GENERAL MUNICIPAL MONEY MARKET FUNDS INC
N-30D, 1999-08-06
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General Municipal
Money Market Fund

SEMIANNUAL REPORT
May 31, 1999



<PAGE>

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


Year 2000 Issues
(Unaudited)

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


<PAGE>

                                    Contents

                                    The Fund
- --------------------------------------------

                              2     Letter from the President

                              3     Discussion of Fund Performance

                              6     Statement of Investments

                             13     Statement of Assets and Liabilities

                             14     Statement of Operations

                             15     Statement of Changes in Net Assets

                             16     Financial Highlights

                             18     Notes to Financial Statements

                                    For More Information
- --------------------------------------------------------

                                    Back Cover


<PAGE>

                                               General Municipal      The Fund
                                               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, 1998 through May 31,
1999. 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, Karen Hand.

Yields on both taxable and tax-exempt money market securities generally declined
early in the reporting period in the wake of the Federal Reserve Board's
decision in the fall of 1998 to ease monetary policy. While the U.S. economy has
continued to grow, the Federal Reserve was concerned about persistent economic
weakness abroad. Their adoption of lower short-term interest rates was intended
to stimulate not just domestic economic growth, but the economies of other
nations as well.

Despite lower nominal interest rates for tax-exempt money market instruments,
very low inflation continued to support attractive real returns, which are
nominal yields less the rate of inflation.

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 14, 1999

2

<PAGE>

DISCUSSION OF FUND PERFORMANCE
- ------------------------------
Karen Hand, Portfolio Manager

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

For the six-month period ended May 31, 1999, General Municipal Money Market
Fund, Inc. produced an annualized, tax-exempt yield of 2.62% for Class A shares
and 2.22% for Class B shares. After taking into account the effect of
compounding, the fund's Class A shares provided an annualized effective yield of
2.65% while the fund's Class B shares produced an annualized effective yield of
2.25%.(1)

For the six-month period ended May 31, 1999, the fund's Class A shares and Class
B shares provided total returns of 1.31% and 1.11%,(2) respectively, compared to
the Lipper Tax Exempt Money Market Funds category average total return of 1.27%
for the same time period.(3)

What is the fund's investment approach?

Our goal is to seek a high level of federally tax-exempt income while
maintaining a stable $1.00 share price. We also seek to provide a competitive
total return, and we attempt to be especially vigilant in our efforts to
preserve capital.

To achieve these objectives, we employ two primary strategies. First, we attempt
to add value by constructing a diverse portfolio of high-quality, tax-exempt
money market instruments that we believe are likely to provide highly
competitive returns with relatively little risk. Second, we actively manage the
portfolio's average maturity in anticipation of interest rate trends and
supply-and-demand changes in the short-term municipal marketplace.

For example, if we expect supply to increase temporarily when many
municipalities issue short-term debt at once -- as they tend to do in July, for
example -- we may reduce the portfolio's average maturity to make cash available
for the purchase of higher yielding securities. That's because yields tend to
rise if many issuers are competing for investor interest. If

                                                                      The Fund 3



<PAGE>

DISCUSSION OF FUND PERFORMANCE (continued)

we expect demand to surge at a time when we anticipate little issuance and,
therefore, lower yields -- as often happens in January -- we may increase the
portfolio's average maturity prior to that time to maintain current yields for
as long as possible. Overall, we try to maintain an average maturity that
reflects our view of short-term interest rate trends, note issuance and
anticipated cash flows.

What other factors influenced the fund's performance?

Although the fund, by definition, contains only securities from U.S. issuers,
the entire domestic fixed-income marketplace was influenced just prior to the
reporting period by economic events overseas. When the Asian currency and credit
crisis threatened Latin America last summer and fall, the Federal Reserve Board
and other central banks reduced key short-term interest rates. This move was
intended to help boost economic activity by making borrowing less expensive for
corporations. An additional consequence was lower yields on money market
securities.

