DREYFUS MUNICIPAL MONEY MARKET FUND INC
N-30D, 1998-08-03
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[Dreyfus lion "d" logo]                           (reg.tm)


[Dreyfus logo]                                   (reg.tm)

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.

P.O. Box 9671

Providence, RI 02940











Printed in U.S.A.                                              910AR985

Municipal Money

Market Fund, Inc.

Annual Report

May 31, 1998




DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are  pleased  to  report  the  performance for the Dreyfus Municipal Money
Market Fund, Inc. for the 12-month period ended May 31, 1998. Your Fund produced
a  yield  of 3.08% and, after taking into account the effect of compounding, the
effective yield was 3.13%.*

MONEY MARKET OVERVIEW

Over the past several months, mixed economic signals have made it difficult to
discern  the  direction  in  which  the  economy  is  moving.  Consumer spending
increased  0.5%  in  both  April  and  May, fueled by both strong employment and
income  growth.  In  addition, construction spending also rose 0.8% in April for
the  fifth straight monthly increase. On the other hand, spring housing data was
mixed,  with  new  home sales rising to record levels in April and existing-home
sales  and new housing starts dropping off. The U.S. trade gap also continued to
widen,  as  manufacturers  reported  declines  in  exports  to  Asia,  and tough
competition  from  cheaper  Asian  imports.  With  arguments to be made for both
continued  growth  and  emerging weakness, it appears that Federal Reserve Board
monetary  policy  will  remain on hold at least until something major happens to
sway Board members' opinions one way or another.

  Inflation  has remained benign throughout the period. Incoming data from April
did show a small 0.2% increase in the Consumer Price Index, although this modest
rise was the largest in six months. With no consensus as to the direction of the
economy,  the  Federal  Reserve  Board  Open  Market  Committee  left short-term
interest  rates unchanged at its May meeting; however, the decision to do so may
not  have  been  unanimous. Those most wary of inflation may win out in upcoming
meetings if the economy does not cool on its own. Interest rates on money market
securities   fluctuated   modestly  during  the  period,  but  remained  largely
unchanged.  As  U.S.  Treasury borrowing needs continued to reduce the supply of
money market securities, demand remained steady.

MARKET ENVIRONMENT/PORTFOLIO OVERVIEW

  While  the  Fed has remained quiet over the past six months, market technicals
(i.e.  supply/demand  fluctuations)  have  played  a  major  role in our overall
investment  strategy.  The  municipal money market has experienced some of these
changes  in  seasonal  cash  flows  and note issuance since our last report. For
example,  in late December, the short-term municipal market experienced a sharp,
albeit  temporary,  rise  in  short-term rates as a result of corporate seasonal
window  dressing.  Dealers  priced  securities  at attractive levels in order to
minimize their inventories, which helped to boost your Fund's yield at year end.
The  situation  reversed  in  January  as assets flowed back into the tax-exempt
money  funds,  thereby  putting downward pressure on yields. During this period,
yields  on  tax-exempt money market funds fluctuated in response to these supply
and    demand    imbalances.

  By  mid-January,  the  market  stabilized and normal trading patterns, for the
most  part,  returned  and  continued  through March. In April, money funds were
tapped  for  income tax payments which, once again, put upward pressure on rates
as  funds  experienced redemptions.  Supply conditions in late May reversed this
trend  as  municipal  fund  managers  anticipated the effect of over $10 billion
notes    leaving    the    market    when    they    mature    this    month.

  Unlike  previous  summer  financing periods, this year's calendar of municipal
notes  appropriate  for  purchase  for  your  Fund  was drastically reduced by a
combination  of  factors. Due to the strength of local and state economies, many
issuers  reduced the amount of short-term borrowings. Additionally, many issuers
came  to  market  with  maturities  outside  of  the  13-month  maximum maturity
allowable  for  money  funds,  whereas these notes were eligible for purchase in
prior  years.  Other  issues were converted to a synthetic structure that is not
currently  permitted  for  purchase in your Fund. The overall result was a lower
yield  for  those  note  issues that were considered appropriate investments for
your  Fund.  We  expect  to  choose  selectively among these issues and those to
follow  in the coming weeks to structure the portfolio in an attempt to maximize
current  yield  while  maintaining  our  commitment  to  high quality tax-exempt
investments.

