GENERAL MUNICIPAL MONEY MARKET FUND INC
N-30D, 1998-08-07
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Dreyfus
General Municipal
Money Market
Fund
Semi-Annual Report


May 31, 1998

<PAGE>

General Municipal Money Market Fund, Inc.
- -------------------------------------------------------------------------------
Letter to Shareholders

Dear Shareholder:

   We are pleased to report the performance for General Municipal Money Market
Fund for the six-month reporting period ended May 31, 1998 as shown in the
following table:

                                            Annualized Yield   Effective Yield*
                                            ----------------   ---------------
        Class A Shares....................        3.04%              3.08%
        Class B Shares....................        2.69%              2.72%

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.

<PAGE>

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,

                                      /s/ Richard J. Moynihan

                                      Richard J. Moynihan
                                      Director, Municipal Portfolio Management
                                      The Dreyfus Corporation

June 18, 1998
New York, N.Y.

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


<PAGE>



General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Statement of Investments                               May 31, 1998 (Unaudited)

<TABLE>
<CAPTION>
                                                                                              Principal
Tax Exempt Investments--100.0%                                                                 Amount            Value
- -------------------------------------------------------------------------------              -----------      -----------
<S>                                                                                          <C>              <C>
Alaska--2.7%
Alaska Housing Finance Corporation, VRDN
   3.85%, Series A (BPA: Credit Suisse and Westdeutsche Landesbank)(a).........              $15,200,000      $15,200,000

Arizona--5.8%
Arizona Educational Loan Marketing Corporation, Educational Loan Revenue, VRDN
   3.95%, Series A (BPA; Fuji Bank and Insured; MBIA)(a).......................               10,675,000       10,675,000
Glendale Industrial Development Authority, HR, VRDN
   (West Valley Camelback) 3.85% (LOC; Northwest Bank Corp.)(a,b)..............                8,100,000        8,100,000
Pima County Industrial Development Authority, Industrial Revenue, VRDN
   (Tucson Electric) 3.90% (LOC; Toronto-Dominion Bank)(a, b)..................               14,100,000       14,100,000

California--3.5%
California Higher Education Loan Authority, Student Loan Revenue, Refunding
   3.80%, Series A, 5/1/99 (LOC; National Westminster Bank)(b).................                8,000,000        8,000,000
   3.95%, 6/1/98 (LOC; Student Loan Marketing Association)(b)..................                4,500,000        4,500,000
California Housing FInance Agency, Home Mortgage Revenue
   3.95%, Series J, 8/3/98 (Insured; FGIC).....................................                7,070,000        7,070,000

Connecticut--7.0%
State of Connecticut Development Authority, VRDN:
   Health Care Revenue (Corp. for Independent Living Project)
      3.70% (LOC; Chase Manhattan Bank) (a,b)..................................                5,000,000        5,000,000
   PCR, Refunding (Connecticut Light and Power Co. Project)
      3.80%, Series A (LOC; Deutsche Bank)(a,b)................................               13,700,000       13,700,000
State of Connecticut, Revenue:
   Special Assessment Unemployment Compensation Advance Fund
      (Connecticut Unemployment)
      3.90%, 7/1/98 (Insured and Liquidity Facility; FGIC).....................                7,000,000        7,000,000
   Special Tax Obligation, VRDN (Transportation Infrastructure-1)
      3.75% (LOC; Commerzbank)(a,b)............................................               13,900,000       13,900,000

Delaware--.1%
Delaware Economic Development Authority, IDR, VRDN
  (Orient Chemical Corp. Project) 4.45% (LOC; Sumitomo Bank)(a,b)..............                  480,000          480,000
District of Columbia--1.8%
District of Columbia Housing Finance Agency, SFMR
   4.15%, Series A, 7/1/98 (LOC; Assured Management Corp.)(b)..................               10,000,000       10,000,000

Florida--.8%
Florida Multi-Family Housing Financing Agency, Refunding (Iowa Lakes Project)
   3.85%, Series D, 4/1/99 (LOC; Continental Casualty)(a)......................                4,655,000        4,655,000