Despite economic weakness in some overseas markets, the U.S. economy remained
strong. Because municipalities have enjoyed higher tax revenues during this
period of economic prosperity, many have had less need to borrow. As a result,
fewer short-term tax-exempt money market securities were issued than in the same
six-month period one year ago. Yet, demand from investors seeking to minimize
their income tax liabilities remained high. This imbalance between supply and
demand helped push short-term tax-exempt yields down during the final months of
1998. Tax-exempt yields have remained relatively stable so far in 1999.

4


<PAGE>

What is the fund's current strategy?

We have continued to focus on high-quality money market instruments from a wide
array of tax-exempt issuers. Some of the most frequently used instruments
include Variable Rate Demand Notes (VRDNs), which are issued by investment banks
through the securitization of longer-term municipal bonds. With a put feature of
either one or seven days attached to each VRDN, we believe that VRDNs afford a
high degree of liquidity as well as high quality to the Portfolio. Accordingly,
as of May 31, 1999, approximately 60% of the portfolio was composed of VRDNs.
The remaining 40% was comprised of municipal notes and tax-exempt commercial
paper.

June 14, 1999
[FN]
1 Annualized effective yield is based upon dividends declared daily and
  reinvested monthly. Past performance is no guarantee of future results. Yields
  fluctuate. An investment in the fund is not insured or guaranteed by the FDIC
  or any other government agency. 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.

2 Total return includes reinvestment of dividends. The fund's Class B shares'
  return figure provided reflects 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 shares' return would have been lower. Income may be subject to
  state and local taxes, and some income may be subject to the Federal
  Alternative Minimum Tax (AMT) for certain shareholders.

3 Source: Lipper Analytical Services, Inc.
</FN>
                                                                  The Fund  5

<PAGE>

STATEMENT OF INVESTMENTS
May 31, 1999 (Unaudited)
<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                                  Principal
Tax Exempt Investments--100.2%                                    Amount ($)      Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                              <C>            <C>
Alabama--.7%

Stevenson,  IDB, EIR, VRDN (Mead Corp. Project)
  3.20%, Series B (LOC; First Chicago Corp.)(a)                     5,000,000       5,000,000

Alaska--2.3%

Alaska Housing Finance Corporation, VRDN
  3.20%, Series A (BPA: Credit Suisse and
  Westdeutsche Landesbank)(a)                                      15,200,000      15,200,000

Arizona--4.9%

Arizona Educational Loan Marketing Corporation,
  Educational Loan Revenue, VRDN
  3.25%, Series A (BPA; Fuji Bank and Insured; MBIA)(a)            10,675,000      10,675,000

Glendale Industrial Development Authority, HR, VRDN
  (West Valley Camelback)
  3.25% (LOC; Northwest Bank Corp.)(a)                              7,800,000       7,800,000

Pima County Industrial Development Authority,
  Industrial Revenue, VRDN
  (Tuscon Electric)
  3.25% (LOC; Toronto-Dominion Bank)(a)                            14,100,000      14,100,000

California--1.2%

California Higher Education Loan Authority,
  Student Loan Revenue, Refunding
  3.18%, Series A, 5/1/2000
  (LOC; National Westminster Bank)                                  8,000,000       8,000,000

Connecticut--1.1%

State of Connecticut Special Assessment Unemployment
  Compensation Advance Fund, Revenue
  (Connecticut Unemployment)
  3.60%, Series C, 7/1/1999
  (Insured; FGIC and Liquidity Facility; FGIC)                      7,000,000       7,000,000

District of Columbia--.8%

District of Columbia, TRAN
  3.75%, Series B, 9/30/1999
  (LOC: Canadian Imperial Bank of Commerce,
  Morgan Guaranty Trust Co. and Societe Generale)                   5,000,000       5,010,487

