GENERAL MUNICIPAL MONEY MARKET FUNDS INC
N-30D, 1999-02-05
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YEAR 2000 ISSUES (UNAUDITED)

  The  fund  could  be  adversely  affected  if the computer systems used by The
Dreyfus  Corporation  and  the  fund' s  other service providers do not properly
process  and  calculate date-related information from and after January 1, 2000.
The  Dreyfus  Corporation  is working to avoid Year 2000-related problems in its
systems  and  to  obtain  assurances  from other service providers that they are
taking  similar  steps.  In  addition,  issuers  of securities in which the fund
invests may be adversely affected by Year 2000-related problems. This could have
an impact on the value of the fund's investments and its share price.

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

  We  are  pleased  to report the performance for General Municipal Money Market
Fund  for  the 12-month period ended November 30, 1998 as shown in the following
table:
<TABLE>
<CAPTION>


                                                                           YIELD                      EFFECTIVE YIELD*
                                                                          _______                       _____________
<S>                                                                         <C>                             <C>
        Class A Shares . . . . . . . . . . . . . . . . . . . .              2.98%                           3.02%

        Class B Shares . . . . . . . . . . . . . . . . . . . .              2.61%                           2.64%
</TABLE>

ECONOMY

  During  1998,  the  main  regions  of  the  world  had very different economic
fundamentals.  The  U.S.  entered  the  year  with  a  strong  economy near full
employment, with unemployment only slightly above 4%. The tight labor market led
the  Federal  Reserve Board to contemplate a rise in interest rates early in the
year.  The  U.S.  economy  cooled enough over the months that the Fed decided to
stand  pat.  Evidence  of  economic  cooling continued to accumulate and worries
about  the  world economy intensified. Financial stresses pushed the Fed to ease
beginning  in September. After many years of subpar economic growth, continental
Europe  moved  into a sustained economic expansion. The overall European economy
benefited  as  interest  rates  in  peripheral countries such as Spain and Italy
fell, approaching the lower level established by Germany, on the eve of currency
unification.  Unlike  the  U.S.,  Europe  has  substantial  excess  capacity  of
productive  plants and labor. In Asia, weak economies were pervasive as a result
of  the  Asian  financial  crisis.  The Latin American economies weakened as the
financial stresses spread throughout that region.

  A  main  influence  on  the  U.S.  economy this year was the foreign financial
crisis  and cooling of the world economy. The positive effects hit first. Actual
inflation  and  expected  inflation  dropped,  causing  a  decline  in long-term
Treasury bond yields and mortgage rates. This caused a boom in housing. The drop
in inflation helped the consumer sector as more of the growth in consumer income
was  left  over  after  inflation to buy goods and services. Consumers benefited
from a combination of good growth in real income, a strong labor market and past
increases in the prices of assets they owned.

  The  negative  effect of Asian weakness was felt in the industrial sector more
than  the  consumer  sector.  Corporate  profits weakened, especially in sectors
affected  by  the Asian crisis such as world-traded commodities (oil, metals and
paper) and exports. One result of the industrial weakness was to cool off a U.S.
economy that had been growing rapidly.

  The  major  change  in  the  economic  outlook  over  recent months has been a
downward  shift  in  expectations  for  world  economic  growth. A credit crunch
developed in emerging countries and former communist countries, sharply reducing
the   economic   outlook   for   Asia   and   Latin   America  as  well  as  for
commodity-exporting countries throughout the world. The effect on Europe and the
U.S. has been to lower expectations of profit growth and drive down bond yields.
Monetary policy has begun to ease in Europe as well as the U.S.

  Evidence  of  a  weaker  world  economy  accumulated as the financial stresses
continued.  A  worsened financial crisis occurred between the Russian default in
mid-August  and  the  fallout  from  the Long-Term Capital Management hedge fund
crisis  through  early October. However, proactive steps were taken to stabilize
the  Japanese  banks,  design  a  support  package  for Brazil and ease monetary
policy.  There  appears to be a shift in the priorities of key policymakers from
fighting potential inflation to restimulating future world economic growth.

MARKET ENVIRONMENT/PORTFOLIO OVERVIEW

  The  manner in which the Federal Reserve eased this past quarter was a gradual
process.  For  three  successive months, beginning in September, the Fed reduced
the  target  rate for Fed Funds a total of 75 basis points. The Fed also lowered
the  Discount  Rate by 25 basis points each, in November and December. The Fed's
actions provided even greater strength to an already strong short-term municipal
money  market.  Prior to these rate cuts, the short-term market had already felt
the  effects  of  the diminished supply of eligible new issuance over the summer
months.  This  year's  summer calendar of municipal notes (consisting mainly of
California  paper)  was  drastically reduced by a combination of factors. Due to
the strength of local and state economies, several issuers reduced the amount of
short-term  borrowing  needed.  Additionally,  many  issuers came to market with
securities with maturities beyond the 13-month maximum restriction allowable for
tax-exempt  money  funds.  Other  issues were converted to a shortened synthetic
structure,  thus  eliminating the ability to extend out into the one-year range.
This  reduction in supply resulted in lower yields for most one-year paper, both
national and state specific.

  We  extended  your  Fund's  average maturity beyond 65 days during the summer
months,  just  prior  to  the market strengthening. Your Fund benefited from our
purchase of securities in the one-year range at yields significantly higher than
what  is  currently  available  in  the market. As the summer progressed, yields
began  to drop as they reflected the diminished supply of one-year notes. During
this  period  we  utilized  the  commercial  paper market to maintain the Fund's
average  maturity.  As year-end approaches, we will continue to search for those
longer-term  investment  opportunities  which  will  lock  in higher rates while
providing  an  attractive  return to the tax-exempt investor. As always, we will
structure   the  portfolio  in  an  attempt  to  maximize  current  yield  while
maintaining our commitment to high quality tax-exempt investments.

              Very truly yours,


             [Richard J. Moynihan signature]



              Richard J. Moynihan

              Director, Municipal Portfolio Management

              The Dreyfus Corporation

December 15, 1998

New York, N.Y.

* Effective yield takes into account the effect of compounding and is based upon
dividends declared daily and reinvested monthly.

