GENERAL MUNICIPAL MONEY MARKET FUNDS INC
N-30D, 2000-08-07
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General Municipal

Money Market Fund

SEMIANNUAL REPORT May 31, 2000

(reg.tm)





The  views  expressed herein are current to the date of this report. These views
and  the  composition  of the fund's portfolio are subject to change at any time
based on market and other conditions.

           * Not FDIC-Insured
           * Not Bank-Guaranteed
           * May Lose Value


                                 Contents

                                 THE FUND
--------------------------------------------------

                             2   Letter from the President

                             3   Discussion of Fund Performance

                             6   Statement of Investments

                            15   Statement of Assets and Liabilities

                            16   Statement of Operations

                            17   Statement of Changes in Net Assets

                            18   Financial Highlights

                            21   Notes to Financial Statements

                                 FOR MORE INFORMATION
---------------------------------------------------------------------------

                                 Back Cover

                                                                       The Fund

                                                              General Municipal

                                                              Money Market Fund

LETTER FROM THE PRESIDENT

Dear Shareholder:

We  are  pleased  to  present this semiannual report for General Municipal Money
Market Fund, covering the six-month period from December 1, 1999 through May 31,
2000.  Inside  you' ll  find valuable information about how the fund was managed
during  the  reporting  period, including a discussion with the fund's portfolio
manager, Colleen Meehan.

When  the  reporting  period  began,  international  and domestic economies were
growing  at  a  very  strong  pace,  giving  rise  to concerns that long-dormant
inflationary  pressures  might  reemerge.  Consumers continued to spend heavily,
unemployment  levels  reached  new  lows  and  the  stock  market,  while highly
volatile,    continued    to    climb.

Because  robust economic growth may trigger unwanted inflationary pressures, the
Federal  Reserve  Board  raised short-term interest rates three times during the
reporting  period.  In  total,  the  Federal Reserve Board has raised short-term
interest  rates  by  1.75  percentage  points  since late June 1999. While these
economic  influences  overall adversely affected long-term municipal bonds, they
positively    influenced    tax-exempt    money    market    yields.

We  appreciate  your  confidence over the past six months and we look forward to
your   continued   participation   in  General  Municipal  Money  Market  Fund.

Sincerely,


/s/Stephen E. Canter
Stephen E. Canter

President and Chief Investment Officer
The Dreyfus Corporation
June 15, 2000

2



DISCUSSION OF FUND PERFORMANCE

Colleen Meehan, Portfolio Manager

How did General Municipal Money Market Fund perform during the period?

For  the six-month period ended May 31, 2000, the fund's Class A shares produced
an  annualized  yield of 3.26%, Class B shares provided a 2.89% annualized yield
and  Class  X  shares provided a 2.87% annualized yield. Taking into account the
effects  of  compounding, the fund's Class A, B and X shares provided annualized
effective  yields  of  3.31% , 2.92%  and  2.91% , respectively,  for  the  same
period.(1)

We  attribute  the  fund' s  performance  to  higher  short-term  interest rates
implemented  by  the  Federal  Reserve  Board  (the "Fed"), which helped enhance
tax-exempt money market yields and interest-rate trends.

What is the fund's investment approach?

The  fund  seeks  to maximize current income exempt from federal personal income
tax  to  the  extent that is consistent with the preservation of capital and the
maintenance of liquidity.

In so doing, we employ two primary strategies. First, we attempt to add value by
constructing  a  diverse  portfolio  of  high  quality,  tax-exempt money market
instruments  from  issuers  throughout  the  United  States and its territories.
Second,  we  actively manage the portfolio's average maturity in anticipation of
what  we  believe  are  supply-and-demand  changes  in  the short-term municipal
marketplace and interest-rate trends.

For  example, if we expect an increase in short-term supply, we may decrease the
average  maturity  of  the portfolio, which could enable us to take advantage of
opportunities  when  short-term supply increases. Generally, yields tend to rise
when  there  is an increase in new-issue supply competing for investor interest.
New securities are generally issued with maturities in the one-year range, which
in    turn    may    lengthen    the

                                                                      The Fund 3


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

portfolio's average maturity. If we anticipate limited new-issue supply, we may
then  look to extend the portfolio's average maturity to maintain current yields
for  as  long  as  we  believe  practical. At other times, we try to maintain an
average  maturity  that reflects our view of short-term interest-rate trends and
future supply-and-demand considerations.

What other factors influenced the fund's performance?

The  fund  was  positively  influenced  over  the past six months by robust U.S.
economic growth and rising interest rates.

By  the  time  the  reporting  period  began  on December 1, 1999, it had become
apparent  that  the  high  rate  of  economic  growth  in  the United States was
unsustainable.  Consumer  confidence  remained  near  a 30-year high, oil prices
bounced back from the previous year's lows, and employment remained strong, with
hourly  wages  rising.  These economic forces raised concerns among fixed-income
investors  that long-dormant inflationary pressures might reemerge. In response,
the  Fed  raised  short-term  interest  rates  three  times during the reporting
period.  When combined with the three interest-rate hikes implemented before the
reporting  period  began,  the  Fed  had  raised  interest rates a total of 1.75
percentage points since last summer.

However,  tax-exempt  money  market  yields generally rose less in comparison to
taxable  yields  over the past six months. This was due to the fact that many of
the  nation's  states and municipalities enjoyed higher tax revenues during the
reporting period. As a result, this reduced their need to borrow and resulted in
a lower supply of securities.

What is the fund's current strategy?

While  our  strategy  continues  to involve active management of the portfolio's
weighted  average  maturity  and  asset  mix  according to our interest-rate and
supply-and-demand  expectations, we believe that the current economic outlook is
uncertain.  On  the  one hand, many in the investment community believe that the
Fed  is  likely to raise short-term interest rates further at their next meeting
in  late  June.  On  the  other  hand,  recent economic reports suggest that the
economy    may    be

4

slowing   in   response   to  previous  interest-rate  increases,  creating  the
possibility  that  the  current  round  of  rate hikes may be over. Also, yields
generally  tend  to rise when there is an increase in new-issue supply competing
for investor interest.

In  the  face  of these uncertainties, we have recently adjusted the portfolio's
average  weighted  maturity  toward  a  point that is modestly longer than other
federally  tax-exempt  money market funds. This maturity management strategy was
designed  to help us lock in then current yields while retaining the flexibility
required to act quickly if interest rates rise further.

Our  asset mix currently emphasizes Variable Rate Demand Notes ("VRDNs") because
of  the competitively high yields they offer. VRDNs generally feature adjustable
yields, short maturities and afford the portfolio a high degree of liquidity and
credit  quality. We have also increased our holdings of insured municipal bonds,
pre-refunded  securities  and  tax-exempt  commercial  paper.  We  have  focused
primarily  on  securities with maturities in the three- to six-month range which
should  help  protect the fund's tax-exempt yield but not drastically extend the
fund's weighted average maturity. Of course, portfolio composition is subject to
change at any time.

June 15, 2000

(1)  ANNUALIZED  EFFECTIVE  YIELD IS BASED  UPON  DIVIDENDS  DECLARED  DAILY AND
     REINVESTED  MONTHLY.  PAST  PERFORMANCE IS NO GUARANTEE OF FUTURE  RESULTS.
     YIELDS FLUCTUATE.  INCOME MAY BE SUBJECT TO STATE AND LOCAL TAXES, AND SOME
     INCOME MAY BE  SUBJECT TO THE  FEDERAL  ALTERNATIVE  MINIMUM  TAX (AMT) FOR
     CERTAIN  INVESTORS.  AN INVESTMENT IN THE FUND IS NOT INSURED OR GUARANTEED
     BY THE FDIC OR THE U.S. GOVERNMENT. ALTHOUGH THE FUND SEEKS TO PRESERVE THE
     VALUE OF YOUR  INVESTMENT AT $1.00 PER SHARE,  IT IS POSSIBLE TO LOSE MONEY
     BY INVESTING IN THE FUND.  YIELDS PROVIDED FOR THE FUND'S CLASS B AND CLASS
     X SHARES REFLECT THE ABSORPTION OF FUND EXPENSES BY THE DREYFUS CORPORATION
     PURSUANT TO AN  UNDERTAKING  IN EFFECT THAT MAY BE EXTENDED,  TERMINATED OR
     MODIFIED AT ANY TIME.  HAD THESE  EXPENSES  NOT BEEN  ABSORBED,  THE FUND'S
     CLASS B AND  CLASS X SHARES  WOULD  HAVE BEEN  LOWER.  WITHOUT  THE  FUND'S
     EXPENSE  ABSORPTION,  THE  FUND'S  CLASS B SHARES  WOULD HAVE  PRODUCED  AN
     ANNUALIZED  NET YIELD OF 2.81%  AND AN  ANNUALIZED  EFFECTIVE  NET YIELD OF
     2.85%,  AND THE FUND'S CLASS X SHARES WOULD HAVE PRODUCED AN ANNUALIZED NET
     YIELD OF 2.67% AND AN ANNUALIZED EFFECTIVE NET YIELD OF 2.71%.