Florida--3.4%

Florida Housing Financing Agency:
  Multi-Family, Refunding (Iowa Lakes Project)
    3.25%, Series D, 4/1/2000
    (LOC; Continental Casualty)                                     6,155,000       6,155,000
  (Wood Forest II Project)
    3.15%, Series BBB, 12/1/1999
    (LOC; Continental Casuality)                                    6,000,000       6,000,000

Miami-Dade County School District, TAN 4%, 6/30/1999               10,450,000      10,452,805
</TABLE>

6


<PAGE>

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                                  Principal
Tax Exempt Investments (continued)                                Amount ($)      Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                              <C>            <C>
Georgia--6.9%

Appling County Development Authority, PCR, VRDN
  (Georgia Power and Light Hatch Co. Project)
  3.35% (Corp. Guaranty; Georgia Power and Light Co.)(a)         13,700,000      13,700,000

Burke County Development Authority, PCR
  (Oglethorpe Power Corp.):
    CP 3.05%, Series B, 7/28/1999 (Insured; AMBAC
      and Liquidity Facility; Rabobank Netherland)               10,000,000      10,000,000
    Refunding, VRDN 3.15%, Series A (BPA; Credit
      Locale de France and Insured; FGIC)(a)                      7,900,000      7,900,000

Fulton County School District, Construction Sales, TAN
  3.25%, 12/31/1999                                               9,000,000       9,011,188

Savannah Economic Development Authority,
  Exempt Facility Revenue, VRDN
  (Home Depot Project) 3.30%, Series B
  (LOC; Sun Trust Bank)(a)                                        5,000,000       5,000,000

Idaho--.8%

State of Idaho, TAN 4.50%, 6/30/1999                              5,000,000       5,003,450

Illinois--6.2%

Chicago Midway Airport, Revenue, VRDN (Second Lien)
  3.50%, Series A
  (Insured; MBIA and Liquidity Facility; FNB Chicago)(a)         17,800,000      17,800,000

Illinois Health Facilities Authority, Revenue, VRDN
  (Rehab Institute of Chicago Project)
  3.25% (LOC; Bank of America)(a)                                13,500,000      13,500,000

Southwestern Development Authority, EIR, VRDN
  (Shell Oil Co.-Wood River Project)
  4.45% (Corp. Guaranty; Shell Oil Co.)(a)                       10,300,000      10,300,000

Kansas--1.1%

Butler County, Solid Waste Disposal and Cogeneration
  Revenue, VRDN
  (Texaco Refining and Marketing) 3.50%, Series B
  (Corp. Guaranty; Texaco Inc.)(a)                                7,400,000       7,400,000

Kentucky--1.5%

Boone County, IDR, VRDN (Curtin Matheson Scientific Project)
  3.40% (LOC; Toronto-Dominion Bank)(a)                           2,500,000       2,500,000

Kentucky Housing Corporation, Housing Revenue
  3.20%, Series C, 12/31/1999                                     7,500,000       7,500,000

Louisiana--5.0%

Ascension Parish, Revenue, VRDN
  (BASF Corp. Project)
  3.40% (Corp. Guaranty; BASF Corp.)(a)                          12,000,000      12,000,000
</TABLE>

                                                                     The Fund  7


<PAGE>

STATEMENT OF INVESTMENTS (Unaudited) (continued)
<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                                  Principal
Tax Exempt Investments (continued)                                Amount ($)      Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                              <C>            <C>
Louisiana (continued)

Saint Charles Parish, PCR, VRDN
  (Shell Oil Co. Norco Project)
  3.45% (Corp. Guaranty; Shell Oil Co.)(a)                        9,000,000       9,000,000

West Baton Rouge Parish Industrial District Number 3,
  Revenue, VRDN
  (Dow Chemical Co. Project)
  3.50% (Corp. Guaranty; Dow Chemical Co.)(a)                    12,500,000      12,500,000