<TABLE>
<CAPTION>
GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    NOVEMBER 30, 1998

                                                                                                   Principal
Tax Exempt Investments--99.6%                                                                       Amount            Value
- -------------------------------------------------------                                          ____________     _____________
<S>                                                                                            <C>               <C>
Alabama--.7%

McIntosh, IDB, EIR, Refunding, VRDN (CIBC Speciality)

   3.35%, Series E (Corp. Guaranty; CIBC Specialty) (a)  . . . . . . . . . . . . . . . . .     $    4,400,000    $    4,400,000

Alaska--2.3%

Alaska Housing Finance Corporation, VRDN

   3.20%, Series A (BPA: Credit Suisse and Westdeutsche Landesbank) (a)  . . . . . . . . .         15,200,000        15,200,000

Arizona--5.0%

Arizona Educational Loan Marketing Corporation, Educational Loan Revenue, VRDN

   3.25%, Series A (BPA; Fuji Bank and Insured; MBIA) (a)  . . . . . . . . . . . . . . . .         10,675,000        10,675,000

Glendale Industrial Development Authority, HR, VRDN

   (West Valley Camelback) 3.15% (LOC; Northwest Bank Corp.) (a) . . . . . . . . . . . . .          7,800,000         7,800,000

Pima County Industrial Development Authority, Industrial Revenue, VRDN

   (Tucson Electric) 3.15% (LOC; Toronto-Dominion Bank) (a)  . . . . . . . . . . . . . . .         14,100,000        14,100,000

California--1.2 %

California Higher Education Loan Authority, Student Loan Revenue, Refunding

   3.80%, Series A, 5/1/99 (LOC; National Westminster Bank)  . . . . . . . . . . . . . . .          8,000,000         8,000,000

Connecticut--3.2%

State of Connecticut, Revenue:

  Special Assessment Unemployment Compensation Advance Fund

    (Connecticut Unemployment)

       3.60%, 7/1/99 (Insured; FGIC and Liquidity Facility; FGIC)  . . . . . . . . . . . .          7,000,000         7,000,000

   Special Tax Obligation, VRDN (Transportation Infrastructure-1):

       3.10% (LOC; Commerzbank) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .         13,100,000        13,100,000

       3.20% (LOC; Commerzbank) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .            800,000           800,000

District of Columbia--.8%

District of Columbia Housing Finance Agency, SFMR

  3.75%, Series B, 9/30/99 (LOC: Canadian Imperial Bank of Commerce,

   Morgan Guaranty Trust Co. and Societe Generale) . . . . . . . . . . . . . . . . . . . .          5,000,000         5,026,260

Florida--4.1%

Florida  Housing Financing Agency:

  Multi-Family, Refunding (Iowa Lakes Project)

       3.85%, Series D, 4/1/99 (LOC; Continental Casualty) . . . . . . . . . . . . . . . .          4,655,000         4,655,000

   (Wood Forest II Project)

       3.15%, Series BBB, 12/1/99 (LOC; Continental Casualty)  . . . . . . . . . . . . . .          6,000,000         6,000,000

Miami-Dade County School Board, COP, Refunding

   4%, Series C, 5/1/99 (Insured; FSA) . . . . . . . . . . . . . . . . . . . . . . . . . .          5,560,000         5,582,689

Miami-Dade County School District, TAN 4%, 6/30/99 . . . . . . . . . . . . . . . . . . . .         10,450,000        10,470,407

Georgia--3.5%

Burke County Development Authority, PCR, Refunding (Oglethorpe Power Corp.):

  CP 3.05%, Series A, 3/10/99 (Insured; AMBAC and Liquidity Facility;

       Rabobank Netherland)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         10,000,000        10,000,000

   VRDN 3.05%, Series A (BPA; Credit Locale de France and Insured; FGIC) (a) . . . . . . .          7,900,000         7,900,000

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                     NOVEMBER 30, 1998

                                                                                                   Principal

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

Georgia (continued)

Savannah Economic Development Authority, Exempt Facility Revenue, VRDN

   (Home Depot Project) 3.25%, Series B (LOC; Sun Trust Bank) (a)  . . . . . . . . . . . .     $    5,000,000    $    5,000,000

Idaho--.8%

State of Idaho, TAN 4.50%, 6/30/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,025,100

Illinois--9.5%

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

Chicago Midway Airport,  Revenue, VRDN (Second Lien)

   3.40%, Series A (Insured; MBIA and Liquidity Facility; FNB Chicago) . . . . . . . . . .         17,800,000        17,800,000

Illinois Health Facilities Authority, Revenue, VRDN:

   (Rehab Institute of Chicago Project) 3.15% (LOC; Bank of America) (a) . . . . . . . . .         13,500,000        13,500,000

   (Resurrection Health Care System) 3.35% (a) . . . . . . . . . . . . . . . . . . . . . .         11,000,000        11,000,000

Southwestern Development Authority, EIR, VRDN

   (Shell Oil Co.-Wood River Project) 3.45% (Corp. Guaranty; Shell Oil Co.) (a)  . . . . .         10,300,000        10,300,000

Indiana--2.1%

City of  Indianapolis, RRR, VRDN (Ogden Martin Systems)

   3.35% (LOC; Westdeutsche Landesbank) (a)  . . . . . . . . . . . . . . . . . . . . . . .          8,000,000         8,000,000

Indianapolis Local Public Improvement  Bond Bank

   4.25%, Series A , 1/11/99 (Insured; FGIC) . . . . . . . . . . . . . . . . . . . . . . .          5,500,000         5,503,628

Iowa--.5%

Iowa Finance Authority, SWDR, VRDN (Cedar River Paper Co. Project)

   3.35% (LOC; Bank of  Nova Scotia) (a) . . . . . . . . . . . . . . . . . . . . . . . . .          3,300,000         3,300,000

Kentucky--.4%

Boone County, IDR, VRDN (Curtin Matheson Scientific Project)

   3.35% (LOC; Toronto-Dominion Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . .          2,500,000         2,500,000

Louisiana--3.5%

Ascension Parish, Revenue, VRDN

   (B.A.S.F. Corp. Project) 3.35% (LOC;  B.A.S.F. Corp.) . . . . . . . . . . . . . . . . .         10,800,000        10,800,000

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

   (Dow Chemical Co. Project) 3.55% (Corp. Guaranty; Dow Chemical Co.) (a) . . . . . . . .         12,500,000        12,500,000

Maryland--1.0%

Baltimore County, PCR, CP (Baltimore Gas and Electric)

   3.50% (LOC; Toronto-Dominion Bank) (a,b)  . . . . . . . . . . . . . . . . . . . . . . .          6,600,000         6,600,000

Massachusetts--4.2%

City of Springfield, BAN:

   3.625%, 3/2/99 (LOC; Fleet Bank)  . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,006,557

   4%, 6/25/99 (LOC; Fleet Bank) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          3,910,000         3,916,373

   4%, 7/15/99 (LOC; Fleet Bank) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         13,000,000        13,027,114

Montachusett Regional Vocational Technical School District, BAN 4%, 7/23/99. . . . . . . .          5,660,000         5,670,404

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                     NOVEMBER 30, 1998

                                                                                                   Principal

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

Michigan--2.9%

Macomb Township Economic Development Corporation, LOR, VRDN (ACR Industries
Project)

   3.30% (LOC; Comerica Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . .    $       550,000   $       550,000

Michigan Strategic Fund, SWDR, VRDN (Grayling Generating Project)

   3.15% (LOC; Barclays Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . .          3,800,000         3,800,000

Midland County Economic Development Corporation, LOR, VRDN

   (Dow Chemical Co. Project) 3.35%, Series A (LOC; Dow Chemical Co.) (a)  . . . . . . . .         15,100,000        15,100,000

Minnesota--2.2%

Cohasset, Revenue, Refunding, VRDN (Minnesota Power and Light Co. Project)

   3.25%, Series A (LOC: ABN-Amro Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . .          7,600,000         7,600,000

Minneapolis and St. Paul Housing and Redevelopment Authority,  Health Care
System Revenue,