                                                             The Fund 5

May 31, 2000 (Unaudited)



STATEMENT OF INVESTMENTS

<TABLE>
<CAPTION>


                                                                                              Principal
TAX EXEMPT INVESTMENTS--99.2%                                                                Amount ($)               Value ($)
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                                                          <C>                      <C>

ALABAMA--3.8%

Cossa County, IDB, IDR,VRDN (Avondale Mills Inc. Project)

   4.45% (LOC; Wachovia Bank and Trust Co.)                                                   7,500,000  (a)           7,500,000

Macintosh, IDB, EIR, Refunding, VRDN (CIBA Specialty)

   4.60%, Series E (Corp. Guaranty; CIBA Specialty Chemicals)                                11,800,000  (a)          11,800,000

Stevenson, IDB, EIR, Refunding, VRDN (Mead Corp. Project)

   4.45%, Series A (LOC; Bank Austria)                                                        6,900,000  (a)           6,900,000

ARIZONA--4.7%

Apache County Industrial Development Authority, IDR, VRDN

  (Tucson Electric Power Springerville Project)

   4.15%, Series B (LOC; The Bank of New York)                                                6,300,000  (a)           6,300,000

Arizona Educational Loan Marketing Corporation,

  Educational Loan Revenue, VRDN

  4.20%, Series A (Insured; MBIA and LOC;

   State Street Bank and Trust Co.)                                                          10,675,000  (a)          10,675,000

Phoenix Industrial Development Authority,

  MFHR, Refunding, VRDN

  (Southwest Village Apartments Project)

   4.32% (LOC; FNMA)                                                                         10,600,000  (a)          10,600,000

Pima County Industrial Development Authority,

   SFMR, Refunding 4.10%, Series B-3, 9/1/2000                                                4,820,000                4,820,000

CALIFORNIA--6.7%

Calcasieu Parish Incorporated, IDB, Environmental Revenue,

  VRDN (Citgo Petroleum Corp. Proj.)

   4.60% (LOC; Banque Nationale de Paris)                                                    11,200,000  (a)          11,200,000

California Higher Education Loan Authority,

  Student Loan Revenue, Refunding:

    (Senior Lien) 3.50%, Series A-1, 7/1/2000

         (LOC; Student Loan Marketing Association                                            11,850,000               11,850,000

      VRDN 5.25%, Series A
         (LOC; National Westminster Bank)                                                     8,000,000  (a)           8,000,000

California School Cash Reserves Program Authority

   4%, Series A, 7/3/2000 (Insured; AMBAC)                                                   15,000,000               15,011,444

CONNECTICUT--1.0%

Connecticut Special Assessment Unemployment

  Compensation Advance Fund, Revenue

  (Connecticut Unemployment) 3.38%, Series C,

   7/1/2000 (Insured; FGIC and Liquidity Facility; FGIC)                                      7,000,000                7,000,000



6

                                                                                              Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                           Amount ($)                Value ($)
------------------------------------------------------------------------------------------------------------------------------------

DELAWARE--.9%

Delaware Economic Development Authority,

  Solid Waste Disposal and

  Sewage Facility Revenue, VRDN (CIBA Specialty)

   4.45%, Series A (Corp. Guaranty;
   CIBA Specialty Chemicals)                                                                  6,000,000  (a)           6,000,000

DISTRICT OF COLUMBIA--3.8%

District of Columbia Housing Finance Agency, Mortgage

   Revenue, Refunding 4.35%, Series B, 3/21/2001                                             10,000,000               10,000,000

District of Columbia, VRDN:

  Refunding:

      4.45%, Series A-1 (LOC; Societe Generale)                                               1,700,000  (a)           1,700,000

      4.45%, Series A-4 (LOC; Societe Generale)                                               1,700,000  (a)           1,700,000

   Revenue (George Washington University)

      4.40%, Series B (Insured; MBIA and LOC;

      Bank of America)                                                                       12,700,000  (a)          12,700,000

FLORIDA--3.9%

Florida Housing Financing Agency (Wood Forest II Project)

   4.15%, Series BBB, 12/1/2000
   (LOC; Continental Causality)                                                               6,000,000                6,000,000

Highlands County Health Facility Authority, Revenue,

  VRDN (Adventist Health System/Sunbelt Inc.)

   4.35%, Series A (Liquidity Facility; FNB Chicago
   and LOC; Capital Markets Assurance)                                                        7,000,000  (a)           7,000,000

Lee County Housing Finance Authority, MFHR, VRDN

  (Forestwood Apartment Project)

   4.10%, Series A (LOC; FNMA)                                                                9,485,000  (a)           9,485,000

Miami-Dade County Housing Finance Authority,

  Home Ownership Mortgage Revenue

  4.80%, Series A-2, 4/16/2001

   (LOC; American Insurance Group Funding Inc.)                                               4,280,000                4,280,000

GEORGIA--2.2%

Cobb County Housing Authority, MFHR, Refunding, VRDN

   (Six Flags Association) 4.30% (LOC; FHLM)                                                  5,490,000  (a)           5,490,000

Columbia County Development Authority, Revenue, VRDN

  (Augusta Preparatory Project) 4.35%

   (LOC; Wachovia Bank of North Carolina)                                                     4,500,000  (a)           4,500,000

                                                                                                                          The Fund 7

STATEMENT OF INVESTMENTS (Unaudited) (CONTINUED)

                                                                                               Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                            Amount ($)              Value ($)
-----------------------------------------------------------------------------------------------------------------------------------

GEORGIA (CONTINUED)

Savannah Economic Development Authority,Exempt Facility

  VRDN (Home Depot Project) Revenue,

   4.40%, Series B (LOC; Sun Trust Bank)                                                      5,000,000  (a)           5,000,000

ILLINOIS--6.5%

Glendale Heights, Multi-Family Revenue, Refunding, VRDN

   (Glendale Lakes Project) 4.32% (LOC; FHLM)                                                 4,845,000  (a)           4,845,000

Illinois Development Finance Authority, PCR, VRDN

  (Illinois Power Co.)

   4.50%, Series B (LOC; Morgan Guaranty Trust Co.)                                          10,000,000  (a)          10,000,000

Illinois Educational Facilities Authority, Revenue, VRDN

  (Art Institute of Chicago)

   4.30%, Series A (LOC; Harris Trust and Savings Bank)                                      10,800,000  (a)          10,800,000

Illinois Health Facilities Authority, Revenue, VRDN:

  (Rehab Institute of Chicago Project)

      4.40% (LOC; Bank of America)                                                           13,500,000  (a)          13,500,000

   (Resurrection Health)

      4.15%, Series B (Insured; FSA and LOC;

      La Salle National Bank)                                                                 5,600,000  (a)           5,600,000

INDIANA--.5%

Indiana Bond Bank Advanced Funding Program

   4.75%, Series A-2, 1/18/2001 (LOC; Bank of America)                                        3,500,000                3,512,334

IOWA--1.4%

Iowa Finance Authority, SWDR, VRDN

  (Cedar River Paper Co. Project)

   4.65% (LOC; Union Bank of Switzerland)                                                     2,900,000  (a)           2,900,000

Louisa County, PCR, Refunding, VRDN

   (Midwest Power System Inc. Project) 4.35%                                                  7,000,000  (a)           7,000,000

KANSAS--1.7%

Butler County, Solid Waste Disposal and

  Cogeneration Revenue, VRDN

  (Texaco Refining and Marketing)

   4.60%, Series B ( Corp. Guaranty; Texaco Inc.)                                             5,500,000  (a)           5,500,000

Wichita, Renewal and Improvement Temporary Notes, RAN

   4.50%, 8/24/2000                                                                           6,000,000                6,007,311

KENTUCKY--2.0%

Kentucky Association of Counties, Advance Revenue/

   Cash Flow Borrowing Program, COP, TRAN
   4%, 6/30/2000                                                                              7,500,000                7,503,158

Ohio County, PCR, VRDN (Big Rivers Electric Corp. Project)

   4.15% (Insured; AMBAC and Liquidity Facility;
   Credit Suisse)                                                                             5,900,000  (a)           5,900,000


8

                                                                                              Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                           Amount ($)                 Value ($)
-----------------------------------------------------------------------------------------------------------------------------------

LOUISIANA--1.3%

Ascension Parish, Revenue, VRDN (BASF Corp. Project)

   4.65% (Corp. Guaranty; BASF Corp.)                                                         4,000,000  (a)           4,000,000

West Baton Rouge Parish

  Industrial District Number 3, Revenue, VRDN

  (Dow Chemical Co. Project)

   4.60% (Corp. Guaranty; Dow Chemical Co.)                                                   4,900,000  (a)           4,900,000

MAINE--1.5%

Maine Health and Higher Educational Facilities

  Authority, Revenue, Refunding, VRDN

  4.15%, Series A (Insured; AMBAC and

   Liquidity Facility; Kreditbank)                                                           10,000,000  (a)          10,000,000

MARYLAND--.7%

Baltimore County Authority, Revenue, VRDN

   (Golf System) 4.30% (LOC; Allied Irish Banks)                                              5,050,000  (a)           5,050,000

MASSACHUSETTS--2.3%

Acton, BAN 4.45%, 3/5/2001                                                                    7,000,000                7,016,301

Hampden and Wilbraham Regional School District,

   BAN 4.75%, 4/13/2001                                                                       3,760,000                3,768,389

Millbury, BAN 4.50%, 4/19/2001                                                                5,000,000                5,006,749

MINNESOTA--2.1%

Becker, PCR, CP (Northern State Power Co.)