Maryland--5.0%

Anne Arundel County, CP 3.40%, Series B, 7/8/1999
  (LOC; Westdeutsche Landesbank)                                 18,000,000      18,000,000

Maryland Community Development Administration,
  Department of Housing and Community Development
  (Residential) 3.15%, Series B, 1/14/2000                       15,000,000      15,000,000

Massachusetts--4.0%

City of Springfield, BAN:
  4%, 6/25/1999 (LOC; Fleet Bank)                                 3,910,000       3,910,742
  4%, 7/15/1999 (LOC; Fleet Bank)                                13,000,000      13,005,279

Massachusetts Water Resource Authority, CP
  2.90%, 7/14/1999
  (LOC; Morgan Guaranty Trust Co.)                                4,000,000       4,000,000

Montachusett Regional Vocational Technical
  School District, BAN 4%, 7/23/1999                              5,660,000       5,662,312

Michigan--3.8%

Macomb Township Economic Development Corporation,
  LOR, VRDN (ACR Industries Project)
  3.35% (LOC; Comerica Bank)(a)                                     450,000         450,000

Michigan Strategic Fund, SWDR, VRDN
  (Grayling Generating Project)
  3.35% (LOC; Barclays Bank)(a)                                   3,800,000       3,800,000

Midland County Economic Development Corporation,
  Economic Development, LOR, VRDN
  (Dow Chemical Co. Project) 3.40%, Series A
  (Corp. Guaranty; Dow Chemical Co.)(a)                          20,900,000      20,900,000

Minnesota--2.0%

Cohasset, Revenue, Refunding, VRDN
  (Minnesota Power and Light Co. Project)
  3.30%, Series A (LOC; ABN-Amro Bank)(a)                         7,900,000       7,900,000

Minnesota Housing Finance Agency, Single Family
  Mortgage 3.14 %, Series F, 6/1/2000                             5,700,000       5,700,000
</TABLE>

8

<PAGE>

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                                  Principal
Tax Exempt Investments (continued)                                Amount ($)      Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                              <C>            <C>
Missouri--4.7%

Independence Industrial Development Authority, IDR,
  Revenue, Refunding, VRDN
  (Grooves and Graceland) 3.30%, Series A
  (LOC; Credit Local de France)(a)                               21,900,000      21,900,000

Missouri Health and Educational Facilities Authority,
  Health Facilities Revenue, VRDN:
    (Deaconess Long Term Care) 3.30%, Series A
      (LOC; Bank One)(a)                                          9,395,000       9,395,000
    (Saint John's Regional Health Center)
      3.75%, Series A (LOC; Bank One)(a)                            105,000         105,000

Nevada--4.1%

Clark County, IDR, VRDN (Nevada Cogeneration Project)
  3.40% (LOC; Canadian Imperial Bank of Commerce)(a)             12,200,000      12,200,000

Washoe County, Water Facilities Revenue, VRDN
  (Sierra Pacific Power Co. Project)
  3.50% (LOC; Union Bank of Switzerland)(a)                      15,300,000      15,300,000

New Jersey--1.2%

New Jersey Economic Development Authority, EDR
  3%, 6/15/1999 (LOC; Societe Generale)                           8,000,000      8,000,000

New Mexico--1.5%

State of New Mexico, TRAN 4.25%, 6/30/1999                       10,000,000     10,004,985

New York--6.7%

State of New York, CP 2.70%, Series V, 7/12/1999
  (LOC; Westdeutsche Landesbank)                                 10,000,000      10,000,000

New York State Housing Finance Agency,
  Housing Revenue, VRDN (Normandie Court II)
  3.10%, Series A (LOC; Fleet Bank)(a)                            4,000,000       4,000,000

New York State Local Government Assistance
  Corporation, VRDN:
    3%, Series A (LOC: Bayerische Landesbank and
      Westdeutsche Landesbank)(a)                                 4,900,000       4,900,000
    3%, Series C (LOC; Landesbank Hessen-Thueringen)(a)          15,750,000      15,750,000