Georgia--4.1%
Burke County Development Authority, PCR, Refunding (Oglethorpe Power Corp.):
   CP 3.50%, Series A, 7/24/98 (Insured; AMBAC and LOC; Rabobank Nederland)(b).               10,000,000       10,000,000
   VRDN 3.90%, Series A (BPA; Credit Locale de France and Insured; FGIC)(a)....                7,900,000        7,900,000

</TABLE>

<PAGE>

General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Statement of Investments (continued)                   May 31, 1998 (Unaudited)
<TABLE>
<CAPTION>


                                                                                              Principal
Tax Exempt Investments (continued)                                                              Amount             Value
- -------------------------------------------------------------------------------              -----------       -----------
<S>                                                                                         <C>                <C>
Georgia--4.1% (continued)
Savannah Economic Development Authority, Exempt Facility Revenue, VRDN
   (Home Depot Project) 3.95%, Series B (LOC; Sun Trust Bank)(a,b).............             $  5,000,000       $  5,000,000

Hawaii--1.5%
Honolulu City and County, MFHR, VRDN (Halekua Gardens Project)
   4.25%, Series A (LOC; Bank of Tokyo-Mitsubishi)(a,b)........................                8,250,000         8,250,000

Idaho--.9%
State of Idaho, TAN 4.625%, 6/30/98............................................                5,000,000         5,002,848

Illinois--6.0%
City of Chicago 3.55%, 2/4/99 (LOC; Morgan Guaranty Trust Co.)(b)..............               10,000,000        10,000,000
Illinois Health Facilities Authority, Revenue, VRDN
   (Rehab Institute of Chicago Project) 3.85% (LOC; Bank of America)(a,b)......               13,500,000        13,300,000
Southwestern Development Authority, Environmental Improvement Revenue, VRDN
   (Shell Oil Co.-Wood River Project) 4.15% (Corp. Guaranty; Shell Oil Co.)(a).               10,300,000        10,300,000

Indiana--2.3%
City of Indianapolis, RRR, VRDN (Ogden Martin Systems)
   4.05% (LOC; WestDeutsche Landesbank)(a,b)...................................               13,060,000        13,060,000

Kentucky--.5%
Boone County, IDR, VRDN (Curtin Matheson Scientific Project)
   3.90% (LOC; Toronto-Dominion Bank)(a,b).....................................                2,500,000         2,500,000

Louisiana--2.2%
West Baton Rouge Parish Industrial District Number 3, Revenue, VRDN
   (Dow Chemical Co. Project) 4.20% (Corp. Guaranty; Dow Chemical Co.)(a)......               12,500,000        12,500,000

Maryland--1.2%
Baltimore County, PCR, CP (Baltimore Gas and Electric)
   3.65% (LOC; Toronto-Dominion Bank) (a,b)....................................                6,600,000         6,600,000

Massachusetts--.5%
City of Springfield, BAN 4.40%, 6/26/98........................................                3,000,000         3,000,888

Michigan--5.6%
Macomb Township Economic Development Corporation, LOR, VRDN
   (ACR Industries Project) 3.95% (LOC; Comerica Bank)(a,b)....................                  550,000           550,000
Midland County Economic Development Corporation, Economic Development, LOR,
   VRDN (Dow Chemical Co. Project) 4%, Series A (LOC; Dow Chemical Co.)(a,b)...                22,000,000       22,000,000
Michigan Municipal Bond Authority, Revenue, Notes 4.50%, Series B, 7/2/98......                 5,000,000        5,002,573
Michigan Strategic Fund, SWDR, VRDN (Grayling Generating Project)
   4% (LOC; Barclays Bank)(a,b)................................................                 3,800,000        3,800,000

Minnesota--.5%
State of Minnesota, GO Notes 4.75%, 5/1/99.....................................                 2,000,000        2,017,769
Minnesota Public Facilities Authority, Water PCR 6.70%, Series A, 3/1/99......                  1,000,000        1,021,467
</TABLE>