   4.15%, Series A, 8/11/2000 (Corp. Guaranty;
   Northern State Power Corp.)                                                                9,000,000                9,000,000

Minnesota Housing Finance Agency,

  Single Family Mortgage

   3.20%, Series F, 6/1/2000                                                                  5,700,000                5,700,000

MISSOURI--2.8%

Missouri Health and Educational Facilities Authority,

  Health Facilities Revenue, VRDN

   (Deaconess Long Term Care) 4.40%, Series A
   (LOC; Bank One Corp.)                                                                      9,205,000  (a)           9,205,000

Saint Charles County Industrial Development Authority,

  Industrial Revenue,

  Refunding, VRDN (Country Club Apartments Project)

   4.32% (LOC; LaSalle National Bank)                                                        10,000,000  (a)          10,000,000

NEBRASKA--.3%

Nebraska Public Power District,

  Power Supply System Revenue,

   Refunding, Prerefunded 5.20%, 1/1/2001                                                     1,900,000                1,911,811

                                                                                                     The Fund 9

STATEMENT OF INVESTMENTS (Unaudited) (CONTINUED)

                                                                                              Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                           Amount ($)                Value ($)
-----------------------------------------------------------------------------------------------------------------------------------

NEVADA--1.0%

Nevada Housing Division, Multi-Unit Housing,

  VRDN (Silverado)

   4.45%, Series A (LOC; FNMA)                                                                6,710,000  (a)           6,710,000

NEW HAMPSHIRE--1.0%

New Hampshire Business Finance Authority, PCR, CP

  (New England Power Co. Project) 4.65%,
  Series A, 9/11/2000

   (Corp. Guaranty; New England Power Co.)                                                    5,000,000                5,000,000

New Hampshire Housing Finance Authority, SFMR

   3.95%, Series C, 12/1/2000                                                                 2,000,000                2,000,000

NEW MEXICO--1.5%

State of New Mexico, TRAN 4%, 6/30/2000                                                      10,000,000               10,005,903

NEW YORK--2.3%

Metropolitan Transportation Authority,

  Transit Facility Revenue, CP

   4.05%, 9/1/2000 (LOC; ABN-Amro Bank)                                                       9,000,000                9,000,000

Suffolk County, TAN 4.50%, Series 1, 8/10/2000

  (LOC: Credit Local de France, Landesbank Hessen

   and Westdeutschebank)                                                                      7,000,000                7,006,512

NORTH CAROLINA--.4%

Durham County Industrial Facilities and Pollution Control

  Financing Authority, Development Revenue, VRDN

  (Cormetech Inc. Project) 4.45% (LOC;

   Wachovia Bank of North Carolina)                                                           3,000,000  (a)           3,000,000

OHIO--3.6%

Hamilton County, Hospital Facilities Revenue, VRDN

  (Episcopal Retirement Project Homes)

   4.40%, Series A (LOC; Fifth Third Bank)                                                    5,000,000  (a)           5,000,000

State of Ohio, Higher Educational Facility Revenue, CP

  (Case Western Reserve University)

   4.05%, 7/18/2000 (LOC; Bank One Corp.)                                                     5,000,000                5,000,000

Ohio Housing Finance Agency,

  Mortgage Revenue (Residential)

   4.15%, Series C, 9/1/2000                                                                  5,000,000                5,000,000

Summit County, BAN 3.80%, Series A, 6/1/2000                                                 10,000,000               10,000,000

PENNSYLVANIA--3.4%

Berks County Industrial Development Authority,

  Revenue, VRDN (EJB Paving and Materials)

   4.50% (LOC; First Union National Bank)                                                     2,000,000  (a)           2,000,000

10

                                                                                              Principal

TAX EXEMPT INVESTMENTS (CONTINUED)                                                           Amount ($)                Value ($)
-----------------------------------------------------------------------------------------------------------------------------------

PENNSYLVANIA (CONTINUED)

Emmaus General Authority, Revenue, VRDN

   4.15% (Insured; FSA and LOC;
   First Union National Bank)                                                                11,100,000  (a)          11,100,000

Lancaster County Hospital Authority,

  Health Center Revenue, VRDN (Masonic Homes)

   4.15% (Insured; AMBAC and
   Liquidity Facility; PNC Bank)                                                             10,000,000  (a)          10,000,000

RHODE ISLAND--1.7%

Rhode Island Industrial Facilities Corporation, IDR, VRDN

  (Cololey Inc. Project):

      4.45% (LOC; Royal Bank of Scotland)                                                     2,750,000  (a)           2,750,000

      5.20% (LOC; Royal Bank of Scotland)                                                       550,000  (a)             550,000

Rhode Island Student Loan Authority,

  Student Loan Revenue, VRDN

  4.20%, Series 1 (LOC;

   State Street Bank and Trust Co.)                                                           8,000,000  (a)           8,000,000

SOUTH CAROLINA--.7%

South Carolina Jobs Economic Development Authority,

   EDR, VRDN (Wellman Inc. Project) 4.55
   (LOC; Wachovia Bank and Trust Co.)                                                         4,900,000  (a)           4,900,000

TENNESSEE--8.4%

Metropolitan Government Nashville and

  Davidson County Health and

  Educational Facilities Board, Revenue, VRDN

   (Vanderbilt University) 4.70%, Series A                                                    9,000,000  (a)           9,000,000

Sevier County Public Building Authority, VRDN

  (Local Government Public Improvement):

      4.30%, Series A-1 (Insured; AMBAC)                                                      6,485,000  (a)           6,485,000

      4.30%, Series A-2 (Insured; AMBAC)                                                      3,695,000  (a)           3,695,000

      4.30%, Series III-C-2 (Insured; AMBAC and

         Liquidity Facility; Landesbank Hessen)                                              14,425,000  (a)          14,425,000

      4.45%, Series IV-A-4 (Insured; FSA and

         Liquidity Facility; Morgan Guaranty Trust Co.)                                       6,335,000  (a)           6,335,000

      5.05%, Series III-C-2 (Insured; AMBAC and

         Liquidity Facility; Landesbank Hessen)                                                 335,000  (a)             335,000

      5.05%, Series III-C-3 (Insured; AMBAC and

         Liquidity Facility; Landesbank Hessen)                                                 240,000  (a)             240,000

                                                                                                     The Fund 11

STATEMENT OF INVESTMENTS (Unaudited) (CONTINUED)

                                                                                               Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                            Amount ($)               Value ($)
------------------------------------------------------------------------------------------------------------------------------------

TENNESSEE (CONTINUED)

Shelby County Health Educational and

  Housing Facility Board, HR, CP

  (Baptist Memorial Hospital):

      4.65%, 11/17/2000 (LOC; Bank of America)                                                4,000,000                4,000,000

      4.60%, 11/22/2000 (LOC; Bank of America)                                               13,000,000               13,000,000

TEXAS--17.7%

Brazos River Authority, PCR, VRDN

  (Texas Utilities Electric Co.):

      4.55%, Series A (LOC; Morgan Guaranty Trust Co.)                                       13,500,000  (a)          13,500,000

      Refunding:

         4.25%, Series C (Liquidity Facility;
            The Bank of New York)                                                            20,000,000  (a)          20,000,000

         4.55%, Series C (Insured; AMBAC and
            Liquidity Facility; The Bank of New York)                                        13,700,000  (a)          13,700,000

         4.65%, Series A (Insured; MBIA and
            Liquidity Facility; The Bank of New York)                                         4,300,000  (a)           4,300,000

Dallas County, Permanent Improvement

   3.30%, Series C, 6/15/2000 (Liquidity Facility;
   Union Bank of Switzerland)                                                                 6,500,000                6,500,000

Gulf Coast Industrial Development Authority, SWDR, VRDN

  (Citgo Petroleum Corp. Project):

      4.60% (LOC; Bank of America)                                                           19,100,000  (a)          19,100,000

      4.60% (LOC; Wachovia Bank of Georgia)                                                   9,400,000  (a)           9,400,000

Houston, Water and Sewer System Revenue, CP

   4.55%, Series A, 10/12/2000                                                               10,000,000               10,000,000

Panhandle-Plains Higher Education Authority,

  Student Loan Revenue, Refunding, VRDN

  4.15%, Series A (LOC; Student Loan

   Marketing Association)                                                                    12,700,000  (a)          12,700,000

State of Texas:

   Refunding 6%, Series B, 10/1/2000                                                          1,000,000                1,005,733

   TRAN 4.50%, Series A, 8/31/2000                                                           11,000,000               11,020,039

UTAH--2.0%

Intermountain Power Agency,

  Power Supply Revenue, CP:

    4%, Series B-2, 6/15/2000 (Liquidity Facility:

         Bank of America and Bank of Nova Scotia)                                             9,000,000                9,000,000