  Refunding, VRDN (Children's Health Care Project)

   3.30%, Series B (Insured: FSA and Norwest Bank and LOC; Norwest Corp.) (a)  . . . . . .          6,800,000         6,800,000

Missouri--2.4%

Missouri Health and Educational Facilities Authority, Health Facilities Revenue,
VRDN

  (Deaconess Long Term Care) :

       3.25%, Series A (LOC; Bank One) (a) . . . . . . . . . . . . . . . . . . . . . . . .          9,500,000         9,500,000

       3.30%, Series A (LOC; Bank One) (a) . . . . . . . . . . . . . . . . . . . . . . . .            200,000           200,000

Independence Industrial Development Authority, IDR, Revenue, Refunding, VRDN

   (Grooves and Graceland) 3.25%, Series A (LOC; Credit Locale de France) (a)  . . . . . .          6,300,000         6,300,000

Nevada--1.9%

Clark County, IDR, VRDN (Nevada Cogeneration Project)

   3.45% (LOC; Canadian Imperial Bank of Commerce) (a) . . . . . . . . . . . . . . . . . .          7,200,000         7,200,000

Washoe County, Water Facilities Revenue, VRDN (Sierra Pacific Power Co. Project

   3.45% (LOC; Union Bank of Switzerland) (a)  . . . . . . . . . . . . . . . . . . . . . .          5,400,000         5,400,000

New Mexico--1.5%

State of New Mexico, TRAN 4.25%,  6/30/99. . . . . . . . . . . . . . . . . . . . . . . . .         10,000,000        10,036,271

New York--6.3%

Long Island Power Authority, Electric System Revenue:

   CP 3.375%, Sub-Series 1, 12/9/98
       (LOC: Bayerische Landesbank and Westdeutsche Landesbank)  . . . . . . . . . . . . .        12,000,0000        12,000,000

   VRDN 3.15%, Sub-Series 7 (Insured; MBIA and LOC; Credit Suisse) (a) . . . . . . . . . .          5,000,000         5,000,000

State of New York, CP 3.10%, 2/19/99 (LOC; Westdeutsche Landesbank). . . . . . . . . . . .         10,000,000        10,000,000

New York State Energy Resource and Development Authority, PCR, VRDN

   (Niagara Mohawk Power) 3.75%, Series A (LOC; Toronto-Dominion Bank) (a) . . . . . . . .          5,850,000         5,850,000

New York State Housing Finance Agency, Housing Revenue, VRDN (Normandie Court
II)

   3%, Series A (LOC; Fleet Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . .          4,000,000         4,000,000

New York State Local Government Assistance Corporation, VRDN

  2.90%, Series A (Liquidity; Union Bank of Switzerland and LOC: Credit Suisse

   and Union Bank of Switzerland) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,000,000

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------


STATEMENT OF INVESTMENTS (CONTINUED)                     NOVEMBER 30, 1998

                                                                                                   Principal

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

North Carolina--1.0%

Craven County Industrial Facilities and Pollution Control Financing Authority,
VRDN

   (Craven Wood Energy) 3.45%, Series C (LOC; ABN-Amro Bank) (a) . . . . . . . . . . . . .     $    6,900,000    $    6,900,000

Ohio--7.5%

Cincinnati City School District:

   BAN 4%, 9/16/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          7,830,000         7,859,902

   TAN 4.08%, 12/31/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,000,000         5,001,908

Greene County, Certificates of Indebtedness, GO  Notes 3.75%, 5/6/99 . . . . . . . . . . .          8,000,000         8,000,651

Montgomery County, Revenue, Refunding,  CP (Miami Valley Hospital)

   3.60%, Series A, 12/14/98 (LOC; Morgan Guaranty Trust Co.)  . . . . . . . . . . . . . .          8,000,000         8,000,000

Ohio Air Quality Development Authority, PCR, CP

   3%, Series B, 3/12/99 (Insured and Liquidity; 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.)  . . . . . . . . . . . . . . . .          5,670,000         5,670,000

Oregon--1.0%

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--3.8%

City of Philadelphia, TRAN 4.25%, Series A, 6/30/99. . . . . . . . . . . . . . . . . . . .          5,000,000         5,017,129

Philadelphia School District, TRAN 4.25%, Series A, 6/3/99 . . . . . . . . . . . . . . . .         20,000,000        20,065,167

South Carolina--.7%

South Carolina Housing Finance and Development Authority, Mortgage Revenue

   3.60%, Series A, 7/1/99 (Escrowed in; U.S. Treasury Bills)  . . . . . . . . . . . . . .          4,485,000         4,485,000

Tennessee--2.3%

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

   3.15%, Series III-C-2 (Insured; AMBAC and Liquidity Facility; Landesbank-Hessen) (a)  .         10,200,000        10,200,000

   3.15%, Series III-C-3 (Insured; AMBAC and Liquidity Facility; Landesbank-Hessen) (a)  .          4,800,000         4,800,000

Texas--15.6%

Brazos River Authority, PCR, Refunding, VRDN (Texas Utilities Electric Co.):

   3.35%, Series A (BPA; The Bank of New York) (a) . . . . . . . . . . . . . . . . . . . .          4,000,000         4,000,000

   3.45%, Series C (BPA; The Bank of New York and Insured; MBIA) (a) . . . . . . . . . . .         14,245,000        14,245,000

   3.45%, Series C (BPA; The Bank of New York and Insured; AMBAC) (a)  . . . . . . . . . .         13,700,000        13,700,000

   3.80%, Series B (Insured; AMBAC) (a)  . . . . . . . . . . . . . . . . . . . . . . . . .         12,000,000        12,000,000

Brazos River Harbor Naval District, Harbor Revenue, VRDN:

   (B.A.S.F. Corp.) 3.35% (Corp. Guaranty; B.A.S.F. Corp.) (a) . . . . . . . . . . . . . .         16,500,000        16,500,000

   (Dow Chemical Co. Project) 3.55% Series A (Corp. Guaranty; Dow Chemical Corp.) (a)  . .         12,800,000        12,800,000

Gulf Coast Industrial Development Authority, Marine Terminal Revenue, VRDN

   (Amoco Oil Co. Project) 3.45%  (LOC; Amoco Credit Corp.) (a)  . . . . . . . . . . . . .         11,300,000        11,300,000

Harris County Industrial Development Corporation, PCR, Refunding, VRDN (Exxon
Corp. Project)

   3.40% (LOC; Exxon Corp.) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,500,000         5,500,000

Panhandle-Plains Higher Education Authority, Student Loan Revenue, Refunding,
VRDN

   3.15%, Series A (LOC; Student Loan Marketing Association) (a) . . . . . . . . . . . . .         12,700,000        12,700,000

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                     NOVEMBER 30, 1998

                                                                                                   Principal

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

Virginia--6.7%

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

   3.50% (LOC; Bank of America) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . .      $  34,000,000     $  34,000,000

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

   3.70%, Series A (LOC; Banque Paribas) (a) . . . . . . . . . . . . . . . . . . . . . . .         10,000,000        10,000,000