  Included  in  this report is a series of detailed statements about your Fund's
holdings  and its financial condition. We hope they are informative. Please know
that  we  greatly  appreciate  your continued confidence in this 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 18, 1998

New York, N.Y.

* Effective yield is based upon dividends declared daily and reinvested monthly

<TABLE>
DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                         MAY 31, 1998

                                                                                                  Principal

Tax Exempt Investments--100.0%                                                                      Amount            Value
- -------------------------------------------------------

                                                                                                _____________     _____________
<S>                                                                                            <C>               <C>


California--3.5%

Fresno, RAN 4.25%, 6/30/98                                                                      $  12,500,000     $  12,504,302

Los Angeles County, TRAN 4.50%, Series A, 6/30/98                                                  19,000,000        19,009,446

Delaware--8.7%

Delaware Economic Development Authority, Revenue, VRDN

 (Hospital Billing and Collection Service Limited Project):

    4%, Series A (Insured; MBIA and Liquidity Facility; Morgan Stanley) (a)                        25,000,000        25,000,000

    4%, Series B (Insured; MBIA and Liquidity Facility; Morgan Stanley) (a)                        19,000,000        19,000,000

    4%, Series C (Insured; MBIA and Liquidity Facility; Morgan Stanley) (a)                        34,400,000        34,400,000

District of Columbia--2.2%

District of Columbia Housing Finance Agency, SFMR

  4.15%, Series A, 7/1/98 (Liquidity Facility; Assured Management Corp.)                           20,000,000        20,000,000

Florida--2.8%

Dade County, Water and Sewer Systems Revenue, VRDN

  3.90% (Insured; FGIC and Liquidity Facility; Commerzbank) (a)                                     7,600,000         7,600,000

Sunshine State Governmental Finance Commission, Revenue, CP

  3.55%, Series B, 7/15/98 (LOC; Bank of Nova Scotia) (a,b)                                        17,362,000        17,362,000

Georgia--3.6%

Athens-Clarke County Industrial Development Authority, IDR, VRDN

  (Nakanishi Manufacturing Corp. Project) 4.325% (LOC; Sumitomo Bank) (a,b)                         6,000,000         6,000,000

Burke County Development Authority, PCR, CP (Oglethorpe Power Corp. Project)

  3.50%, Series A, 7/24/98 (Insured: AMBAC and LOC; Rabobank Nederland) (b)                        10,000,000        10,000,000

Savannah Economic Development Authority, Revenue Exempt Facilities, VRDN

  (Home Depot Project) 4%, 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)

  4.25%, Series B (LOC; Bank of Tokyo-Mitsubishi) (a,b)                                             9,225,000         9,225,000

Illinois--9.9%

City of Chicago, Mandatory Tender Notes:

  3.55%, 10/29/98 (LOC; Morgan Guaranty Trust Co.) (b)                                             12,871,000        12,871,000

  3.55%, 2/4/99 (LOC; Morgan Guaranty Trust Co.) (b)                                               10,000,000        10,000,000

Illinois Development Finance Authority, PCR, VRDN (Illinois Power Co.)