      4.50%, Series B-5, 7/25/2000 (Liquidity Facility:
         Bank of America and Bank of Nova Scotia)                                             5,000,000                5,000,000


12

                                                                                              Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                           Amount ($)                Value ($)
------------------------------------------------------------------------------------------------------------------------------------

VIRGINIA--3.8%

Henrico County Economic Development Authority, Revenue,

  Refunding, VRDN (White Oak Limited Project)

   4.15% (LOC; Citibank)                                                                     10,538,000  (a)          10,538,000

Hopewell Industrial Development Authority, Revenue, VRDN

   (Hadson Power 13) 4.55%, Series A (LOC; Credit Suisse)                                     3,200,000  (a)           3,200,000

Richmond Industrial Development Authority, Revenue, VRDN

  (Cogentrix of Richmond Project)

   4.60%, Series A (LOC; Banque Paribas)                                                     10,000,000  (a)          10,000,000

Southampton County Industrial Development Authority,

   Revenue, VRDN (Hadson Power 11) 4.55%,
   Series A (LOC; Credit Suisse)                                                              2,000,000  (a)           2,000,000

WEST VIRGINIA--.9%

Marion County, Community Solid Waste Disposal Facility

  Revenue, VRDN (Granttown Project)

   4.10%, Series B (LOC; National Westminster Bank)                                           3,700,000  (a)           3,700,000

Pendleton County, IDR, VRDN

   (Greer Steel Project) 4.50% (LOC; PNC Bank)                                                2,315,000  (a)           2,315,000

WISCONSON--.7%

Green Bay Area Public School District,

   BAN 4.90%, 4/13/2001                                                                       5,000,000               5,001,142
-----------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $680,654,826)                                                             99.2%              680,654,826

CASH AND RECEIVABLES (NET)                                                                          .8%                5,760,711

NET ASSETS                                                                                       100.0%              686,415,537

                                                                                                     The Fund 13
</TABLE>


STATEMENT OF INVESTMENTS (CONTINUED)

<TABLE>
<CAPTION>


Summary of Abbreviations
<S>                      <C>                                     <C>                       <C>

AMBAC                     American Municipal Bond                IDB                       Industrial Development Board
                             Assurance Corporation

BAN                       Bond Anticipation Notes                IDR                       Industrial Development Revenue

COP                       Certificate of Participation           LOC                       Letter of Credit

CP                        Commercial Paper                       MBIA                      Municipal Bond Investors
                                                                                           Assurance Insurance
                                                                                           Corporation

EDR                       Economic Development Revenue           MFHR                      Multi-Family Housing Revenue

EIR                       Environment Improvement
                             Revenue                             PCR                       Pollution Control Revenue

FGIC                      Financial Guaranty Insurance
                             Company                             RAN                       Revenue Anticipation Notes

FHLM                      Federal Home Loan Mortgage             SFMR                      Single Family Mortgage Revenue

FNMA                      Federal National Mortgage
                             Association                         SWDR                      Solid Waste Disposal Revenue

FSA                       Financial Security Assurance           TAN                       Tax Anticipation Notes

HR                        Hospital Revenue                       TRAN                      Tax and Revenue Anticipation
                                                                                             Notes

                                                                 VRDN                      Variable Rate Demand Notes



</TABLE>

Summary of Combined Ratings (Unaudited)

<TABLE>
<CAPTION>


Fitch                or          Moody's               or        Standard & Poor's                           Value (%)
------------------------------------------------------------------------------------------------------------------------------------
<S>                              <C>                             <C>                                             <C>

F1+/F1                           VMIG1/MIG1, P1                  SP1+/SP1, A1+/A1                                 90.8

AAA/AA(b)                        Aaa/Aa(b)                       AAA/AA(b)                                         5.5

Not Rated(c)                     Not Rated(c)                    Not Rated(c)                                      3.7

                                                                                                                 100.0

(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 OR STANDARD & POOR'S
     HAVE BEEN  DETERMINED BY THE MANAGER TO BE OF  COMPARABLE  QUALITY TO THOSE
     RATED SECURITIES IN WHICH THE FUND MAY INVEST.
</TABLE>


SEE NOTES TO FINANCIAL STATEMENTS.


14

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2000 (Unaudited)

                                                             Cost        Value
--------------------------------------------------------------------------------

ASSETS ($):

Investments in securities--See Statement of
Investments                                           680,654,826   680,654,826

Cash                                                                    362,637

Interest receivable                                                   5,817,553

Prepaid expenses                                                         59,530

                                                                    686,894,546
--------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                           425,006

Accrued expenses                                                         54,003

                                                                        479,009
--------------------------------------------------------------------------------

NET ASSETS ($)                                                      686,415,537
--------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                     686,427,562

Accumulated net realized gain (loss) on investments                    (12,025)
--------------------------------------------------------------------------------

NET ASSETS ($)                                                      686,415,537

NET ASSET VALUE PER SHARE

<TABLE>
<CAPTION>


                                                                              Class A               Class B                 Class X
------------------------------------------------------------------------------------------------------------------------------------

<S>                                                                       <C>                    <C>                        <C>
Net Assets ($)                                                            272,466,315            413,652,272                296,950

Shares Outstanding                                                        272,757,994            413,653,893                296,950
------------------------------------------------------------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                                                    1.00                  1.00                    1.00

SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>


                                                             The Fund 15

STATEMENT OF OPERATIONS

Six Months Ended May 31, 2000 (Unaudited)

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

INVESTMENT INCOME ($):

INTEREST INCOME                                                     12,454,996

EXPENSES:

Management fee--Note 2(a)                                            1,610,934

Shareholder servicing costs--Note 2(c)                                 667,834

Distribution fees (Class B and Class X)--Note 2(b)                     398,296

Professional fees                                                       45,867

Registration fees                                                       37,301

Custodian fees                                                          28,937

Prospectus and shareholders' reports                                    27,383

Directors' fees and expenses--Note 2(d)                                 16,442

Miscellaneous                                                           14,431

TOTAL EXPENSES                                                       2,847,425

Less--reduction in management fee due to

  undertaking--Note 2(a)                                             (160,095)

NET EXPENSES                                                         2,687,330

INVESTMENT INCOME--NET, REPRESENTING NET INCREASE
  IN NET ASSETS RESULTING FROM OPERATIONS                            9,767,666

SEE NOTES TO FINANCIAL STATEMENTS.

16

STATEMENT OF CHANGES IN NET ASSETS

                                         Six Months Ended
                                             May 31, 2000          Year Ended
                                               (Unaudited)  November 30, 1999(a)
-------------------------------------------------------------------------------

OPERATIONS ($):

Investment income--net                          9,767,666           15,935,283

Net realized gain (loss) on investments                --                7,897

NET INCREASE (DECREASE) IN NET ASSETS
   RESULTING FROM OPERATIONS                    9,767,666           15,943,180
-------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A shares                                (4,036,676)          (7,034,104)

Class B shares                                (5,729,017)          (8,901,177)

Class X shares                                    (1,973)                  (2)

TOTAL DIVIDENDS                               (9,767,666)         (15,935,283)
-------------------------------------------------------------------------------

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

Net proceeds from shares sold:

Class A shares                                712,893,121        1,238,026,201

Class B shares                                947,716,251        1,689,638,089

Class X shares                                    295,000               1,000

Dividends reinvested:

Class A shares                                  3,836,393           6,758,293

Class B shares                                  5,583,976           8,719,782

Class X shares                                      1,950                 --

Cost of shares redeemed:

Class A shares                              (730,112,075)      (1,239,336,213)

Class B shares                              (915,752,137)      (1,699,894,974)

Class X shares                                    (1,000)                 --

INCREASE (DECREASE) IN NET ASSETS FROM
   CAPITAL STOCK TRANSACTIONS                 24,461,479            3,912,178

TOTAL INCREASE (DECREASE) IN NET ASSETS       24,461,479            3,920,075
--------------------------------------------------------------------------------

NET ASSETS ($):

Beginning of Period                           661,954,058         658,033,983

END OF PERIOD                                 686,415,537         661,954,058

(A)  FROM JUNE 1, 1999 (COMMENCEMENT OF INITIAL OFFERING) TO NOVEMBER 30, 1999
FOR CLASS X SHARES.

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund 17

FINANCIAL HIGHLIGHTS

The  following  tables  describe  the  performance  for each share class for the
fiscal  periods  indicated.  All  information  reflects  financial results for a
single fund share. Total return shows how much your investment in the fund would
have  increased  (or  decreased) during each period, assuming you had reinvested
all dividends and distributions. These figures have been derived from the fund's
financial statements.