West Virginia--1.0%

Marion County, County Community Solid Waste Disposal Facility Revenue, VRDN

   (Granttown Project) 3.25%, Series B (LOC; National Westminster Bank) (a)  . . . . . . .          3,700,000         3,700,000

Pendleton County, IDR, VRDN (Greer Steel Project) 3.45% (LOC; PNC Bank) (a). . . . . . . .          3,015,000         3,015,000

                                                                                                                  _____________

TOTAL INVESTMENTS (cost $655,679,560). . . . . . . . . . . . . . . . . . . . . . . . . . .              99.6%      $655,679,560
                                                                                                      =======     =============


CASH AND RECEIVABLES (NET) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                .4%    $    2,354,423
                                                                                                      =======     =============

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             100.0%      $658,033,983
                                                                                                      =======      =============
</TABLE>


<TABLE>
<CAPTION>
Summary    of    Abbreviations
- -----------------------------------------------------------------------------
<S>         <C>                                                      <C>        <C>
AMBAC       American Municipal Bond Assurance Corporation            LOC        Letter of Credit

BAN         Bond Anticipation Notes                                  LOR        Limited Obligation Revenue

BPA         Bond Purchase Agreement                                  MBIA       Municipal Bond Investors Assurance

COP         Certificate of Participation                                           Insurance Corporation

CP          Commercial Paper                                         PCR        Pollution Control Revenue

EIR         Environment Improvement Revenue                          RRR        Resources Recovery Revenue

FGIC        Financial Guaranty Insurance Company                     SFMR       Single Family Mortgage Revenue

FSA         Financial Security Assurance                             SWDR       Solid Waste Disposal Revenue

GO          General Obligation                                       TAN        Tax Anticipation Notes

HR          Hospital Revenue                                         TRAN       Tax and Revenue Anticipation Notes

IDB         Industrial Development Board                             VRDN       Variable Rate Demand Notes

IDR         Industrial Development Revenue

Summary of Combined Ratings (Unaudited)
</TABLE>


<TABLE>
<CAPTION>
- --------------------------------------------------------------------------

Fitch                or            Moody's             or            Standard & Poor's              Percentage of Value
_______                            ________                          __________________            ____________________
<S>                                <C>                               <C>                                 <C>
F1+/F1                             VMIG1/MIG1, P1                    SP1+/SP1, A1+/A1                    92.6%

AAA/AA (b)                         Aaa/Aa, A1 (b)                    AAA/AA (b)                            2.1

Not Rated (c)                      Not Rated (c)                     Not Rated (c)                         5.3
                                                                                                       _______
                                                                                                        100.0%
                                                                                                       =======
Notes to Statement of Investments:
</TABLE>
- -----------------------------------------------------------------------------

(a) Securities  payable  on demand. Variable interest rate--subject to periodic
    change.

(b) Notes  which  are not F, MIG or SP rated are represented by bond ratings of
    the issuers.

(c) Securities  which,  while not rated by Fitch, Moody's and Standard & Poor's
    have been determined by the Manager to be of comparable quality to those
    rated securities in which the Fund may invest.

                      SEE NOTES TO FINANCIAL STATEMENTS.

<TABLE>
<CAPTION>
GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                         NOVEMBER 30, 1998

                                                                                                    Cost              Value
                                                                                                 ____________       ___________
<S>                                                                                              <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments . .     $655,679,560      $655,679,560

                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .                            4,729,071

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                            3,892,914

                                 Prepaid expenses  . . . . . . . . . . . . . . . . . . . .                               38,919
                                                                                                                  _____________

                                                                                                                    664,340,464
                                                                                                                  _____________

LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                              224,116

                                 Due to Distributor  . . . . . . . . . . . . . . . . . . .                                4,517

                                 Payable for investment securities purchased . . . . . . .                            6,000,000

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                               77,848
                                                                                                                  _____________

                                                                                                                      6,306,481
                                                                                                                  _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $658,033,983
                                                                                                                  ==============


REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                         $658,053,905

                                 Accumulated net realized gain (loss) on investments . . .                             (19,922)
                                                                                                                  -------------

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $658,033,983
                                                                                                                  ===============

                                          NET ASSET VALUE PER SHARE
                              --------------------------------------------------

                                                                                                  Class A           Class B

                                                                                               ______________    ______________

Net Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $280,397,634      $377,636,349

Shares Outstanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        280,692,273       377,642,906

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


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

<TABLE>
<CAPTION>
GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                          YEAR ENDED NOVEMBER 30, 1998

INVESTMENT INCOME
<S>                                                                                        <C>                    <C>
INCOME                           Interest Income . . . . . . . . . . . . . . . . .                                $21,671,949

EXPENSES:                        Management fee--Note 2(a) . . . . . . . . . . . .         $  3,038,316

                                 Shareholder servicing costs--Note 2(c)  . . . . .            1,151,244

                                 Distribution fees (Class B)--Note 2(b)  . . . . .              646,579

                                 Registration fees . . . . . . . . . . . . . . . .              103,954

                                 Professional fees . . . . . . . . . . . . . . . .               53,283

                                 Custodian fees  . . . . . . . . . . . . . . . . .               48,212

                                 Directors' fees and expenses--Note 2(d) . . . . .               33,133

                                 Prospectus and shareholders' reports  . . . . . .               20,790

                                 Miscellaneous . . . . . . . . . . . . . . . . . .               14,774

                                                                                          _____________

                                    Total Expenses . . . . . . . . . . . . . . . .            5,110,285

                                 Less--reduction in shareholder servicing costs due to
                                    undertaking--Note 2(c) . . . . . . . . . . . .             (282,750)

                                                                                          _____________

                                    Net Expenses . . . . . . . . . . . . . . . . .                                  4,827,535
                                                                                                                _____________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                 16,844,414

NET REALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b) . . . . . . . . . . . . . . . .                                    (17,137)
                                                                                                                _____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . .                                $16,827,277
                                                                                                                =============


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>


<TABLE>
<CAPTION>
GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                                                            Year Ended           Year Ended
                                                                                        November 30, 1998    November 30, 1997
                                                                                        _________________    _________________
<S>                                                                                      <C>                  <C>
OPERATIONS

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $     16,844,414     $     12,783,231

   Net realized gain (loss) on investments . . . . . . . . . . . . . . . . . . . .                (17,137)              26,716

   Net unrealized appreciation (depreciation) on investments . . . . . . . . . . .                ---                   (8,845)
                                                                                          _______________      _______________

          Net Increase (Decrease) in Net Assets Resulting from Operations  . . . .             16,827,277           12,801,102
                                                                                          _______________      _______________

DIVIDENDS TO SHAREHOLDERS FROM:

  Investment income--net:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             (8,462,642)          (7,970,586)

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             (8,381,772)          (4,812,645)

   Net realized gain on investments:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                 (5,225)           ----

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                 (5,196)           ----

                                                                                          _______________      _______________

          Total Dividends  . . . . . . . . . . . . . . . . . . . . . . . . . . . .            (16,854,835)         (12,783,231)
                                                                                          _______________      _______________

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

  Net proceeds from shares sold:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,327,446,611        1,212,808,595

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,660,435,145        1,069,980,511