Rochester, BAN 3.10%, Series II, 10/28/1999                      10,000,000      10,001,023

North Carolina--1.0%

Craven County Industrial Facilities and Pollution
  Control Financing Authority, VRDN
  (Craven Wood Energy) 3.50%, Series C
  (LOC; ABN-Amro Bank)(a)                                         6,900,000       6,900,000

Ohio--8.3%

Cincinnati City School District, BAN 4%, 1/16/1999                7,830,000       7,841,071
</TABLE>

                                                                     The Fund  9


<PAGE>

STATEMENT OF INVESTMENTS (Unaudited) (continued)
<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                                  Principal
Tax Exempt Investments (continued)                                Amount ($)      Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                              <C>            <C>
Ohio (continued)

Montgomery County, Revenue, CP (Miami Valley Hospital)
  2.90%, Series B, 7/14/1999
  (Liquidity Facility; Morgan Guaranty Trust Co.)                11,600,000      11,600,000

Ohio Air Quality Development Authority, Revenue, CP
  3.15%, Series B, 7/16/1999
  (Insured and Liquidity Facility; FGIC)                         12,725,000      12,725,000

Ohio Housing Finance Agency, Mortgage Revenue (Residental)
  3.05%, Series A-2, 3/1/2000                                    13,000,000      13,000,000

Summit County, BAN 3.80%, Series A, 6/1/2000                     10,000,000      10,057,800

Pennslyvania--.8%

City of Philadelphia, TRAN 4.25%, Series A, 6/30/1999             5,000,000       5,002,354

South Carolina--.7%

South Carolina Housing Finance and Development Authority,
  Mortgage Revenue
  3.60%, Series A, 7/1/1999
  (Escrowed in; U.S. Treasury Bills)                              4,485,000       4,485,000

Tennessee--2.3%

Sevier County Public Building Authority, VRDN
  (Local Government Public Improvement):
    3.25%, Series III-C-2 (Insured; AMBAC and
      Liquidity Facility; Landesbank-Hessen)(a)                  10,200,000      10,200,000
    3.25%, Series III-C-3 (Insured; AMBAC and
      Liquidity Facility; Landesbank-Hessen)(a)                   4,800,000       4,800,000

Texas--12.7%

Brazos River Authority, PCR, Refunding, VRDN
  (Texas Utilities Electric Co.):
    3.50%, Series C (BPA; The Bank of New York and
      Insured; MBIA)(a)                                           4,245,000       4,245,000
    3.50%, Series C (BPA; The Bank of New York and
      Insured; AMBAC)(a)                                         13,700,000      13,700,000

Brazos River Harbor Naval District, Harbor Revenue, VRDN:
  (BASF Corp.) 3.40% (Corp. Guaranty; BASF Corp.)(a)             16,500,000      16,500,000
  (Dow Chemical Co. Project) 3.50% Series A
    (Corp. Guaranty; Dow Chemical Co.)(a)                        12,800,000      12,800,000

Gulf Coast Industrial Development Authority, VRDN:
  Marine Terminal Revenue (Amoco Oil Co. Project)
    3.45% (Corp. Guaranty; Amoco Credit Corp.)(a)                13,700,000      13,700,000
  Texas Enviornmental Facility (Amoco Oil Co. Project)
    3.45% (Corp. Guaranty; Amoco Credit Corp.)(a)                 6,200,000       6,200,000
</TABLE>

10
<PAGE>

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------
                                                                  Principal
Tax Exempt Investments (continued)                                Amount ($)      Value ($)
- --------------------------------------------------------------------------------------------
<S>                                                              <C>            <C>
Texas (continued)

Panhandle-Plains Higher Education Authority,
  Student Loan Revenue, Refunding, VRDN
  3.25%, Series A (LOC; Student Loan Marketing
  Association)(a)                                                12,700,000      12,700,000