<TABLE>
<CAPTION>


                                          Six Months Ended

                                              May 31, 2000                                 Year Ended November 30,
                                                                    ----------------------------------------------------------------

CLASS A SHARES                                  (Unaudited)         1999         1998           1997           1996          1995
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                   <C>            <C>          <C>         <C>             <C>           <C>

PER SHARE DATA ($):

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

Investment Operations:

Investment income--net                                .016           .027        .030          .031           .029          .034

Distributions:

Dividends from
   investment income--net                           (.016)        (.027)        (.030)         (.031)        (.029)        (.034)

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

TOTAL RETURN (%)                                      3.29(a)      2.71          3.02          3.14           2.97          3.41
------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to
   average net assets                                  .60(a)       .58           .60          .62            .66           .66

Ratio of net investment income
   to average net assets                              3.27(a)      2.68          2.98         3.09           2.93          3.35
------------------------------------------------------------------------------------------------------------------------------------

Net Assets,
   end of period ($ X 1,000)                       272,466       285,849      280,398       273,058       256,862       294,379

(A) ANNUALIZED

SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

18

<TABLE>
<CAPTION>

                                          Six Months Ended

                                              May 31, 2000                                 Year Ended November 30,
                                                                    ----------------------------------------------------------------

CLASS B SHARES                                  (Unaudited)         1999          1998          1997           1996       1995(a)
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                   <C>            <C>          <C>         <C>             <C>           <C>
PER SHARE DATA ($):

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

Investment Operations:

Investment income--net                                .014          .023          .026          .028           .027          .020

Distributions:

Dividends from
   investment income--net                           (.014)        (.023)        (.026)         (.028)        (.027)        (.020)

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

TOTAL RETURN (%)                                   2.91(b)          2.31         2.64           2.86           2.70         3.01(b)
------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to
   average net assets                               .98(b)          .98           .96            .95            .85         1.10(b)

Ratio of net investment income
   to average net assets                           2.87(b)         2.29          2.59           2.87           2.65          2.83

Decrease reflected in
   above expense ratios
   due to undertakings by
   The Dreyfus Corporation                          .08(b)          .07           .09            .16            .29          .09(b)
------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period
   ($ X 1,000)                                     413,652      376,104       377,636        263,008         17,491         3,024

(A) FROM MARCH 31, 1995 (COMMENCEMENT OF INITIAL OFFERING) TO NOVEMBER 30, 1995.

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>


                                                             The Fund 19

FINANCIAL HIGHLIGHTS (CONTINUED)

                                               Six Months Ended
                                                   May 31, 2000   Year Ended
CLASS X SHARES                                      (Unaudited)  November 30,
1999(a)
--------------------------------------------------------------------------------

PER SHARE DATA ($):

Net asset value, beginning of period                     1.00          1.00

Investment Operations:

Investment income--net                                   .014          .012

Distributions:

Dividends from investment income--net                  (.014)        (.012)

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

TOTAL RETURN (%)                                      2.89(b)       2.43(b)
--------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets               1.05(b)       1.05(b)

Ratio of net investment income
   to average net assets                              3.02(b)       2.22(b)

Decrease reflected in above expense ratios
   due to undertakings by The Dreyfus Corporation      .20(b)        .18(b)
-------------------------------------------------------------------------------

Net Assets, end of period ($ X 1,000)                    297           1

(A) FROM JUNE 1, 1999 (COMMENCEMENT OF INITIAL OFFERING) TO NOVEMBER 30, 1999.

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.


NOTES TO FINANCIAL STATEMENTS (Unaudited)

20

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.,
which is a wholly-owned subsidiary of Mellon Financial Corporation.

Effective  March  22,  2000, Dreyfus Service Corporation ("DSC"), a wholly-owned
subsidiary of Mellon Financial Corporation, became the distributor of the fund's
shares,  which are sold to the public without a sales charge. Prior to March 22,
2000,  Premier  Mutual  Fund  Services,  Inc.  was  the distributor. The fund is
authorized  to  issue  16.5  billion shares of $.001 par value Common Stock. The
fund  is  currently  authorized  to  issue  three classes of shares: Class A (15
billion  shares  authorized) , Class B (1 billion shares authorized) and Class X
shares (500 million shares authorized). Class A shares, Class B shares and Class
X shares are identical except for the services offered to and the expenses borne
by  each class and certain voting rights. Class B and Class X 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  series.  Expenses directly attributable to each series are charged to that
series'  operations;  expenses  which are applicable to all series are allocated
among them on a pro rata basis.

                                                             The Fund 21

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

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 $32,994 during the period ended May 31, 2000
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, if it is the policy of the fund not to distribute such gain.


22

(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 $9,000 available
for  Federal  income  tax  purposes  to be applied against future net securities
profits,  if  any, realized subsequent to November 30, 1999. If not applied, the
carryover expires in fiscal 2006.

At  May  31,  2000,  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 fees, 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  through  May  31,  2000 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 .98 of 1% for Class B shares,  of the value of their  average  daily net
assets.  The reduction in management fee, pursuant to the undertakings  amounted
to  $159,962  for Class B and $133 for Class X during the  period  ended May 31,
2000.

                                                             The Fund 23

(b)  Under  the Distribution Plan (the "Plan") with respect to Class B ("Class B
Distribution  Plan") and Class X ("Class X Distribution Plan") adopted pursuant
to  Rule 12b-1 under the Act, Class B and Class X shares directly bear the costs
of   preparing,   printing  and  distributing  prospectuses  and  statements  of
additional  information and of implementing and operating the Plan. In addition,
Class  B and Class X shares reimburse the distributor for payments made to third
parties  for distributing their shares at an annual rate of .20 of 1% and .25 of
1% , respectively,  of  the  value of their average daily net assets. During the
period  ended May 31, 2000, Class B and Class X shares were charged $398,133 and
$163,  respectively, pursuant to the Plan, of which $196,301 and $135, for Class
B and Class X shares, respectively, were paid to DSC.

(c)  Under  the  Shareholder  Services  Plan  with  respect to Class A ("Class A
Shareholder  Services  Plan" ), Class  A  shares  reimburse DSC an amount not to
exceed  an annual rate of .25 of 1% of the value of the average daily net assets
of  Class A for certain allocated expenses of providing personal services and/or
maintaining  shareholder  accounts.  The  services provided may include personal
services  relating  to  shareholder  accounts,  such  as  answering  shareholder
inquiries  regarding Class A shares and providing reports and other information,
and  services  related  to  the  maintenance of shareholder accounts. During the
period  ended  May 31, 2000, Class A shares were charged $35,328 pursuant to the
Class A Shareholder Services Plan.

Under  the  Shareholder  Services  Plan  with  respect  to  Class  B  ("Class B
Shareholder  Services  Plan") and Class X ("Class X Shareholder Services Plan")
Class B and Class X shares pay the distributor at an annual rate of .25 of 1% of
the  value of their average daily net assets for servicing shareholder accounts.
The  services  provided  may  include  personal services relating to shareholder
accounts,    such    as    answering

24

shareholder inquiries regarding Class B and Class X 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.  During  the  period ended May 31, 2000, $597,199 and $163, were charged
pursuant to the Class B and Class X Shareholder Services Plans, respectively, of
which  $294,451 and $135 for Class B and Class X shares, respectively, were paid
to DSC.

The  fund  compensates  Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,   under  a  transfer  agency  agreement  for  providing  personnel  and
facilities  to  perform transfer agency services for the fund. During the period
ended May 31, 2000, the fund was charged $17,222 pursuant to the transfer agency
agreement.

(d)  Each  Board  member also serves as a Board member of other funds within the
Dreyfus complex (collectively, the "Fund Group"). Effective April 13, 2000, each
Board member who is not an "affiliated person" as defined in the Act receives an
annual  fee of $50,000 and an attendance fee of $6,500 for each meeting attended
in  person  and  $500 for telephone meetings. These fees are allocated among the
funds in the Fund Group. The Chairman of the Board receives an additional 25% of
such  compensation.  Prior  to  April 13, 2000, each Board member who was not an
"affiliated  person"  as defined in the Act received from the Company an annual
fee  of  $2,500  and  an attendance fee of $500 per meeting. The Chairman of the
Board  received  an  additional  25% of such compensation. Subject to the fund's
Director  Emeritus  Program  Guidelines, Emeritus Board members, if any, receive
50%  of  the  Company's annual retainer fee and per meeting fee paid at the time
the Board member achieved emeritus status.

                                                             The Fund 25

                                                           For More Information

                        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
                        100 Church Street
                        New York, NY 10286

                      Transfer Agent &
                      Dividend Disbursing Agent

                        Dreyfus Transfer, Inc.

                        P.O. Box 9671

                        Providence, RI 02940

                      Distributor

                        Dreyfus Service Corporation

                        200 Park Avenue

                        New York, NY 10166

To obtain information:

BY TELEPHONE
Call 1-800-645-6561

BY MAIL  Write to:
The Dreyfus Family of Funds
144 Glenn Curtiss Boulevard
Uniondale, NY 11556-0144

BY E-MAIL  Send your request
to [email protected]

ON THE INTERNET  Information
can be viewed online
or downloaded from:

http://www.dreyfus.com

(c) 2000 Dreyfus Service Corporation                                   918SA005


General Minnesota

Municipal Money

Market Fund

SEMIANNUAL REPORT May 31, 2000

(reg.tm)





The  views  expressed herein are current to the date of this report. These views
and  the  composition  of the fund's portfolio are subject to change at any time
based on market and other conditions.