  4.25%, Series C (LOC; Bank of Tokyo-Mitsubishi) (a,b)                                            10,400,000        10,400,000

Illinois Development Finance Authority, Revenue, VRDN (Provena Health)

  4%, Series B (Insured; MBIA and LOC; Bank of America) (a,b)                                      40,000,000        40,000,000

Illinois Health Facilities Authority, Revenue, VRDN (Revolving Fund Pooled
Financing)

  3.80%, Series C (LOC; First National Bank of Chicago) (a,b)                                      16,250,000        16,250,000

Indiana--2.0%

Hammond Local Public Improvement Bond Bank, Revenue, Advance Funding Program
Notes

  4.30%, Series A-2, 1/7/99 (LOC; Bank One) (b)                                                    17,810,000        17,861,669
</TABLE>

<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                             MAY 31, 1998

                                                                                                   Principal

Tax Exempt Investments (continued)                                                                  Amount            Value
- -------------------------------------------------------

                                                                                                _____________     _____________
<S>                                                                                             <C>               <C>

Idaho--1.1%

Idaho State, TAN 4.625%, 6/30/98                                                                $  10,000,000     $  10,005,696

Kansas--4.3%

Butler County, Solid Waste Disposal Cogeneration Revenue, VRDN

  (Texaco Refining and Marketing) 4.20%, Series B (LOC; Texaco Inc.) (a,b)                         27,100,000        27,100,000

Topeka, MFHR, VRDN (Topeka Retirement Center Limited)

  3.70% (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

Louisiana--1.9%

New Orleans Aviation Board, Revenue, VRDN (Passenger Facility Charge Project)

  4.45% (LOC: Banque Paribas and Canadian Imperial Bank of Commerce) (a,b)                          7,400,000         7,400,000

West Baton Rouge Parish Industrial District Number 3, Revenue, Refunding, VRDN

  (Dow Chemical Co. Project) 4.15%, Series B, (LOC; Dow Chemical Co.) (a,b)                         9,300,000         9,300,000

Maine--1.0%

Orrington, RRR, VRDN (Penobscott Energy Recovery Co. Project)

 3.95%, Series B (LOC: Bank of Nova Scotia, Bankers Trust, Canadian Imperial
Bank

  of Commerce, and Toronto Dominian Bank) (a,b)                                                     9,355,000         9,355,000

Michigan--2.9%

Birmingham, EDR, VRDN (Brown Association Project)

  4.075% (LOC; Bankers Trust Co.) (a,b)                                                             1,945,000         1,945,000

Michigan Housing Development Authority, LOR, Refunding, VRDN

  (Harbortown Limited Divide Project) 3.825% (LOC; Bankers Trust Co.) (a,b)                         1,000,000         1,000,000

Michigan Municipal Bond Authority, Revenue

  4.50%, Series B, 7/2/98                                                                          15,000,000        15,007,962

Michigan Strategic Fund, SWDR, VRDN

  (Grayling Generating Project) 4% (LOC; Barclays Bank) (a,b)                                       8,000,000         8,000,000

Minnesota--1.1%

Cloquet, Industrial Facilities Revenue, VRDN (Potlatch Corp. Project)

  3.90%, Series C (LOC; Credit Suisse) (a,b)                                                        5,300,000         5,300,000

St. Paul Housing and Redevelopment Authority, Health Care Systems Revenue,
Refunding

 VRDN (Child Health Care)

  4.05%, Series B (Insured; FSA and LOC: Norwest Bank of Minnesota) (a,b)                           4,800,000         4,800,000

Montana--1.5%

Forsyth, PCR, Refunding, VRDN (Pacific Corp. Project)

  4% (LOC; Rabobank Nederland) (a,b)                                                               13,400,000        13,400,000

Nebraska--1.4%

Nebhelp Incorporated, Revenue, Mutiple Mode Student Loan, VRDN

  3.70%, Series A (Insured; MBIA and LOC; Student Loan Marketing Association) (a,b)                12,995,000        12,995,000
</TABLE>
<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                             MAY 31, 1998

                                                                                                   Principal

Tax Exempt Investments (continued)                                                                  Amount            Value
- -------------------------------------------------------

                                                                                                _____________     _____________
<S>                                                                                             <C>               <C>