   Dividends reinvested:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .              8,202,286            7,678,759

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .              8,193,899            4,696,878

   Cost of shares redeemed:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         (1,328,295,655)      (1,204,301,450)

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         (1,553,986,658)        (829,168,072)
                                                                                          _______________      _______________

          Increase (Decrease) in Net Assets from Captial Stock Transactions  . . .            121,995,628          261,695,221

                                                                                          _______________      _______________

             Total Increase (Decrease) in Net Assets . . . . . . . . . . . . . . .            121,968,070          261,713,092

NET ASSETS:

   Beginning of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .            536,065,913          274,352,821
                                                                                          _______________      _______________

   End of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $    658,033,983     $    536,065,913
                                                                                         ================     ================


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

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

                                                                     ______________________________________________________

                                                                                   Year Ended November 30,

                                                                     ______________________________________________________

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  . . . . . . . . . . . . . . . . ..        .030          .031         .029          .034         .023
                                                                    ______       ______       ______        ______       ______
   Distributions:

   Dividends from investment income--net . . . . . . . . . .         (.030)       (.031)       (.029)        (.034)       (.023)

                                                                    ______       ______       ______        ______       ______

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


TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . .          3.02%        3.14%        2.97%         3.41%        2.27%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . ..         .60%          .62%         .66%          .66%         .64%

   Ratio of net investment income

       to average net assets . . . . . . . . . . . . . . . .         2.98%         3.09%        2.93%         3.35%        2.22%

   Net Assets, end of period (000's Omitted)   . . . . . . .      $280,398     $273,058     $256,862      $294,379     $294,711

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS (CONTINUED)

Contained below is per share operating performance data for a share of Capital
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
                                                                                 ____________________________________________

                                                                                            Year Ended November 30,
                                                                                 ____________________________________________

PER SHARE DATA:                                                                1998          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  . . . . . . . . . . . . . . . . . . . . . .           .026         .028          .027          .020
                                                                                _____        _____         _____         _____

  Distributions:

   Dividends from investment income--net . . . . . . . . . . . . . . .          (.026)       (.028)        (.027)        (.020)
                                                                                _____        _____         _____         _____

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


TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . . . . . . .           2.64%        2.86%         2.70%         3.01%(2)

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . . . . . . .            .96%         .95%          .85%         1.10%(2)

   Ratio of net investment income to average net assets  . . . . . . .           2.59%        2.87%         2.65%         2.83%(2)

   Decrease reflected in above expense ratios

       due to undertakings by the Manager  . . . . . . . . . . . . . .            .09%         .16%          .29%          .09%(2)

   Net Assets, end of period (000's Omitted) . . . . . . . . . . . . .       $377,636     $263,008       $17,491        $3,024

- ------------

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

(2)  Annualized.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

  General  Municipal  Money  Market  Fund (the "Fund") is a separate diversified
series  of  General  Municipal Money Market Funds, Inc. (the "Company") which is
registered  under  the Investment Company Act of 1940, as amended (the "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  (the  "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 shares of $.01 par value Common Stock. The
Fund is currently authorized to issue two classes of shares: Class A (15 billion
shares authorized) and Class B (1 billion shares authorized). Class 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 custody agreement, the Fund
received  net  earnings  credits of $30,865 during the period ended November 30,
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 of 1986, as
amended (the "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.

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

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

  The  Fund  has  an  unused  capital  loss  carryover  of approximately $17,000
available  for  Federal  income  tax  purposes  to be applied against future net
securities  profits,  if  any,  realized subsequent to November 30, 1998. If not
applied, the carryover expires in fiscal 2006.

  At  November 30, 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  November  30,  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 November 30, 1998, Class B shares were charged $646,579 pursuant to
the Distribution Plan.

  (C)  Under  the  Shareholder  Services  Plan with respect to Class A ("Class A
Shareholder   Services   Plan"), 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 November 30, 1998, Class A shares were charged $84,018 pursuant to
the Class A 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 November 30, 1998,
that if the aggregate expenses of Class B shares, exclusive of taxes, brokerage,
interest  on  borrowings  and  extraordinary expenses, exceeded .98 of 1% of the
average  daily net assets of Class B, the Manager will reimburse the expenses of
the Fund under the Class B.

GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

  Shareholder  Services  Plan  to the extent of any excess expense and up to the
full  fee  payable  under  such Plan. During the period ended November 30, 1998,
Class  B  shares  were  charged $969,868 of which $282,750 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  November  30, 1998, the Fund was charged $49,647 pursuant to the transfer
agency agreement.

  (D)  Each  director  who  is  not an "affiliated person" as defined in the Act
receives  from the Company 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.


GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF DIRECTORS

GENERAL MUNICIPAL MONEY MARKET FUND

  We  have  audited  the  accompanying  statement  of  assets  and  liabilities,
including  the  statement of investments, of General Municipal Money Market Fund
(one  of  the Series constituting General Municipal Money Market Funds, Inc.) as
of  November 30, 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 November 30, 1998 by correspondence with the custodian
and brokers. An audit also includes assessing the accounting principles used and
significant  estimates  made  by  management,  as well as evaluating the overall
financial   statement  presentation.  We  believe  that  our  audits  provide  a
reasonable basis for our opinion.

  In  our opinion, the financial statements and financial highlights referred tO
above  present  fairly,  in  all  material  respects,  the financial position of
General  Municipal  Money  Market  Fund at November 30, 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
January 5, 1999


GENERAL MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

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 November
30,  1998  as  "exempt-interest  dividends"  (not  generally  subject to regular
Federal income tax).

                     [This page intentionally left blank.]
                                   (reg.tm)

                                   (reg.tm)

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.                                         918/697AR9811

General Municipal

Money    Market

Fund

Annual Report

November 30, 1998




YEAR 2000 ISSUES (UNAUDITED)

  The  fund  could  be  adversely  affected  if the computer systems used by The
Dreyfus  Corporation  and  the  fund' s  other service providers do not properly
process  and  calculate date-related information from and after January 1, 2000.
The  Dreyfus  Corporation  is working to avoid Year 2000-related problems in its
systems  and  to  obtain  assurances  from other service providers that they are
taking  similar  steps.  In  addition,  issuers  of securities in which the fund
invests may be adversely affected by Year 2000-related problems. This could have
an impact on the value of the fund's investments and its share price.

GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

We are pleased to report the performance for General Minnesota Municipal Money
Market  Fund from the Fund's inception June 1, 1998 through November 30, 1998 as
shown in the following table:
<TABLE>
<CAPTION>



                                                                                               ANNUALIZED
                                                                       ANNUALIZED YIELD     EFFECTIVE YIELD*
                                                                        ______________      _____________
<S>                                                                         <C>                  <C>
        Class A Shares . . . . . . . . . . . . . . . . . . . .              2.80%                2.84%

        Class B Shares . . . . . . . . . . . . . . . . . . . .              2.65%                2.68%
</TABLE>

ECONOMIC REVIEW

  During  1998,  the  main  regions  of  the  world  had very different economic
fundamentals.  The  U.S.  entered  the  year  with  a  strong  economy near full
employment, with unemployment only slightly above 4%. The tight labor market led
the  Federal  Reserve Board to contemplate a rise in interest rates early in the
year.  The  U.S.  economy  cooled enough over the months that the Fed decided to
stand  pat.  Evidence  of  economic  cooling continued to accumulate and worries
about  the  world economy intensified. Financial stresses pushed the Fed to ease
beginning  in September. After many years of subpar economic growth, continental
Europe  moved  into a sustained economic expansion. The overall European economy
benefited  as  interest  rates  in  peripheral countries such as Spain and Italy
fell, approaching the lower level established by Germany, on the eve of currency
unification.  Unlike  the  U.S.,  Europe  has  substantial  excess  capacity  of
productive  plants and labor. In Asia, weak economies were pervasive as a result
of  the  Asian  financial  crisis.  The Latin American economies weakened as the
financial stresses spread throughout that region.

  A  main  influence  on  the  U.S.  economy this year was the foreign financial
crisis  and cooling of the world economy. The positive effects hit first. Actual
inflation  and  expected  inflation  dropped,  causing  a  decline  in long-term
Treasury bond yields and mortgage rates. This caused a boom in housing. The drop
in inflation helped the consumer sector as more of the growth in consumer income
was  left  over  after  inflation to buy goods and services. Consumers benefited
from a combination of good growth in real income, a strong labor market and past
increases in the prices of assets they owned.

  The  negative  effect of Asian weakness was felt in the industrial sector more
than  the  consumer  sector.  Corporate  profits weakened, especially in sectors
affected  by  the Asian crisis such as world-traded commodities (oil, metals and
paper) and exports. One result of the industrial weakness was to cool off a U.S.
economy that had been growing rapidly.

  The  major  change  in  the  economic  outlook  over  recent months has been a
downward  shift  in  expectations  for  world  economic  growth. A credit crunch
developed in emerging countries and former communist countries, sharply reducing
the   economic   outlook   for   Asia   and   Latin   America  as  well  as  for
commodity-exporting countries throughout the world. The effect on Europe and the
U.S. has been to lower expectations of profit growth and drive down bond yields.
Monetary policy has begun to ease in Europe as well as the U.S.

  Evidence  of  a  weaker  world  economy  accumulated as the financial stresses
continued.  A  worsened financial crisis occurred between the Russian default in
mid-August  and  the  fallout  from  the Long-Term Capital Management hedge fund
crisis  through  early October. However, proactive steps were taken to stabilize
the  Japanese  banks,  design  a  support  package  for Brazil and ease monetary
policy.  There  appears to be a shift in the priorities of key policymakers from
fighting potential inflation to restimulating future world economic growth.

MARKET ENVIRONMENT/PORTFOLIO OVERVIEW

  The  manner in which the Federal Reserve eased this past quarter was a gradual
process.  For  three  successive months, beginning in September, the Fed reduced
the  target  rate for Fed Funds a total of 75 basis points. The Fed also lowered
the  Discount  Rate by 25 basis points each, in November and December. The Fed's
actions provided even greater strength to an already strong short-term municipal
money  market.  Prior to these rate cuts, the short-term market had already felt
the  effects  of  the diminished supply of eligible new issuance over the summer
months.  This  year's  summer calendar of municipal notes (consisting mainly of
California  paper)  was  drastically reduced by a combination of factors. Due to
the strength of local and state economies, several issuers reduced the amount of
short-term  borrowing  needed.  Additionally,  many  issuers came to market with
securities with maturities beyond the 13-month maximum restriction allowable for
tax-exempt  money  funds.  Other  issues were converted to a shortened synthetic
structure,  thus  eliminating the ability to extend out into the one-year range.
This  reduction in supply resulted in lower yields for most one-year paper, both
national and state specific.

We extended your Fund's average maturity to the 50-day and over range in early
summer,  just  prior  to  the market strengthening. Your Fund benefited from our
purchase of securities in the one-year range at yields significantly higher than
what  is  currently  available in the market. As the year progressed, due to the
scarcity  of Minnesota exempt paper and aggressive levels in the one-year range,
we utilized the variable rate demand note market in order to meet our investment
needs.  As  a result, this shortened your Fund's average maturity to the 40+ day
range.   As  year-end  approaches,  we  will continue to search for those longer
investment  opportunities  which  will "lock in" higher rates while providing an
attractive  return  to  the  Minnesota  tax-exempt  investor. As always, we will
structure   the  portfolio  in  an  attempt  to  maximize  current  yield  while
maintaining our commitment to high quality tax-exempt investments.

               Very truly yours


               [Richard J. Moynihan signature]

               Richard J. Moynihan

               Director, Municipal Portfolio Manager

               The Dreyfus Corporation

December 15, 1998
New York, N.Y.

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


<TABLE>
<CAPTION>
GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    NOVEMBER 30, 1998

                                                                                                   Principal
Tax Exempt Investments--101.3%                                                                      Amount           Value
- -------------------------------------------------------                                         _____________    ______________
<S>                                                                                            <C>               <C>
Becker, PCR, Refunding, CP (Northern State Power Co.)

   3.35%, Series B, 2/17/99 (LOC; Northern State Power Co.)  . . . . . . . . . . . . . . .     $    2,000,000    $    2,000,000

Beltrami County, Environmental Control Revenue, VRDN (Northwood Panelboard Co.
Project)

   3.35% (LOC; Union Bank of Switzerland) (a)  . . . . . . . . . . . . . . . . . . . . . .          2,700,000         2,700,000

Burnsville, Refunding 3.90%, Series B, 2/1/99. . . . . . . . . . . . . . . . . . . . . . .            100,000           100,027

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

   3.20%, Series C (LOC; Credit Suisse) (a)  . . . . . . . . . . . . . . . . . . . . . . .          2,700,000         2,700,000

Cohasset, Revenue, Refunding, VRDN (Minnesota Power and Light Co. Project)

   3.25%, Series A (LOC; ABN-Amro Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . .            700,000           700,000

Duluth, Tax Increment Revenue, VRDN (Lake Superior Paper)

   3.15% (LOC; Wachovia Bank of Georgia) (a) . . . . . . . . . . . . . . . . . . . . . . .          1,400,000         1,400,000

Eden Prairie, Commercial Development Revenue, Refunding, VRDN (Lakeview Business
Center)

   3.30% (LOC; Firstar Bank of Milwaukee) (a)  . . . . . . . . . . . . . . . . . . . . . .          1,400,000         1,400,000

Golden Valley, IDR, VRDN (Unicare Homes Project)

   3.35% (LOC; Banque Paribas) (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,000,000         1,000,000

Hennepin County, G.O. Notes 4%, Series B, 12/1/99. . . . . . . . . . . . . . . . . . . . .            600,000           605,862

Minneapolis, G.O. Notes:

   3.20%, Series C, 12/1/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .            300,000           300,000

   4.375%, Series A, 12/1/98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .            280,000           280,000

Minneapolis Community Development Agency, PCR, VRDN

   (Northern State Power Co. Project) 3.30% (LOC; Northern State Power Co.) (a)  . . . . .            500,000           500,000