           * Not FDIC-Insured
           * Not Bank-Guaranteed
           * May Lose Value


                                 Contents

                                 THE FUND
--------------------------------------------------

                             2   Letter from the President

                             3   Discussion of Fund Performance

                             6   Statement of Investments

                            10   Statement of Assets and Liabilities

                            11   Statement of Operations

                            12   Statement of Changes in Net Assets

                            13   Financial Highlights

                            15   Notes to Financial Statements

                                 FOR MORE INFORMATION
---------------------------------------------------------------------------

                                 Back Cover

                                                                       The Fund

                                                              General Minnesota

                                                    Municipal Money Market Fund

LETTER FROM THE PRESIDENT

Dear Shareholder:

We are pleased to present this semiannual report for General Minnesota Municipal
Money  Market  Fund  covering the six-month period from December 1, 1999 through
May  31,  2000.  Inside  you'll find valuable information about how the fund was
managed  during  the  reporting  period,  including a discussion with the fund's
portfolio manager, Joseph Irace.

When  the  reporting  period  began,  international  and domestic economies were
growing  at  a  very  strong  pace,  giving  rise  to concerns that long-dormant
inflationary  pressures  might  reemerge.  Consumers continued to spend heavily,
unemployment  levels  reached  new  lows  and  the  stock  market,  while highly
volatile,    continued    to    climb.

Because  robust economic growth may trigger unwanted inflationary pressures, the
Federal  Reserve  Board  raised  key  short-term interest rates three more times
during  the  reporting  period.  In  total, the Federal Reserve Board has raised
short-term  interest rates by 1.75 percentage points since late June 1999. While
these  economic  influences  adversely  affected long-term municipal bonds, they
positively    influenced    tax-exempt    money    market    yields.

We  appreciate  your confidence over the past six months, and we look forward to
your continued participation in General Minnesota Municipal Money Market Fund.

Sincerely,


/S/Stephen E. Canter
Stephen E. Canter
President and Chief Investment Officer
The Dreyfus Corporation

June 15, 2000

2

DISCUSSION OF FUND PERFORMANCE

Joseph Irace, Portfolio Manager

How did General Minnesota Municipal Money Market Fund perform during the period

For  the six-month period ended May 31, 2000, the fund's Class A shares produced
an annualized yield of 3.36% and its Class B shares produced an annualized yield
of 3.19%. Taking into account the effects of compounding, the fund's Class A and
B  shares provided annualized effective yields of 3.41% and 3.24%, respectively,
for    the    same    period.(1)

We  attribute  the  fund's  performance  to  higher  short-term  interest rates
implemented  by  the  Federal  Reserve  Board  (the "Fed"), which helped enhance
tax-exempt money market yields.

What is the fund's investment approach?

The  fund  seeks  to  maximize  current income exempt from federal and Minnesota
state  personal  income  taxes to the extent consistent with the preservation of
capital and the maintenance of liquidity.

In so doing, we employ two primary strategies. First, we attempt to add value by
constructing  a  diverse  portfolio  of  high  quality,  tax-exempt money market
instruments  from  Minnesota issuers. Second, we actively manage the portfolio's
average  maturity in anticipation of supply-and-demand changes in the short-term
municipal marketplace.

For  example, if we expect an increase in short-term supply, we may decrease the
average  maturity  of  the portfolio, which could enable us to take advantage of
opportunities  when  short-term supply increases. Generally, yields tend to rise
when  there  is an increase in new-issue supply competing for investor interest.
New securities are generally issued with maturities in the one-year range, which
in  turn may lengthen the portfolio's average maturity. If we anticipate limited
new-issue supply, we may then look to extend the portfolio's average maturity to
maintain  current  yields  for  as  long  as  we believe practical. At

                                                                      The Fund 3


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

other  times,  we  try to maintain an average maturity that reflects our view of
short-term interest-rate trends and future supply-and-demand considerations.

What other factors influenced the fund's performance?

The  fund  was  positively  influenced  over  the past six months by robust U.S.
economic  growth,  rising  interest  rates  and  a  low  supply  of newly issued
securities.

By  the  time  the  reporting  period  began  on December 1, 1999, it had become
apparent   that   the   pace  of  economic  growth  in  the  United  States  was
unsustainable.  Consumer  confidence  remained  near  a 30-year high, oil prices
bounced  back from the previous year's lows and employment remained strong, with
hourly  wages  rising.  These economic forces raised concerns among fixed-income
investors  that long-dormant inflationary pressures might reemerge. In response,
the  Fed  raised  short-term  interest rates three times. When combined with the
three interest-rate hikes implemented before the reporting period began, the Fed
has raised interest rates a total of 1.75 percentage points since last summer.

However,  tax-exempt  money  market  yields generally rose less when compared to
taxable yields over the past six months. This was due to the fact that Minnesota
and  its municipalities enjoyed higher tax revenues during the reporting period.
These  higher  revenues  reduced  their  need  to borrow and resulted in a lower
supply of securities.

What is the fund's current strategy?

Our  strategy continues to involve active management of the portfolio's weighted
average   maturity   and   asset   mix   according   to  our  interest-rate  and
supply-and-demand  expectations. Although the interest-rate outlook is currently
uncertain,  June  tends to be a period of seasonal issuance for municipal bonds.
These  technical  market  influences often hold greater sway over the tax-exempt
money markets than changes in the Fed's monetary policy.

4

Accordingly, we have recently adjusted the portfolio's average weighted maturity
toward  a  point  that  is  longer  than other Minnesota tax-exempt money market
funds.  This  maturity  management strategy was designed to help us lock in then
current    yields.

In  April,  we  took  advantage of the temporary high yields caused primarily by
tax-season   selling  to  create  a  laddered  portfolio  of  municipal  notes,
emphasizing  those  with  relatively  small issue sizes. This laddered portfolio
contains  securities  that  mature every month until the end of 2000, a strategy
designed to maintain prevailing yields if interest rates fall, while making some
cash available for reinvestment in case interest rates rise further.

Our  asset  mix  currently  also emphasizes Variable Rate Demand Notes ("VRDNs")
because  of  the  competitively  high yields they offer. VRDNs generally feature
adjustable  yields,  short  maturities and afford the portfolio a high degree of
liquidity  and  credit  quality.  Of course, portfolio composition is subject to
change at any time.

June 15, 2000

(1)  ANNUALIZED  EFFECTIVE  YIELD IS BASED  UPON  DIVIDENDS  DECLARED  DAILY AND
     REINVESTED  MONTHLY.  PAST  PERFORMANCE IS NO GUARANTEE OF FUTURE  RESULTS.
     YIELDS  FLUCTUATE.  INCOME  MAY BE  SUBJECT  TO STATE AND  LOCAL  TAXES FOR
     NON-MINNESOTA  RESIDENTS,  AND SOME  INCOME MAY BE  SUBJECT TO THE  FEDERAL
     ALTERNATIVE  MINIMUM TAX (AMT) FOR CERTAIN INVESTORS.  AN INVESTMENT IN THE
     FUND IS NOT  INSURED  OR  GUARANTEED  BY THE FDIC OR THE  U.S.  GOVERNMENT.
     ALTHOUGH THE FUND SEEKS TO PRESERVE THE VALUE OF YOUR  INVESTMENT  AT $1.00
     PER SHARE,  IT IS POSSIBLE TO LOSE MONEY BY INVESTING  IN THE FUND.  YIELDS
     PROVIDED FOR THE FUND'S CLASS A AND CLASS B SHARES  REFLECT THE  ABSORPTION
     OF FUND EXPENSES BY THE DREYFUS  CORPORATION  PURSUANT TO AN UNDERTAKING IN
     EFFECT THAT MAY BE EXTENDED,  TERMINATED OR MODIFIED AT ANY TIME. HAD THESE
     EXPENSES  NOT BEEN  ABSORBED,  THE FUND'S  CLASS A AND CLASS B SHARES WOULD
     HAVE BEEN LOWER. WITHOUT THE FUND'S EXPENSE ABSORPTION,  THE FUND'S CLASS A
     SHARES  WOULD  HAVE  PRODUCED  AN  ANNUALIZED  NET  YIELD OF  3.28%  AND AN
     ANNUALIZED  EFFECTIVE  NET YIELD OF 3.33%,  AND THE  FUND'S  CLASS B SHARES
     WOULD HAVE  PRODUCED  AN  ANNUALIZED  NET YIELD OF 2.81% AND AN  ANNUALIZED
     EFFECTIVE NET YIELD OF 2.85%.