Nevada--2.8%

Las Vegas Valley Water District, CP 3.75%, Series A, 7/29/98

  (LOC: United Bank of Switzerland and Westdeutsche Landesbank) (a,b)                           $  25,000,000     $  25,000,000

New Mexico--.9%

New Mexico Mortgage Finance Authority, Single Family Mortgage Program

  3.90%, Issue 2, 10/15/98 (Insured; FGIC)                                                          8,000,000         8,000,000

New York--9.0%

New York City:

 RAN 4.50%, Series A, 6/30/98 (LOC: Bayerische Landesbank, Landesbank Hessen,

    National Westminster Bank and Societe Generale) (b)                                             7,000,000         7,004,183

  VRDN 4.10%, Series B (Insured; FGIC) (a)                                                          6,800,000         6,800,000

New York State Energy, Research and Development Authority, PCR (LILCO Project)

  3.58%, Series A, 3/1/99 (LOC; Deutsche Bank) (b)                                                 13,530,000        13,530,000

New York State Housing Finance Agency, Service Contract Obligation, Revenue,
VRDN

  3.85%, Series A (LOC; Commerzbank) (a,b)                                                          4,000,000         4,000,000

New York State Local Government Assistance Corporation, VRDN

  3.85%, Series A (LOC: Credit Suisse, and Union Bank of Switzerland) (a,b)                        35,700,000        35,700,000

Suffolk County, TAN 4.25%, Series A-1, 8/13/98 (LOC: Canadian Imperial Bank of
Commerce,

  National Westminster Bank and Westdeutsche Landesbank) (b)                                       14,000,000        14,016,445

North Carolina--.5%

Craven County Industrial Facilities and Pollution Control Finance Authority,
Resource

  VRDN (Craven Wood Energy) 4.20%, Series C (LOC; ABN-Amro Bank) (a,b)                              4,100,000         4,100,000

Ohio--4.3%

Cincinnati City School District, BAN 4.32%, 9/17/98                                                10,000,000        10,010,503

Columbus Electric System, Revenue, VRDN 3.50% (LOC; Union Bank of Switzerland) (a,b)                1,300,000         1,300,000

Cuyahoga County, HR, VRDN (Cleveland Clinic Foundation)

  3.75%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b)                                            3,200,000         3,200,000

Greene County, Certificate of Indebtness, GO Notes 3.75%, 5/6/99                                    8,000,000         8,001,416

Hamilton County, Hospital Facilities Revenue, VRDN (Bethesda Hospital Inc.)

  3.75% (LOC; Rabobank Nederland) (a,b)                                                             2,000,000         2,000,000

Ohio Housing Finance Agency, Mortgage Revenue

  3.80%, Series A-3, 3/1/99 (LOC; Trinity Funding Corp.) (b)                                       11,880,000        11,880,000

Piqua, IDR, VRDN (Berwick Steel Co. Project) 3.95% (LOC; Sanwa Bank ) (a,b)                         1,000,000         1,000,000

Sharonville, IDR, VRDN (Edgecomb Metals Co. Project)

  3.70% (LOC; Banque Nationale de Paris) (a,b)                                                      1,150,000         1,150,000

Oregon--1.1%

Klamath Falls, Electric Revenue (Salt Caves Hydroelectric)

  3.80%, Series C, 5/3/99 (Escrowed in; U.S. Treasury Bills)                                       10,000,000        10,000,000
</TABLE>
<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                             MAY 31, 1998

                                                                                                   Principal

Tax Exempt Investments (continued)                                                                  Amount          Value
- -------------------------------------------------------

                                                                                                 _____________   _____________
<S>                                                                                            <C>               <C>

Pennsylvania--4.0%

Columbia County Industrial Development Authority, IDR, VRDN (Kleerdex Co.
Project)

  4.50% (LOC: Bank of Tokyo-Mitsubishi and Sanwa Bank) (a,b)                                   $    4,800,000    $    4,800,000

Pennsylvania Higher Education Assistance Agency, Student Loan Revenue, VRDN:

  4%, Series A (LOC; Student Loan Marketing Association) (a,b)                                     12,100,000        12,100,000

  4%, Series C (LOC; Student Loan Marketing Association) (a,b)                                      8,900,000         8,900,000

Philadelphia, TRAN 4.50%, Series A, 6/30/98                                                        10,000,000        10,003,819

South Carolina--1.9%

South Carolina Jobs Economic Development Authority, EDR, VRDN

  (Wellman Inc., Project) 4.15% (LOC; Wachovia Bank and Trust Co.) (a,b)                           10,010,000        10,010,000

York County, Industrial Revenue, VRDN (Textron Project)

  5.50% (LOC; Bankers Trust) (a,b)                                                                  7,500,000         7,500,000

Tennessee--2.9%

Oak Ridge, IDB, Solid Waste Revenue, VRDN (M4 Environmental)

  4% (LOC; Sun Trust Bank) (a,b)                                                                   10,000,000        10,000,000

Sevier County Public Building Authority, Local Government Public Improvement,
VRDN:

  3.75%, Series A-1 (Insured; AMBAC and SBPA; Krediet Bank) (a)                                     7,020,000         7,020,000

  3.75%, Series B-1 (Insured; AMBAC and SBPA; Krediet Bank) (a)                                     4,600,000         4,600,000

  3.75%, Series B-2 (Insured; AMBAC and SBPA; Krediet Bank) (a)                                     4,600,000         4,600,000

Texas--16.2%

Brazos River Authority, PCR, VRDN (Utility Electric Co.):

  4.15%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b)                                           20,000,000        20,000,000

  Refunding 3.95%, Series A (Insured; MBIA and LOC; The Bank of New York) (a,b)                     3,000,000         3,000,000

Brazos River Harbor Naval District, VRDN (Dow Chemical Co. Project):

  Brazoria County Revenue 4.20% (LOC; Dow Chemical Co.) (a,b)                                      19,100,000        19,100,000

  Harbor Revenue 4.20% (LOC; Dow Chemical Co.) (a,b)                                               10,000,000        10,000,000

Greater East Texas Higher Education Authority Inc., Student Loan Revenue

  3.95%, Series B, 9/1/98 (LOC; Student Loan Marketing Association) (b)                             8,000,000         8,000,000

Greater Texas Student Loan Corporation, Student Loan Revenue, Refunding

  3.60%, Series A, 3/1/99 (LOC; Student Loan Marketing Association) (b)                             8,000,000         8,000,000

Gulf Coast Waste Disposal Authority, Environmental Facilities Revenue, VRDN

  (Bayer Corp. Project) 4.20% (LOC; Bayer Corp.) (a,b)                                             23,000,000        23,000,000

Pan-Handle Plains Higher Education Authority Inc., Student Loan Revenue, VRDN

  4%, Series A (LOC; Student Loan Marketing Association) (a,b)                                     13,000,000        13,000,000

State of Texas, TRAN 4.75%, 8/31/98                                                                32,100,000        32,254,481

Texas Public Finance Authority, Revenue, CP

  3.55%, Series A, 7/21/98 (LOC: Toronto Dominion Bank and Union Bank of Switzerland) (b)          10,300,000        10,300,000

Utah--1.0%

Intermountain Power Agency, Power Supply Revenue, CP

  3.55%, 7/16/98 (Liquidity Facility: Bank of America and Bank of Nova Scotia)                      9,000,000         9,000,000
</TABLE>
<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                             MAY 31, 1998

                                                                                                   Principal

Tax Exempt Investments (continued)                                                                  Amount            Value
- -------------------------------------------------------

                                                                                                _____________     _____________
<S>                                                                                            <C>               <C>

Virginia--5.2%

Charles City and County Industrial Development Authority, Exempt Facilities
Revenue