<PAGE>

General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Statement of Investments (continued)                   May 31, 1998 (Unaudited)
<TABLE>
<CAPTION>
                                                                                              Principal
Tax Exempt Investments (continued)                                                              Amount            Value
- -------------------------------------------------------------------------------              -----------      -------------
<S>                                                                                         <C>              <C>
Missouri--1.8%
Missouri Health and Educational Facilities Authority, Health Facilities
   Revenue, VRDN (Deaconess Long Term Care) 3.875%, Series A
   (LOC; Bank One)(a,b)........................................................             $  9,900,000     $    9,900,000

Montana--1.2%
Forsyth, PCR, VRDN (Portland General Electric Co.)
   4.10% (LOC; Banque Nationale de Paris)(a,b).................................                7,000,000          7,000,000

Nevada--2.2%
Clark County, IDR, VRDN (Nevada Cogeneration Project)
   4.10% (LOC; Canadian Imperial Bank of Commerce)(a,b)........................                7,200,000          7,200,000
Washoe County, Water Facilities Revenue, VRDN (Sierra Pacific Power Co. Project)
   4.15% (LOC; Union Bank of Switzerland)(a,b).................................                5,400,000          5,400,000

New Mexico--1.2%
State of New Mexico, TRAN 4.50%, Series A, 6/30/98.............................                7,000,000          7,003,598

New York--8.5%
City of New York:
   CP 3.40%, 7/13/98 (LOC; Commerzbank)(b).....................................                7,000,000          7,000,000
   RAN 4.50%, Series A, 6/30/98 (LOC: Bayerische Hypotheken, Morgan
      Guaranty Trust Co. and National Westminster Bank)(b)......................               8,000,000          8,004,781
State of New York, CP 3.55%, 7/13/98 (LOC; WestDeutsche Landesbank)(b).........               10,000,000         10,000,000
New York State Housing Finance Agency, Housing Revenue, VRDN (Normandie Court II)
   3.60%, Series A (LOC; Fleet Bank)(a,b)......................................                4,100,000          4,100,000
New York State Local Government Assistance Corporation, VRDN
   3.85%, Series A (Liquidity; Union Bank of Switzerland and LOC: Credit Suisse
   and Union Bank of Switzerland)(a,b).........................................                5,000,000          5,000,000
Triborough Bridge and Tunnel Authority, Special Obligation, VRDN
   3.90% (Insured and Liquidity Facility; FGIC)(a).............................               14,000,000         14,000,000

North Carolina--1.0%
Craven County Industrial Facilities and Pollution Control Financing Authority,
    VRDN (Craven Wood Energy) 4.20%, Series C (LOC; ABN-Amro Bank)(a,b)........                5,700,000          5,700,000

Ohio--8.7%
Cincinnati City School District:
   BAN 4.32%, 9/17/98..........................................................                7,830,000          7,838,224
   TAN 4.08%, 12/31/98.........................................................                5,000,000          5,013,545
Green County, Certificates of Indebtedness, GO Notes 3.75, 5/6/99..............                8,000,000          8,001,416
Montgomery County, Revenue, CP (Miami Valley Hospital)
   3.80%, Series B, 8/11/98 (BPA; Morgan Guaranty Trust Co.)...................                8,000,000          8,000,000
</TABLE>


<PAGE>

General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Statement of Investments (continued)                   May 31, 1998 (Unaudited)
<TABLE>
<CAPTION>

                                                                                               Principal
Tax Exempt Investments (continued)                                                              Amount              Value
- -------------------------------------------------------------------------------              --------------    --------------
<S>                                                                                          <C>               <C>
Ohio--8.7% (continued)
Ohio Air Quality Development Authority, PCR, CP (Cleveland Electric)
   3.75%, Series B, 7/28/98 (Insured and Liquidity Facility; FGIC).............               $ 14,725,000     $  14,725,000
Ohio Housing Finance Agency, Mortgage Revenue
   3.85%, Series A-2, 3/1/99 (LOC; Trinity Funding Corp.)(b)...................                  5,670,000         5,670,000