Minnesota Public Facilities Water Authority, PCR 6.70%, Series A, 3/1/99 . . . . . . . . .          1,000,000         1,007,159

Minnesota School District 3.625%, Series B, 8/27/99. . . . . . . . . . . . . . . . . . . .            500,000           500,000

Minnesota Higher Education Coordinating Board, Revenue, VRDN

   3.35% (LOC; Norwest Bank of Minnesota) (a)  . . . . . . . . . . . . . . . . . . . . . .          2,700,000         2,700,000

Minnesota Housing Finance Agency, Single Family Mortgage 3.70%, Series H, 8/9/99 . . . . .            500,000           500,000

Minnesota Higher Education Facilities Authority, Revenue:

   Refunding (Macalester College) 4.50%, Series U2, 3/1/99 (LOC; Macalester College) . . .            490,000           490,940

   VRDN:

       (Bethel College) 3.05%, Series 4-S (LOC; Allied Irish Banks) (a)  . . . . . . . . .          1,400,000         1,400,000

       (Macalester College) 3.15%, Series 3-Z (LOC; Macalester College) (a)  . . . . . . .            900,000           900,000

Olmstead County, COP, VRDN (Human Services Campus Infrastructure Project)

   3.15% (LOC; Toronto-Dominion Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . .          1,350,000         1,350,000

Red Wing, PCR, VRDN (Northern State Power Co. Project)

   3.30% (LOC; Northern State Power Co.) (a) . . . . . . . . . . . . . . . . . . . . . . .            200,000           200,000

St. Cloud, Health Care Facilites Revenue, VRDN (St. Cloud Hospital)

   3.10%, Series A (LOC; Rabobank Nederland) (a) . . . . . . . . . . . . . . . . . . . . .          1,400,000         1,400,000

St. Paul Housing and Redevelopment Authority, Revenue, VRDN:

   (District Cooling) 3.50%, Series L (LOC; Credit Locale de France) (a) . . . . . . . . .          1,000,000         1,000,000

   (Science Museum of Minnesota) 3.30%, Series B (LOC; First Bank of Milwaukee) (a)  . . .          1,400,000         1,400,000

GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (continued)                     NOVEMBER 30, 1998

                                                                                                  Principal

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

State of Minnesota:

   G.O. Notes 4.75%, 5/1/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $    2,000,000    $    2,008,441

   Prerefunded 6.60%, 8/1/99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,000,000         1,019,365
                                                                                                                  _____________

TOTAL INVESTMENTS (cost $29,561,794) . . . . . . . . . . . . . . . . . . . . . . . . . . .             101.3%     $  29,561,794
                                                                                                      =======     =============


LIABILITIES, LESS CASH AND RECEIVABLES . . . . . . . . . . . . . . . . . . . . . . . . . .             (1.3%)     $    (387,971)
                                                                                                      =======     ==============

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             100.0%     $  29,173,823
                                                                                                      =======     ==============
</TABLE>


<TABLE>
<CAPTION>
Summary    of    Abbreviations
- -----------------------------------------------------------------------------
<S>         <C>                                                      <C>        <C>
COP         Certificate of Participation                             LOC        Letter of Credit

CP          Commercial Paper                                         PCR        Pollution Control Revenue

GO          General Obligation                                       VRDN       Variable Rate Demand Notes

IDR         Industrial Development Revenue

Summary of Combined Ratings (Unaudited)
</TABLE>


<TABLE>
<CAPTION>
- -----------------------------------------------------------------------------

Fitch                or            Moody's             or            Standard & Poor's              Percentage of Value
_______                            ________                          __________________            ____________________
<S>                                <C>                               <C>                                 <C>
F1+/F1                             VMIG1/MIG1, P1                    SP1+/SP1, A1+/A1                    79.7%

AAA/AAA (b)                        Aaa/Aa (b)                        AAA/AA (b)                           20.3
                                                                                                       _______

                                                                                                        100.0%
                                                                                                       _______
Notes to Statement of Investments:
- -----------------------------------------------------------------------------

(a)  Securities payable on demand. Variable interest rate--subject to periodic
     change.

(b)  Notes which are not F, MIG, or SP rated are represented by bond ratings of
     the issuers.

                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

<TABLE>
<CAPTION>
GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF ASSETS AND LIABILITIES                         NOVEMBER 30, 1998

                                                                                                     Cost             Value
                                                                                                 ____________       ___________
<S>                                                                                               <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments . .      $29,561,794       $29,561,794

                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .                               99,448

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                              140,371

                                 Prepaid expenses  . . . . . . . . . . . . . . . . . . . .                               31,610
                                                                                                                   ____________

                                                                                                                     29,833,223
                                                                                                                   ============


LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                                  172

                                 Due to Distributor  . . . . . . . . . . . . . . . . . . .                               11,789

                                 Payable for investment securities purchased . . . . . . .                              605,862

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                               41,577
                                                                                                                   ____________

                                                                                                                        659,400
                                                                                                                   ____________

NET ASSETS at value, represented by paid-in capital. . . . . . . . . . . . . . . . . . . .                          $29,173,823
                                                                                                                   ============



                           NET ASSET VALUE PER SHARE
                              --------------------

                                                                                                  Class A           Class B
                                                                                                _____________  ______________

Net Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         $1,014,128       $28,159,695

Shares Outstanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,014,128        28,159,695


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




                       SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>


<TABLE>
<CAPTION>
GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS

FROM JUNE 1, 1998 (COMMENCEMENT OF OPERATIONS) TO NOVEMBER 30, 1998

INVESTMENT INCOME
<S>                                                                                          <C>                     <C>
INCOME                           Interest Income . . . . . . . . . . . . . . . . .                                   $452,018

EXPENSES:                        Management fee--Note 2(a) . . . . . . . . . . . .           $   65,816

                                 Legal fees  . . . . . . . . . . . . . . . . . . .               41,350

                                 Shareholder servicing costs--Note 2(c)  . . . . .               38,008

                                 Distribution fees (Class B)--Note 2(b)  . . . . .               25,313

                                 Auditing fees . . . . . . . . . . . . . . . . . .               20,700

                                 Registration fees . . . . . . . . . . . . . . . .               16,627

                                 Prospectus and shareholders' reports  . . . . . .                6,594

                                 Directors' fees and expenses--Note 2(d) . . . . .                  510

                                 Custodian fees  . . . . . . . . . . . . . . . . .                  391

                                 Miscellaneous . . . . . . . . . . . . . . . . . .                2,448
                                                                                          _____________

                                    Total Expenses . . . . . . . . . . . . . . . .              217,757

                                 Less--reimbursement of expenses and shareholder
                                    servicing costs from the Manager due to
                                    undertakings--Note 2(a,c)  . . . . . . . . . .             (113,213)
                                                                                          _____________

                                    Net Expenses . . . . . . . . . . . . . . . . .                                    104,544
                                                                                                                   __________

INVESTMENT INCOME--NET, representing net increase in net assets from operations. . . . . . .                         $347,474
                                                                                                                   ==========