  VRDN (Chambers Project) 3.90% (LOC; Morgan Guaranty Trust Co.) (a,b)                         $    7,400,000    $    7,400,000

Henrico County Industrial Development Authority, Health Facility Revenue, VRDN

  (Hermitage Project) 4.10% (LOC; Nations Bank of Virginia) (a,b)                                  14,930,000        14,930,000

Peninsula Ports Authority, Revenue, Refunding, VRDN (Zelger Coal)

  4.15% (LOC; Bank of America) (a,b)                                                               14,950,000        14,950,000

Richmond Industrial Development Authority, Revenue, VRDN (Cogentrix of Richmond
Project)

  4.50%, Series A (LOC; Banque Paribas) (a,b)                                                      10,000,000        10,000,000

Wisconsin--1.3%

Wisconsin Health and Educational Facilities Authority, Revenue, CP (Alexian
Village)

  3.70%, Series A, 8/20/98 (Insured; MBIA and LOC; First Chicago Corp.) (b)                        11,440,000        11,440,000

                                                                                                                  _____________

TOTAL INVESTMENTS (cost $902,663,993)                                                                              $902,662,922

                                                                                                                  =============
</TABLE>
<TABLE>

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------


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

EDR         Economic Development Revenue                            PCR         Pollution Control Revenue

FGIC        Financial Guaranty Insurance Company                    RAN         Revenue Anticipation Notes

FSA         Financial Security Assurance                            RRR         Resources Recovery Revenue

GO          General Obligation                                      SBPA        Standby Bond Purchase Agreement

HR          Hospital Revenue                                        SFMR        Single Family Mortgage Revenue

IDB         Industrial Development Board                            SWDR        Solid Waste Disposal Revenue

IDR         Industrial Development Revenue                          TAN         Tax Anticipation Notes

LOC         Letter of Credit                                        TRAN        Tax Revenue Anticipation Notes

LOR         Limited Obligation Revenue                              VRDN        Variable Rate Demand Notes

Summary of Combined Ratings (Unaudited)
- -----------------------------------------------------------------------------

Fitch (c)            or            Moody's             or            Standard & Poor's              Percentage of Value

_______                            ________                          _________________              ___________________

F1+/F1                             VMIG1/MIG1, P1 (d)                SP1+/SP1, A1+/A1 (d)                 95.4%

AAA/AAA (e)                        Aaa/A/ (e)                        AAA/AA (e)                            1.2

Not Rated (f)                      Not Rated (f)                     Not Rated (f)                         3.4
                                                                                                          ____

                                                                                                         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, 1998, 67.9% of the Fund's net
assets are backed by letters of credit issued by domestic banks, foreign banks,
 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)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 Manager 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, 1998

                                                                                                    Cost             Value

                                                                                                _____________     _____________
<S>                              <C>                                                             <C>               <C>

ASSETS:                          Investments in securities--See Statement of Investments         $902,663,993      $902,662,922

                                 Interest receivable                                                                  9,176,369

                                 Prepaid expenses and other assets                                                       68,715

                                                                                                                  _____________

                                                                                                                    911,908,006

                                                                                                                  _____________

LIABILITIES:                     Due to The Dreyfus Corporation and affiliates                                          458,199

                                 Cash overdraft due to Custodian                                                      7,586,464

                                 Accrued expenses and other liabilities                                                 146,109

                                                                                                                  _____________

                                                                                                                      8,190,772

                                                                                                                  _____________

NET ASSETS                                                                                                         $903,717,234

                                                                                                                  =============


REPRESENTED BY:                  Paid-in capital                                                                   $903,741,097

                                 Accumulated undistributed investment income--net                                       133,918

                                 Accumulated net realized gain (loss) on investments                                  (156,710)

                                 Accumulated gross unrealized (depreciation) on investments                             (1,071)

                                                                                                                  _____________

NET ASSETS                                                                                                         $903,717,234

                                                                                                                  =============


SHARES OUTSTANDING

(5 billion shares of $.01 par value Common Stock authorized)                                                        905,516,620