Oregon--1.2%
Klamath Falls, Electric Revenue (Salt Cave Hydroelectric)
   3.80%, Series C, 5/3/99 (Escrowed in; U.S. Treasury Bills)..................                  7,000,000         7,000,000

Pennsylvania--.9%
City of Philadelphia, TRAN 4.50%, Series A, 6/30/98............................                  5,000,000         5,001,909

Tennessee--.5%
Morristown Industrial Development Board, IDR, VRDN
   (Camvac International Inc. Project) 4.075% (LOC; Bankers Trust)(a,b)........                  3,000,000         3,000,000

Texas--14.5%
Brazos River Authority, PCR, Refunding, VRDN (Texas Utilities Electric Co.):
   3.95%, Series A (BPA; The Bank of New York)(a)..............................                  4,500,000         4,500,000
   4.15%, Series C (BPA; The Bank of New York and Insured; MBIA)(a)............                 14,245,000        14,245,000
   4.15%, Series C (BPA; The Bank of New York and Insured; AMBAC)(a)...........                 13,700,000        13,700,000
Brazos River Harbor Naval District, Harbor Revenue, VRDN:
   (Dow Chemical Co. Project) 4.20% Series A (Corp. Guaranty; Dow Chemical
   Corp.)(a)...................................................................                 12,800,000        12,800,000
   (BASF Corp.) 4% (Corp. Guaranty; BASF Corp.)(a).............................                  3,200,000         3,200,000
Dallas County, Permanent Improvement
   3.95%, Series C, 9/1/98 (BPA; Union Bank of Switzerland)....................                  4,220,000         4,220,000
Greater East Texas Higher Education Authority, Inc., Student Loan Revenue
   3.95%, Series B, 9/1/98 (LOC; Student Loan Marketing Association)(b)........                  5,000,000         5,000,000
Gulf Coast Industrial Development Authority, Marine Terminal Revenue, VRDN
   (Amoco Oil Co. Project) 4.15% (LOC; Amoco Credit Corp.)(a,b)................                 11,300,000        11,300,000
Panhandle-Plains Higher Education Authority, Student Loan Revenue, Refunding,
  VRDN 4%, Series A (LOC; Student Loan Marketing Association)(a,b).............                 12,700,000        12,700,000

Utah--1.8%
Intermountain Power Agency, Power Supply Revenue, CP
   3.55%, 7/16/98 (Liquidity: Bank of America and Bank of Nova Scotia).........                 10,200,000        10,200,000

Virginia--6.2%
Peninsula Ports Authority, Revenue, Refunding, VRDN (Zelgler Coal)
   4.15% (LOC; Bank of America)(a,b)...........................................                 25,000,000        25,000,000
Richmond Industrial Development Authority, Revenue, VRDN
   (Cogentrix of Richmond Project)
   4.50%, Series A (LOC; Banque Paribas)(a,b)..................................                  5,000,000         5,000,000
Richmond Redevelopment and Housing Authority, MFHR
   (Richmeade LP Project) 4.625%, 6/25/98......................................                  4,800,000         4,800,000

</TABLE>

<PAGE>

General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Statement of Investments (continued)                   May 31, 1998 (Unaudited)
<TABLE>
<CAPTION>

                                                                                                Principal
Tax Exempt Investments (continued)                                                                Amount             Value
- -------------------------------------------------------------------------------              ---------------    --------------
<S>                                                                                           <C>                <C>
West Virginia--1.2%
Marion County, County Community Solid Waste Disposal Facility Revenue, VRDN
   (Granttown Project) 4%, Series B (LOC; National Westminster Bank)(a,b)......               $   3,700,000      $  3,700,000
Pendleton County, IDR, VRDN (Greer Steel Project) 4.05% (LOC; PNC Bank)(a,b)...                   3,015,000         3,015,000