                     SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>


<TABLE>
<CAPTION>
GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

FROM JUNE 1, 1998 (COMMENCEMENT OF OPERATIONS) TO NOVEMBER 30, 1998


OPERATIONS:
<S>                                                                                        <C>                    <C>
   Investment income--net, representing net increase in net assets resulting from operations . . . . . . . . . .  $     347,474
                                                                                                                   ____________


DIVIDENDS TO SHAREHOLDERS FROM:

  Investment income--net:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        (14,199)

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       (333,275)
                                                                                                                   ____________

          Total Dividends  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       (347,474)
                                                                                                                   ____________


CAPITAL STOCK TRANSACTIONS ($1.00 per share):

  Net proceeds from shares sold:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      1,000,000

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     44,810,839

   Dividends reinvested:

       Class A shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         14,128

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        326,009

   Cost of shares redeemed:

       Class B shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    (16,977,153)
                                                                                                                   ____________

          Increase (Decrease) in Net Assets from Capital Stock Transactions  . . . . . . . . . . . . . . . . . .     29,173,823
                                                                                                                   ____________

             Total Increase (Decrease) in Net Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     29,173,823

NET ASSETS:

       Beginning of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        --

                                                                                                                   ____________

       End of Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    $29,173,823
                                                                                                                   ============



                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

GENERAL MINNESOTA 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  the  period  from  June 1, 1998 (commencement of
operations)  to  November  30,  1998. This information has been derived from the
Fund's financial statements.
<TABLE>
<CAPTION>




                                                                                             Class A                Class B
PER SHARE DATA:                                                                               Shares                 Shares
                                                                                             _______                 _______
<S>                                                                                            <C>                     <C>
   Net asset value, beginning of period  . . . . . . . . . . . . . . . . . . . . . . . . .     $1.00                   $1.00
                                                                                             _______                 _______

   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      .014                    .013
                                                                                             _______                 _______

   Distributions:

   Dividends from investment income--net . . . . . . . . . . . . . . . . . . . . . . . . .     (.014)                  (.013)
                                                                                             _______                 _______

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

TOTAL INVESTMENT RETURN* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     2.81%                   2.67%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets*  . . . . . . . . . . . . . . . . . . . . . . .       .65%                    .80%

   Ratio of net investment income to average net assets* . . . . . . . . . . . . . . . . .      2.80%                   2.63%

   Decrease reflected in above expense ratios

       due to undertakings by the Manager* . . . . . . . . . . . . . . . . . . . . . . . .       .76%                    .87%

   Net Assets, end of period (000's Omitted)*  . . . . . . . . . . . . . . . . . . . . . .    $1,014                 $28,160

- ------------
* Annualized.


                      SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS

NOTE 1--SIGNIFICANT ACCOUNTING POLICIES:

  General  Minnesota  Municipal  Money  Market  Fund  (the "Fund") is a separate
non-diversified  series  of  General  Municipal  Money  Market  Funds, Inc. (the
" Company") which  is  registered  under the Investment Company Act of 1940, as
amended (the "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 and State
of  Minnesota  income  taxes  to  the extent consistent with the preservation of
capital   and  the  maintenance  of  liquidity.  The  Dreyfus  Corporation  (the
" Manager") serves  as  the  Fund's investment adviser. The Manager is a direct
subsidiary of Mellon Bank, N.A.

  At  November  30, 1998, MBC Investment Corp., an indirect subsidiary of Mellon
Bank Corporation, held the following shares:

            Class A  . . . . . . . . . . . . . . . . . .1,014,128

            Class B  . . . . . . . . . . . . . . . . . .1,013,358

  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 4 billion shares of $.01 par value Common Stock. The Fund
is  currently  authorized  to  issue  two  classes of shares: Class A (2 billion
shares authorized) and Class B (2 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 custody agreement, the Fund
received  net  earnings  credits  of $1,826 during the period ended November 30,
1998  based on available cash balances left on deposit. Income earned under this
arrangement is included in interest income.

GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

  The  Fund  follows  an  investment  policy of investing primarily in municipal
obligations  of  one  state. Economic changes affecting the state and certain of
its  public  bodies  and municipalities may affect the ability of issuers within
the  state to pay interest on, or repay principal of, municipal obligations held
by the Fund.

  (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 of 1986, as
amended (the "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 qualify as a
regulated  investment  company,  which  can  distribute tax exempt dividends, by
complying  with the applicable provisions of the Code, and to make distributions
of  income  and  net  realized  capital  gain  sufficient  to  relieve  it  from
substantially all Federal income and excise taxes.

  At  November 30, 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.  The Manager had undertaken from June 1, 1998 through November
30, 1998 to  reduce  the  management  fee paid by the Fund, to the extent that
the Fund's aggregate  annual  expenses  (exclusive  of certain expenses as
described above) exceeded  an  annual  rate of .65 of 1% of the value of the
Fund's average daily net  assets.  The expense reimbursement pursuant to the
undertaking, amounted to $75,244 during the period ended November 30, 1998.

(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 November 30, 1998, Class B shares were charged $25,313 pursuant to
the Distribution Plan.

  (C)  Under  the  Shareholder  Services  Plan with respect to Class A ("Class A
Shareholder   Services   Plan"  ), 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.

GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

  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 June 1, 1998 through November 30, 1998, that
if  the  aggregate  expenses  of  Class B shares, exclusive of taxes, brokerage,
interest  on  borrowings  and  extraordinary expenses, exceeded .80 of 1% 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
November  30,  1998,  Class  B  shares  were  charged  $37,969  all of which 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  November  30,  1998,  the  Fund  was charged $39 pursuant to the transfer
agency agreement.

  (D)  Each  director  who  is  not an "affiliated person" as defined in the Act
receives  from the Company 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.

GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF DIRECTORS

GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND

  We  have  audited  the  accompanying  statement  of  assets  and  liabilities,
including  the  statement  of  investments, of General Minnesota Municipal Money
Market  Fund  (one  of  the  Series  constituting General Municipal Money Market
Funds,  Inc.)  as of November 30, 1998, and the related statements of operations
and  changes  in net assets and financial highlights for the period from June 1,
1998  (commencement  of  operations)  to  November  30,  1998.  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 audit.

  We  conducted  our  audit  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 November 30, 1998 by correspondence with the custodian
and brokers. An audit also includes assessing the accounting principles used and
significant  estimates  made  by  management,  as well as evaluating the overall
financial   statement  presentation.  We  believe  that  our  audit  provides  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
General  Minnesota  Municipal  Money  Market  Fund at November 30, 1998, and the
results  of  its  operations,  the  changes  in its net assets and the financial
highlights  for the period from June 1, 1998 to November 30, 1998, in conformity
with generally accepted accounting principles.


                                              [ERNST & YOUNG LLP SIGNATURE LOGO]


New York, New York
January 5, 1999


GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

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 November
30,  1998  as  "exempt-interest  dividends"  (not  generally  subject to regular
Federal  and,  for  individuals  who are Minnesota residents, Minnesota personal
income taxes).

                                   [reg.tm logo]

                                   (reg.tm)


GENERAL MINNESOTA 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.                                         917/706AR9811

General Minnesota

Municipal Money

Market Fund

Annual Report

November 30, 1998




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