NET ASSET VALUE, offering and redemption price per share                                                                  $1.00
                                                                                                                 =====

</TABLE>
                      SEE NOTES TO FINANCIAL STATEMENTS.
<TABLE>
DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                               YEAR ENDED MAY 31, 1998

INVESTMENT INCOME
<S>                              <C>                                                             <C>                <C>
INCOME                           Interest Income                                                                    $37,351,905

EXPENSES:                        Management fee--Note 2(a)                                       $  5,001,054

                                 Shareholder servicing costs--Note 2(b)                             1,184,145

                                 Registration fees                                                    126,065

                                 Custodian fees                                                        81,483

                                 Professional fees                                                     62,207

                                 Directors' fees and expenses--Note 2(c)                               59,846

                                 Prospectus and shareholders' reports                                  28,715

                                 Miscellaneous                                                         23,117

                                                                                                 ____________

                                 Total Expenses                                                                    6,566,632

                                                                                                                   ____________

INVESTMENT INCOME--NET                                                                                               30,785,273

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b)                                                                     (34,746)

                                                                                                                   ____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                                                                $30,750,527

                                                                                                                   ============
</TABLE>

                      SEE NOTES TO FINANCIAL STATEMENTS.
<TABLE>
DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                                                               Year Ended        Year Ended

                                                                                              May 31, 1998       May 31, 1997
                                                                                             _______________  _______________
<S>                                                                                         <C>                <C>

OPERATIONS:

  Investment income--net                                                                    $     30,785,273   $     29,166,497

  Net realized gain (loss) on investments                                                            (34,746)            (2,582)

  Net unrealized appreciation (depreciation) on investments                                         --                   (6,289)

                                                                                             _______________    _______________

       Net Increase (Decrease) in Net Assets Resulting from Operations                            30,750,527         29,157,626

                                                                                             _______________    _______________

DIVIDENDS TO SHAREHOLDERS FROM:

  Investment income--net                                                                         (30,785,273)       (29,166,510)

  Net realized gain on investments                                                                  --                  (22,722)

                                                                                             _______________    _______________

       Total Dividends                                                                           (30,785,273)       (29,189,232)

                                                                                             _______________    _______________

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

  Net proceeds from shares sold                                                                2,925,580,744      3,175,303,462

  Dividends reinvested                                                                            17,843,487         18,593,500

  Cost of shares redeemed                                                                     (3,064,320,922)    (3,196,745,808)

  Net assets received in connection with reorganization (Dreyfus Michigan Municipal
    Money Market Fund)--Note 1                                                                      --               42,809,635

  Net assets received in connection with reorganization (Dreyfus Ohio Municipal
    Money Market Fund)--Note 1                                                                      --               34,121,878

                                                                                             _______________    _______________

       Increase (Decrease) in Net Assets from Capital Stock Transactions                        (120,896,691)        74,082,667

                                                                                             _______________    _______________

         Total Increase (Decrease) in Net Assets                                                (120,931,437)        74,051,061

NET ASSETS:

  Beginning of Period                                                                          1,024,648,671        950,597,610

                                                                                             _______________    _______________

  End of Period                                                                              $   903,717,234     $1,024,648,671

                                                                                             _______________    _______________


Undistributed investment income--net                                                         $       133,918     $      133,918

                                                                                             _______________    _______________

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>
<TABLE>
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 period indicated. This information has been
derived from the Fund's financial statements.