Wyoming--2.1%
Lincoln County, PCR, VRDN (Exxon Project):
   3.95%, Series A (Corp. Guaranty; Exxon Corp.)(a)............................                   2,600,000         2,600,000
   4.05%, Series B (Corp. Guaranty; Exxon Corp.)(a)............................                   9,500,000         9,500,000
                                                                                                                 ------------
TOTAL INVESTMENTS (cost $564,424,018)..........................................                                  $564,424,018
                                                                                                                 ============
</TABLE>


Summary of Abbreviations
- -------------------------------------------------------------------------------
<TABLE>
<S>        <C>                                             <C>         <C>

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

Summary of Combined Ratings
- -------------------------------------------------------------------------------
<TABLE>
<CAPTION>

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)             93.0%
AAA/AA (e)                   Aaa/Aa, A1 (e)                AAA/AA (e)                        2.0
Not Rated (f)                Not Rated (f)                 Not Rated (f)                     5.0
                                                                                          ------
                                                                                           100.0%
                                                                                          ======

Notes to Statement of Investments:
- -------------------------------------------------------------------------------
<FN>
(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, 56.4% of the Fund's net
    assets are backed by letters of credit issued by domestic banks, foreign
    banks 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.
</FN>
</TABLE>

                       See notes to financial statements.


<PAGE>


General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Statement of Assets and Liabilities                    May 31, 1998 (Unaudited)
<TABLE>
<CAPTION>
                                                                                                Cost             Value
                                                                                            -------------    ------------
<S>                          <C>                                                            <C>              <C>
ASSETS:                      Investments in securities--See Statement of Investments        $564,424,018     $564,424,018
                             Cash..............................................                                 1,090,247
                             Interest receivable...............................                                 4,251,964
                             Prepaid expenses..................................                                    48,857
                                                                                                            -------------
                                                                                                              569,815,086
                                                                                                            -------------

LIABILITIES:                 Due to The Dreyfus Corporation and affiliates.....                                   157,876
                             Due to Distributor................................                                    19,239
                             Accrued expenses and other liabilities............                                    72,211
                                                                                                            -------------
                                                                                                                  249,326
                                                                                                            -------------
NET ASSETS.....................................................................                              $569,565,760
                                                                                                            =============
REPRESENTED BY:              Paid-in capital...................................                              $569,579,786
                             Accumulated net realized gain (loss) on investments                                 (14,026)
                                                                                                            -------------
NET ASSETS.....................................................................                              $569,565,760
                                                                                                            =============
</TABLE>


                            NET ASSET VALUE PER SHARE
<TABLE>
<CAPTION>

                                                                                   Class A                     Class B
                                                                                --------------              -------------
<S>                                                                              <C>                         <C>
Net Assets.....................................................................  $288,692,020                $280,873,740
Shares Outstanding.............................................................   288,984,080                 280,876,982

NET ASSET VALUE PER SHARE......................................................         $1.00                      $1.00
                                                                                        =====                      =====

</TABLE>


                       See notes to financial statements.


<PAGE>


General Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Operations               Six Months Ended May 31, 1998 (Unaudited)

INVESTMENT INCOME

<TABLE>
<S>                           <C>                                                           <C>              <C>
INCOME                        Interest Income.............................                                    $10,224,205


EXPENSES:                     Management fee--Note 2(a)...................                  $1,402,474
                              Shareholder servicing costs--Note 2(c)......                     522,959
                              Distribution fees (Class B)--Note 2(b)......                     282,545
                              Registration fees...........................                      47,056
                              Professional fees...........................                      24,359
                              Custodian fees..............................                      24,335
                              Directors' fees and expenses--Note 2(d).....                      16,716
                              Prospectus and shareholders' reports........                       3,447
                              Miscellaneous...............................                       6,325
                                                                                           -----------
                                Total Expenses............................                   2,330,216
                              Less--reduction in shareholder servicing costs
                                due to undertaking--Note 2(c).............                    (129,064)
                                                                                           -----------
                                Net Expenses..............................                                      2,201,152
                                                                                                             ------------

INVESTMENT INCOME--NET....................................................                                      8,023,053
                                                                                                             ------------

NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b)...........                                        (11,241)
                                                                                                             ------------

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS......................                                   $  8,011,812
                                                                                                             ============
</TABLE>

                       See notes to financial statements.