                                                             The Fund 5

STATEMENT OF INVESTMENTS

May 31, 2000 (Unaudited)

STATEMENT OF INVESTMENTS

<TABLE>
<CAPTION>


                                                                                              Principal
TAX EXEMPT INVESTMENTS--94.9%                                                                Amount ($)               Value ($)
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                                                           <C>                      <C>
Beltrami County, Environmental Control Revenue, VRDN

  (Northwood Panelboard Co. Project)

   4.55% (LOC; Union Bank of Switzerland)                                                     1,400,000  (a)           1,400,000

Cloquet, Industrial Facilities Revenue, VRDN

  (Potlatch Corp. Project)

   4.35%, Series C (LOC; Wachovia Bank)                                                       1,700,000  (a)           1,700,000

Cohasset, Revenue, Refunding, VRDN

  (Minnesota Power and Light Co. Project)

   4.40%, Series B (LOC; ABN-Amro Bank)                                                         565,000  (a)             565,000

Cottage Grove, Environmental Control Revenue, VRDN

  (Minnesota Mining and Manufacturing)

   4.64% (Corp. Guaranty; Minnesota Mining and Manufacturing)                                 1,000,000  (a)           1,000,000

Dakota County Housing and Redevelopment Authority, SFMR

   5.50%, Series A, 10/1/2000 (LOC; FNMA)                                                        40,000                   40,000

Duluth Economic Development Authority,

  Health Care Facilities Revenue, Refunding,

  VRDN (Miller Dwan Medical Center Project):

      4.40% (LOC; Credit Locale de France)                                                    1,100,000  (a)           1,100,000

      5.30% (LOC; Credit Locale de France)                                                      100,000  (a)             100,000

East Central Solid Waste Commission,

  Solid Waste RRR, Refunding

   4.20% , 6/1/2000 (Insured; FSA)                                                              250,000                  250,000

Hennepin County, GO Notes, Refunding

   4.50%, Series A, 12/1/2000                                                                   100,000                  100,117

Inver Grove Heights, GO Notes 4.40%, Series A, 2/1/2001                                         125,000                  125,000

Mankato, Revenue, VRDN (Mankato Area Family YMCA Project)

   4.55% (LOC; U.S. Bank of Minneapolis)                                                      1,240,000  (a)           1,240,000

Maple Grove, GO Notes 4.20%, Series B, 12/21/2000                                               130,000                  130,000

Mc Leod County, Capital Improvement, GO Notes

   4.30%, Series A, 2/1/2001                                                                    175,000                  175,000

Metropolitan Council, Minneapolis-St. Paul Metropolitan Area:

   4.25%, Series B, 6/1/2000                                                                    300,000                  300,000

   GO, Refunding 5.75%, 12/1/2000                                                               530,000                  533,787

Minneapolis:

  HR (Fairview Hospital and Health Care)

      6.10%, Series B, 1/1/2001 (Insured; MBIA)                                                 500,000                  505,086

   MFHR, VRDN:

      (Hennipin) 4.45% (LOC; St. Pauls Companies, Inc.)                                       4,000,000  (a)           4,000,000

      (Swinford) 4.45% (LOC; St. Pauls Companies, Inc.)                                       1,700,000  (a)           1,700,000


6

                                                                                              Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                           Amount ($)                 Value ($)
-----------------------------------------------------------------------------------------------------------------------------------

Minneapolis and St. Paul Housing and Redevelopment Authority,

  Health Care Systems Revenue:

    Prerefunding (Health One Obligation):

         8%, 8/15/2000                                                                          200,000                  205,625

         8.11%, 8/15/2000 (Escrowed in; U.S. Securities)                                      4,000,000                4,103,400

      Refunding:

         (Healthspan) 4.40%, Series A, 11/15/2000

            (Insured; AMBAC)                                                                    250,000                  250,273

         VRDN (Children's Health Care) 4.45%

            (Insured; FSA and LOC; Norwest Bank)                                              1,500,000  (a)           1,500,000

Minnesota Housing Finance Agency, Rental Housing Revenue

   4.50%, Series A, 2/1/2001                                                                    235,000                  235,000

Minnesota Rural Water Finance Corporation (Public Projects)

   4.25%, 9/1/2000 (LOC; CDC Funding Corp.)                                                   4,175,000                4,176,232

Osseo Independent School District Number 279, GO Notes

   4.75%, Series A, 2/1/2001                                                                  1,000,000                1,002,879

Rosemount Independent School District Number 196,

  Revenue, Refunding 5.30%, Series C, 2/1/2001

   (Insured; FGIC)                                                                              100,000                  100,516

Saint Louis Park, HR Facilities (Methodist Hospital)

  Prerefunding:

      7.25%, Series C, 7/1/2000 (Escrowed in; U.S. Securities)                                  250,000                  255,516

      7.30%, Series C, 7/1/2000 (Escrowed in; U.S. Securities)                                  500,000                  511,145

Saint Paul:

   GO Notes 4.75%, Series B, 3/1/2001                                                           400,000                  401,301

   Revenue, Refunding 5%, 12/1/2000 (Insured; AMBAC)                                            250,000                  250,844

Saint Paul Port Authority, IDR, VRDN (Ideal Printers Inc.)

   4.55%, Series A (Corp. Guaranty; Marshall and Isley Corp.)                                 1,140,000  (a)           1,140,000

Shoreview, Refunding, GO Notes 3.90%, Series D, 12/1/2000                                       260,000                  259,837

Southern Municipal Power Agency,

  Power Supply Systems Revenue, CP

  (Power Supply System)

  3.55%, 2/10/2000 (Liquidity Facility: ABN-Amro Bank,

   Bank of Nova Scotia and Credit Agricole-Indosuez)                                          1,000,000                1,000,000

Stillwater, GO Notes 4.30%, Series A, 2/1/2001                                                  170,000                  170,000

Wadena, IDR, VRDN (Homecrest Industry Inc. Project)

   4.55% (LOC; U.S. Bank of Minneapolis)                                                      3,000,000  (a)           3,000,000

Winona Independent School District Number 861

   3.80%, 9/30/2000                                                                             925,000                  924,366

                                                                                                     The Fund 7

STATEMENT OF INVESTMENTS (Unaudited) (continued)

                                                                                              Principal
TAX EXEMPT INVESTMENTS (CONTINUED)                                                           Amount ($)                Value ($)
------------------------------------------------------------------------------------------------------------------------------------

State of Minnesota:

  GO Notes:

    Various Purpose:

         5.60%, 8/1/2000                                                                        340,000                  341,544

         6.60%, 8/1/2000                                                                        200,000                  200,533

      Refunding:

         4.875%, 8/1/2000                                                                       350,000                  350,408

         5%, 4/1/2000                                                                           500,000                  502,405

         5.20%, 8/1/2000                                                                        550,000                  550,899

   Prerefunded, Infrastructure Development 7%, 8/1/2000                                         180,000                  180,889
------------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $36,576,187)                                                              94.9%               36,577,602

CASH AND RECEIVABLES (NET)                                                                         5.1%                1,945,874

NET ASSETS                                                                                       100.0%               38,523,476

8

</TABLE>



Summary of Abbreviations

<TABLE>
<CAPTION>
<S>                       <C>                                     <C>                      <C>


AMBAC                     American Municipal Bond                 LOC                       Letter of Credit
                             Assurance Corporation

CP                        Commercial Paper                        MBIA                      Municipal Bond Investors
                                                                                              Assurance Insurance
                                                                                              Corporation

FNMA                      Federal National Mortgage
                             Association                          MFHR                      Multi-Family Housing Revenue

FSA                       Financial Security Assurance            RRR                       Resources Recovery Revenue

GO                        General Obligation                      SFMR                      Single Family Mortgage Revenue

HR                        Hospital Revenue                        VRDN                      Variable Rate Demand Notes

IDR                       Industrial Development Revenue

</TABLE>






Summary of Combined Ratings (Unaudited)
<TABLE>
<CAPTION>


Fitch                or          Moody's               or        Standard & Poor's                           Value (%)
------------------------------------------------------------------------------------------------------------------------------------

<S>                              <C>                             <C>                                             <C>
F1+/F1                           VMIG1/MIG1, P1                  SP1+/SP1, A1+/A1                                 69.1

AAA/AA(b)                        Aaa/Aa(b)                       AAA/AA(b)                                        14.9

Not Rated(c)                     Not Rated(c)                    Not Rated(c)                                     16.0

                                                                                                                 100.0

(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
     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>


                                                             The Fund 9

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2000 (Unaudited)

                                                             Cost         Value
--------------------------------------------------------------------------------

ASSETS ($):

Investments in securities--See Statement of Investments  36,576,187  36,577,602

Cash                                                                    263,459

Receivable for investment securities sold                             1,300,927

Interest receivable                                                     407,665

Prepaid expenses                                                         19,893

                                                                     38,569,546
--------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                            26,312

Accrued expenses                                                         19,758

                                                                         46,070
--------------------------------------------------------------------------------

NET ASSETS ($)                                                       38,523,476
--------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                      38,521,903

Accumulated net realized gain (loss) on investments                         158

Accumulated gross unrealized appreciation on investments                  1,415
--------------------------------------------------------------------------------

NET ASSETS ($)                                                       38,523,476

NET ASSET VALUE PER SHARE

                                                          Class A       Class B
--------------------------------------------------------------------------------

Net Assets ($)                                            105,032    38,418,444

Shares Outstanding                                        105,028    38,416,875
--------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                                1.00          1.00

SEE NOTES TO FINANCIAL STATEMENTS.

