
Fund, Inc.
Annual Report
May 31, 1996














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