<PAGE>


General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Statement of Changes in Net Assets
<TABLE>
<CAPTION>

                                                                                Six Months Ended
                                                                                  May 31, 1998          Year Ended
                                                                                   (Unaudited)       November 30, 1997
                                                                                ---------------     ------------------
<S>                                                                              <C>                  <C>
OPERATIONS:
   Investment income--net..............................................          $    8,023,053        $  12,783,231
   Net realized gain (loss) on investments.............................                 (11,241)              26,716
   Net unrealized appreciation (depreciation) on investments...........                    --                 (8,845)
                                                                                 --------------        -------------
         Net Increase (Decrease) in Net Assets Resulting from Operations              8,011,812           12,801,102
                                                                                 --------------        -------------


DIVIDENDS TO SHAREHOLDERS FROM:
   Investment income--net:
      Class A shares...................................................              (4,236,025)          (7,970,586)
      Class B shares...................................................              (3,787,028)          (4,812,645)
   Net realized gain on investments:
      Class A shares...................................................                  (5,225)               --
      Class B shares...................................................                  (5,196)               --
                                                                                 --------------        -------------
         Total Dividends...............................................              (8,033,474)         (12,783,231)
                                                                                 --------------        -------------


CAPITAL STOCK TRANSACTIONS ($1.00 per share):
   Net proceeds from shares sold:
      Class A shares...................................................             708,090,739        1,212,808,595
      Class B shares...................................................             719,687,185        1,069,980,511
   Dividends reinvested:
      Class A shares...................................................               4,104,369            7,678,759
      Class B shares...................................................               3,717,619            4,696,878
   Cost of shares redeemed:
      Class A shares...................................................            (696,550,061)      (1,204,301,450)
      Class B shares...................................................            (705,528,342)        (829,168,072)
                                                                                 --------------        -------------
         Increase (Decrease) in Net Assets from Capital Stock Transactions           33,521,509          261,695,221
                                                                                 --------------        -------------
            Total Increase (Decrease) in Net Assets....................              33,499,847          261,713,092

NET ASSETS:
   Beginning of Period.................................................             536,065,913           274,352,821
                                                                                 --------------        --------------
   End of Period.......................................................            $569,565,760          $536,065,913
                                                                                 ==============        ==============

</TABLE>




                       See notes to financial statements.


<PAGE>


General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Financial Highlights

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

                                                                            Class A Shares
                                              -----------------------------------------------------------------------
                                              Six Months Ended
                                                May 31, 1998                  Year Ended November 30,
                                                               ------------------------------------------------------
PER SHARE DATA:                                  (Unaudited)     1997       1996       1995        1994       1993
                                                 ----------     -----      -----       -----       -----      -----
<S>                                               <C>           <C>        <C>         <C>         <C>        <C>

   Net asset value, beginning of period.....        $1.00       $1.00       $1.00      $1.00       $1.00       $1.00
                                                    -----       -----       -----      -----       -----       -----
   Investment Operations:
   Investment income--net...................         .015        .031        .029       .034        .023        .021
                                                    -----       -----       -----      -----       -----       -----
   Distributions:
   Dividends from investment income--net....        (.015)      (.031)      (.029)     (.034)      (.023)      (.021)
                                                    -----       -----       -----      -----       -----       -----
   Net asset value, end of period...........        $1.00       $1.00       $1.00      $1.00       $1.00       $1.00
                                                    =====       =====       =====      =====       =====       =====
TOTAL INVESTMENT RETURN.....................         3.07%*      3.14%       2.97%      3.41%       2.27%       2.10%
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets..          .61%*       .62%        .66%       .66%        .64%        .63%
   Ratio of net investment income to average
      net assets............................         3.04%*      3.09%       2.93%      3.35%       2.22%       2.08%
   Net Assets, end of period (000's Omitted)     $288,692    $273,058    $256,862   $294,379    $294,711    $352,147

<FN>
- ------------------
* Annualized.