                                                                                         Year Ended May 31,

                                                                  _____________________________________________________________

PER SHARE DATA:                                                    1998          1997         1996         1995         1994

                                                                  ______       ______        ______       ______       ______
<S>                                                               <C>          <C>          <C>           <C>         <C>

   Net asset value, beginning of period                           $  1.00      $  1.00      $  1.00      $  1.00      $  1.00

                                                                  ______       ______        ______       ______       ______

   Investment Operations:

   Investment income--net                                            .031         .029         .031         .029         .020

                                                                  ______       ______        ______       ______       ______

   Distributions:

   Dividends from investment income--net                            (.031)       (.029)       (.031)       (.029)       (.020)

                                                                  ______       ______        ______       ______       ______

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

                                                                  =======      =======       =======      =======      =======


TOTAL INVESTMENT RETURN                                              3.13%        2.98%        3.16%        2.98%        2.00%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets                            .66%         .65%         .64%         .62%         .62%

   Ratio of net investment income
       to average net assets                                         3.08%        2.94%        3.11%        2.91%        1.98%

   Net Assets, end of period (000's Omitted)                     $903,717   $1,024,649     $950,598     $933,311   $1,117,002

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

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. is
the  distributor  of  the  Fund's shares, which are sold to the public without a
sales charge.

  On  August  26, 1996, the Fund acquired all the net assets of Dreyfus Michigan
Municipal Money market Fund ("DMMMMF") pursuant to a plan of reorganization. The
acquisition  was  accomplished  by  a tax-free exchange of shares, at which time
42,858,162  shares  of  DMMMMF,  valued  at $1.00 per share and representing net
assets  of  $42,809,635  were  exchanged  for 42,858,162 shares of the Fund. The
aggregate  net  assets of the Fund and DMMMMF immediately before the acquisition
were $956,664,386 and $42,809,635 respectively.

  On  August  2,  1996,  the  Fund  acquired  all the net assets of Dreyfus Ohio
Municipal Money Market Fund ("DOMMMF") pursuant to a plan of reorganization. The
acquisition  was  accomplished  by  a tax-free exchange of shares, at which time
34,170,011  shares  of  DOMMMF,  valued  at $1.00 per share and representing net
assets  of  $34,121,878  were  exchanged  for 34,170,011 shares of the Fund. The
aggregate  net  assets of the Fund and DOMMMF immediately before the acquisition
were $892,355,560 and $34,121,878 respectively.

  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
represent  amortized  cost. Under the terms of the custodian agreement, the Fund
received  net  earnings  credits of $33,374 during the period ended May 31, 1998
based  on  available  cash  balances  left  on deposit. Income earned under this
arrangement is included in interest income.

  (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, if any, are normally declared and paid
annually, but the Fund may make distributions on a more frequent basis to comply
with  the  distribution requirements of the Internal Revenue Code. 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.

DREYFUS MUNICIPAL MONEY MARKET FUND, INC.
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

  The  Fund  has  an  unused  capital  loss  carryover of approximately $120,000
available  for  Federal  income  tax  purposes  to be applied against future net
securities  profits,  if any, realized subsequent to May 31, 1998. The carryover
does  not  include  net realized securities losses from November 1, 1997 through
May  31,  1998 which are treated, for Federal income tax purposes, as arising in
fiscal  1999.  If  not  applied, $1,000 of the carryover expires in fiscal 2000,
$4,000  expires  in fiscal 2001, $49,000 expires in fiscal 2002, $36,000 expires
in fiscal 2003, $7,000 expires in fiscal 2004, $2,000 expires in fiscal 2005 and
$21,000 expires in fiscal 2006.

  At  May  31, 1998, 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 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.

  (B)  Under  the 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 period ended May
31,  1998,  the  Fund  was charged $805,959 pursuant to the Shareholder Services
Plan.

  The  Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,   under  a  transfer  agency  agreement  for  providing  personnel  and
facilities  to  perform transfer agency services for the Fund. During the period
ended  May  31,  1998,  the  Fund  was charged $287,495 pursuant to the transfer
agency agreement.

  (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.


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, 1998, 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  and  financial  highlights.  Our procedures included confirmation of
securities  owned  as  of  May 31, 1998 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, 1998, 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 6, 1998

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,
1998  as  "exempt-interest  dividends" (not generally subject to regular Federal
income tax).














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