10


STATEMENT OF OPERATIONS

Six Months Ended May 31, 2000 (Unaudited)

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

INVESTMENT INCOME ($):

INTEREST INCOME                                                        846,718

EXPENSES:

Management fee--Note 2(a)                                              106,068

Shareholder servicing costs--Note 2(c)                                  63,555

Distribution fees (Class B)--Note 2(b)                                  42,321

Registration fees                                                       11,760

Professional fees                                                       11,529

Prospectus and shareholders' reports                                     7,205

Custodian fees                                                           3,445

Directors' fees and expenses--Note 2(d)                                  1,199

Miscellaneous                                                            3,747

TOTAL EXPENSES                                                         250,829

Less--reduction in management fee
  due to undertakings--Note 2(a)                                      (81,073)

NET EXPENSES                                                           169,756

INVESTMENT INCOME--NET                                                 676,962
--------------------------------------------------------------------------------

REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--NOTE 1(B):

Net realized gain (loss) on investments                                    158

Net unrealized appreciation (depreciation) on investments                  997

NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS                   1,155

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                   678,117

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund 11

STATEMENT OF CHANGES IN NET ASSETS

                                         Six Months Ended
                                             May 31, 2000         Year Ended
                                              (Unaudited)  November 30, 1999
--------------------------------------------------------------------------------

OPERATIONS ($):

Investment income--net                            676,962              829,916

Net realized gain (loss) on investments               158                   --

Net unrealized appreciation (depreciation)
   on investments                                     997                  418

NET INCREASE (DECREASE) IN NET ASSETS

   RESULTING FROM OPERATIONS                      678,117               830,334
--------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A shares                                    (1,780)              (5,752)

Class B shares                                  (675,182)            (824,164)

TOTAL DIVIDENDS                                 (676,962)            (829,916)
--------------------------------------------------------------------------------

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

Net proceeds from shares sold:

Class A shares                                         --                3,000

Class B shares                                 62,599,093           77,718,879

Dividends reinvested:

Class A shares                                      1,786                5,739

Class B shares                                    665,812              807,618

Cost of shares redeemed:

Class A shares                                    (3,103)            (916,522)

Class B shares                               (65,258,326)         (66,275,896)

INCREASE (DECREASE) IN NET ASSETS FROM
   CAPITAL STOCK TRANSACTIONS                 (1,994,738)          11,342,818

TOTAL INCREASE (DECREASE) IN NET ASSETS       (1,993,583)          11,343,236
-------------------------------------------------------------------------------

NET ASSETS ($):

Beginning of Period                            40,517,059           29,173,823

END OF PERIOD                                  38,523,476           40,517,059

SEE NOTES TO FINANCIAL STATEMENTS.


12

FINANCIAL HIGHLIGHTS

The  following  tables  describe  the  performance  for each share class for the
fiscal  periods  indicated.  All  information  reflects  financial results for a
single  fund share.Total return shows how much your investment in the fund would
have  increased  (or  decreased) during each period, assuming you had reinvested
all dividends and distributions. These figures have been derived from the fund's
financial statements.

<TABLE>
<CAPTION>


                                                                            Six Months Ended
                                                                               May 31, 2000            Year   Ended  November 30,
CLASS A SHARES                                                                    (Unaudited)          1999           1998(a)
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                                                     <C>            <C>             <C>
PER SHARE DATA ($):

Net asset value, beginning of period                                                     1.00          1.00             1.00

Investment Operations:

Investment income--net                                                                   .017          .027             .014

Distributions:

Dividends from investment income--net                                                  (.017)        (.027)           (.014)

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

TOTAL RETURN (%)                                                                      3.39(b)          2.68           2.81(b)
------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                                .65(b)           .65           .65(b)

Ratio of net investment income
   to average net assets                                                              3.35(b)          2.73          2.80(b)

Decrease reflected in above expense ratios
   due to undertakings by The Dreyfus Corporation                                      .08(b)           .16           .76(b)
------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ x 1,000)                                                     105           106           1,014

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

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>


                                                             The Fund 13

FINANCIAL HIGHLIGHTS (CONTINUED)

<TABLE>
<CAPTION>


                                                                            Six Months Ended

                                                                                May 31, 2000            Year   Ended  November
                                                                                                                           30,
                                                                                                       ------------------------

CLASS B SHARES                                                                    (Unaudited)          1999            1998(a)
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                                                      <C>           <C>              <C>
PER SHARE DATA ($):

Net asset value, beginning of period                                                     1.00          1.00             1.00

Investment Operations:

Investment income--net                                                                   .016          .025             .013

Distributions:

Dividends from investment income--net                                                  (.016)        (.025)           (.013)

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

TOTAL RETURN (%)                                                                      3.21(b)          2.52             2.67(b)
------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                                .80(b)           .80           .80(b)

Ratio of net investment income
   to average net assets                                                              3.19(b)          2.49          2.63(b)

Decrease reflected in above expense ratios
   due to undertakings by The Dreyfus Corporation                                      .38(b)           .48           .87(b)
------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ x 1,000)                                                  38,418        40,411          28,160

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

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>


14

NOTES TO FINANCIAL STATEMENTS (Unaudited)

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., which is a wholly-owned subsidiary
of Mellon Financial Corporation.

At  May  31,  2000,  MBC  Investments  Corp.,  an  indirect subsidiary of Mellon
Financial Corporation, held 105,018 Class A shares and 104,734 Class B shares.

Effective  March  22,  2000, Dreyfus Service Corporation ("DSC"), a wholly-owned
subsidiary  of  the  Manager, became the distributor of the fund's shares, which
are  sold to the public without a sales charge. Prior to March 22, 2000, Premier
Mutual  Fund Services, Inc. was the distributor. The fund is authorized to issue
4  billion  shares  of  $.001  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  series.  Expenses  directly  attributable  to  each  series  are

                                                                     The Fund 15

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

charged  to  that fund's operations; expenses which are applicable to all series
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 $3,247 during the period ended May 31, 2000
based  on  available  cash  balances  left  on deposit. Income earned under this
arrangement is included in interest income.

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    are    normally

16

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 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.

At  May  31,  2000,  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 fees, 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  through  May  31,  2000  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% for Class A and .80 of 1% for Class B shares of the value of
their  average  daily  net  assets.  The  expense  reimbursement pursuant to the
undertaking  amounted  to  $41 for Class A and $81,037 for Class B shares during
the period ended May 31, 2000.

                                                             The Fund 17

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

(b)  Under  the Distribution Plan with respect to Class B ("Class B Distribution
Plan"), adopted  pursuant  to Rule 12b-1 under the Act, Class B shares directly
bear  the  costs  of  preparing,  printing  and  distributing  prospectuses  and
statements of additional information and of implementing and operating the Class
B  Distribution  Plan. In addition, Class B shares reimburse the distributor for
payments  made  to third parties for distributing their shares at an annual rate
of .20 of 1% of the value of the average daily net assets of Class B. During the
period  ended  May 31, 2000, Class B shares were charged $42,321 pursuant to the
Distribution Plan, of which $21,990 paid to DSC.

(c)  Under  the  Shareholder  Services  Plan  with  respect to Class A ("Class A
Shareholder  Services  Plan"), Class  A  shares  reimburse DSC 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.

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. During the
period  ended  May 31, 2000, Class B shares were charged $63,482 pursuant to the
Class B Shareholder Services Plan, of which $32,985 was paid to DSC.


18

The  fund  compensates  Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,   under  a  transfer  agency  agreement  for  providing  personnel  and
facilities  to  perform transfer agency services for the fund. During the period
ended  May  31,  2000,  the fund was charged $49 pursuant to the transfer agency
agreement.

(d)  Each  Board  member also serves as a Board member of other funds within the
Dreyfus complex (collectively, the "Fund Group"). Effective April 13, 2000, each
Board member who is not an "affiliated person" as defined in the Act receives an
annual  fee of $50,000 and an attendance fee of $6,500 for each meeting attended
in  person  and  $500 for telephone meetings. These fees are allocated among the
funds in the Fund Group. The Chairman of the Board receives an additional 25% of
such  compensation.  Prior  to  April 13, 2000, each Board member who was not an
" affiliated  person"  as defined in the Act received from the Company an annual
fee  of  $2,500  and  an attendance fee of $500 per meeting. The Chairman of the
Board  received  an  additional  25% of such compensation. Subject to the fund's
Director  Emeritus  Program  Guidelines, Emeritus Board members, if any, receive
50%  of  the  Company's annual retainer fee and per meeting fee paid at the time
the Board member achieved emeritus status.

                                                             The Fund 19

NOTES

                                                           For More Information

                        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
                        100 Church Street
                        New York, NY 10286

                      Transfer Agent &
                      Dividend Disbursing Agent

                        Dreyfus Transfer, Inc.
                        P.O. Box 9671
                        Providence, RI 02940

                      Distributor

                        Dreyfus Service Corporation
                        200 Park Avenue
                        New York, NY 10166

To obtain information:

BY TELEPHONE
Call 1-800-645-6561

BY MAIL  Write to:
The Dreyfus Family of Funds
144 Glenn Curtiss Boulevard
Uniondale, NY 11556-0144

BY E-MAIL  Send your request\
to [email protected]

ON THE INTERNET  Information
can be viewed online or
downloaded from:

http://www.dreyfus.com

(c) 2000 Dreyfus Service Corporation                                   917SA005





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