</FN>
</TABLE>

                       See notes to financial statements.


<PAGE>



General Municipal Money Market Fund
- -------------------------------------------------------------------------------
Financial Highlights (continued)

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

                                                                                       Class B Shares
                                                                       -----------------------------------------------
                                                                       Six Months Ended
                                                                         May 31, 1998       Year Ended November 31,
                                                                                        ------------------------------
PER SHARE DATA:                                                           (Unaudited)    1997        1996       1995(1)
                                                                           ---------    -----       -----      -------
<S>                                                                          <C>         <C>         <C>         <C>
   Net asset value, beginning of period...........................           $1.00       $1.00       $1.00       $1.00
                                                                             -----       -----       -----       -----
   Investment Operations:
   Investment income--net.........................................            .013        .028        .027        .020
                                                                             -----       -----       -----       -----
   Distributions:
   Dividends from investment income--net..........................           (.013)      (.028)      (.027)      (.020)
                                                                             -----       -----       -----       -----
   Net asset value, end of period.................................           $1.00       $1.00       $1.00       $1.00
                                                                             =====       =====       =====       =====
TOTAL INVESTMENT RETURN...........................................            2.71%(2)    2.86%       2.70%       3.01%(2)
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets........................            .96%(2)      .95%        .85%       1.10%(2)
   Ratio of net investment income to average net assets...........           2.68%(2)     2.87%       2.65%       2.83%(2)
   Decrease reflected in above expense ratios due to
      undertakings by the Manager.................................            .09%(2)      .16%        .29%        .09%(2)
   Net Assets, end of period (000's Omitted)......................       $280,874     $263,008     $17,491      $3,024

<FN>

- -----------------
(1) From March 31, 1995 (commencement of initial offering) to November 30, 1995.
(2) Annualized.

</FN>
</TABLE>
                       See notes to financial statements.


<PAGE>



General Municipal Money Market Fund
- -------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (Unaudited)

NOTE 1--Significant Accounting Policies:

   General Municipal Money Market Fund (the "Fund") is a separate diversified
series of General Municipal Money Market Fund, Inc. (the "Company") which is
registered under the Investment Company Act of 1940 ("Act") as an open-end
management investment company and operates as a series company, currently
offering two series, including the Fund. 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.

   Effective April 30, 1998, the Fund's name was changed from "General Municipal
Money Market Fund, Inc." to "General Municipal Money Market Fund".

   Premier Mutual Fund Services, Inc. (the "Distributor") is the distributor of
the Fund's shares, which are sold to the public without a sales load. The Fund
is authorized to issue 16 billion of $.01 par value Common Stock. The Fund is
currently authorized to issue two classes of shares: Class A (15 billion shares
authorized) and Class B (1 billion shares authorized). Class A shares and Class
B shares are identical except for the services offered to and the expenses borne
by each class and certain voting rights. Class B shares are subject to a
Distribution Plan adopted pursuant to Rule 12b-1 under the Act and, in addition,
Class B shares are charged directly for sub-accounting services provided by
Service Agents (a securities dealer, financial institution or other industry
professional) at an annual rate of .05% of the value of the average daily net
assets of Class B shares.

   The Company accounts separately for the assets, liabilities and operations of
each fund. Expenses directly attributable to each fund are charged to that
fund's operations; expenses which are applicable to all funds are allocated
among them on a pro rata basis.

   It is the Fund's policy to maintain a continuous net asset value per share of
$1.00; the Fund has adopted certain investment, portfolio valuation and dividend
and distribution policies to enable it to do so. There is no assurance, however,
that the Fund will be able to maintain a stable net asset value per share of
$1.00.

   The Fund's financial statements are prepared in accordance with generally
accepted accounting principles which may require the use of management estimates
and assumptions. Actual results could differ from those estimates.

   (a) Portfolio valuation: Investments in securities are valued at amortized
cost, which has been determined by the Fund's Board of Directors to represent
the fair value of the Fund's investments.

   (b) Securities transactions and investment income: Securities transactions
are recorded on a trade date basis. Interest income, adjusted for amortization
of premiums and original issue discounts on investments, is earned from
settlement date and recognized on the accrual basis. Realized gain and loss from
securities transactions are recorded on the identified cost basis. Cost of
investments represents amortized cost. Under the terms of the custodian
agreement, the Fund received net earnings credits of $8,024 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 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, if any,
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


<PAGE>


General Municipal Money Market Fund
- -------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

make distributions of income and net realized capital gain sufficient to
relieve it from substantially all Federal income and excise taxes.

   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 ("Agreement") with the Manager, the
management fee is computed at the annual rate of .50 of 1% of the value of the
Fund's average daily net assets and is payable monthly. The Agreement provides
that if in any full fiscal year the aggregate expenses of the Fund, exclusive of
taxes, brokerage, interest on borrowings and extraordinary expenses, exceed 1
1/2% of the average value of the Fund's net assets, the Fund may deduct from
payments to be made to the Manager, or the Manager will bear such excess
expense. During the period ended May 31, 1998, there was no expense
reimbursement pursuant to the Agreement.

   (b) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, Class B
shares directly bear the costs of preparing, printing and distributing
prospectuses and statements of additional information and of implementing and
operating the Class B Distribution Plan. In addition, Class B shares reimburse
the Distributor for payments made to third parties for distributing their shares
at an annual rate of .20 of 1% of the value of the average daily net assets of
Class B. During the period ended May 31, 1998, Class B shares were charged
$282,545 pursuant to the Distribution Plan.

   (c) Under the Shareholder Services Plan with respect to Class A, Class A
shares reimburse 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
average daily net assets of Class A for certain allocated expenses of providing
personal services and/or maintaining shareholder accounts. The services provided
may include personal services relating to shareholder accounts, such as
answering shareholder inquiries regarding Class A shares and providing reports
and other information, and services related to the maintenance of shareholder
accounts. During the period ended May 31, 1998, Class A shares were charged
$44,947 pursuant to the Shareholder Services Plan.

   Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan") Class B shares pay the Distributor at an annual rate
of .25 of 1% of the value of the average daily net assets of Class B shares for
servicing shareholder accounts. The services provided may include personal
services relating to shareholder accounts, such as answering shareholder
inquiries regarding Class B shares and providing reports and other information,
and services related to the maintenance of shareholder accounts. The Distributor
may make payments to Service Agents in respect of their services. The
Distributor determines the amounts to be paid to Service Agents.

   The Manager had undertaken from December 1, 1997 through May 31, 1998, that
if the aggregate expenses of Class B shares, exclusive of taxes, brokerage,
interest on borrowings and extraordinary expenses, exceeded specified annual
percentages of the average daily net assets of Class B, the Manager will
reimburse the expenses of the Fund under the Class B Shareholder Services Plan
to the extent of any excess expense and up to the full fee payable under such
Plan. During the period ended May 31, 1998, Class B shares were charged $423,817
of which $129,064 was reimbursed by the Manager.

   The Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager, under a transfer agency agreement for providing personnel and
facilities to perform transfer agency services for the Fund. During the period
ended May 31, 1998, the Fund was charged $26,674 pursuant to the transfer agency
agreement.

   (d) Each director who is not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $500 per
meeting. The Chairman of the Board receives an additional 25% of such
compensation.

<PAGE>

General Municipal
Money Market Fund
200 Park Avenue
New York, NY 10166

Manager
The Dreyfus Corporation
200 Park Avenue
New York, NY 10166

Custodian
The Bank of New York
90 Washington Street
New York, NY 10286

Transfer Agent &
Dividend Disbursing Agent
Dreyfus Transfer, Inc.
P.O. Box 9671
Providence, RI 02940

Printed in U.S.A.                  918/697SA985



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