Texas Public Finance Authority, Revenue
  3.15%, Series A, 9/15/1999
  (Liquidity Facility; Toronto-Dominion Bank and
  Union Bank of Switzerland)                                      5,000,000       5,000,000

Utah--1.5%

Intermoutain Power Agency, Power Supply Revenue, CP
  3.20%, 9/16/1999 (Insured; AMBAC, Liquidity
  Facility; Morgan Guranty Trust Co. and
  LOC; Morgan Guaranty Trust Co.)                                10,000,000      10,000,000

Virginia--1.5%

Richmond Industrial Development Authority, Revenue,
  VRDN (Cogentrix of Richmond Project)
  3.75%, Series A (LOC; Banque Paribas)(a)                       10,000,000      10,000,000

West Virginia--1.0%

Marion County, County Community Solid Waste
  Disposal Facility Revenue, VRDN
  (Granttown Project) 3.35%, Series B
  (LOC; National Westmins ter Bank)(a)                            3,700,000       3,700,000

Pendleton County, IDR, VRDN (Greer Steel Project)
  3.40% (LOC; PNC Bank)(a)                                        2,715,000       2,715,000

Wisconson--1.5%

Kenosha Union School District Number 1, TRAN
  3%, Series B, 10 /29/1999                                      10,300,000      10,300,000
- -------------------------------------------------------------------------------------------

Total Investments (cost $666,563,496)                                100.2%     666,563,496

Liabilities, Less Cash and Receivables                                 (.2%)     (1,036,775)

Net Assets                                                           100.0%     665,526,721
</TABLE>

                                                                    The Fund  11


<PAGE>

STATEMENT OF INVESTMENTS (Unaudited) (continued)

<TABLE>
<CAPTION>
- -------------------------------------------------------------------------------------------
Summary of Abbreviations

<S>       <C>                                  <C>      <C>
AMBAC     American Municipal Bond              LOC      Letter of Credit
            Assurance Corporation              LOR      Limited Obligation Revenue
BAN       Bond Anticipation Notes              MBIA     Municipal Bond Investors
BPA       Bond Purchase Agreement                         Assurance Insurance Corporation
CP        Commercial Paper                     PCR      Pollution Control Revenue
EDR       Economic Development Revenue         SWDR     Solid Waste Disposal Revenue
EIR       Environment Improvement Revenue      TAN      Tax Anticipation Notes
FGIC      Financial Guaranty Insurance Company          TRAN Tax and Revenue Anticipation
HR        Hospital Revenue                                Notes
IDB       Industrial Development Board         VRDN     Variable Rate Demand Notes
IDR       Industrial Development Revenue
</TABLE>


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

Fitch             or      Moody's     or  Standard & Poor's           Value (%)
- -------------------------------------------------------------------------------
F1+/F1                    VMIG1/MIG1, P1  SP1+/SP1, A1+/A1                 93.6
AAA/AA(b)                 Aaa/Aa, A1(b)   AAA/AA(b)                         1.2
Not Rated(c)              Not Rated(c)    Not Rated(c)                      5.2
                                                                          100.0
[FN]
a Securities payable on demand. Variable interest rate--subject to periodic
  change.
b Notes which are not F, MIG or SP rated are represented by bond ratings of the
  issuers.
c Securities which, while not rated by Fitch, Moody's and Standard & Poor's have
  been determined by the Manager to be of comparable quality to those rated
  securities in which the fund may invest.

See notes to financial statements.
(/FN)

12


<PAGE>

STATEMENT OF ASSETS AND LIABILITIES
May 31, 1999 (Unaudited)

<TABLE>
<CAPTION>
- ------------------------------------------------------------------------------------------------
                                                                            Cost          Value
- ------------------------------------------------------------------------------------------------
<S>                                                                  <C>            <C>
Assets ($):
Investments in securities--See Statement of Investments              666,563,496    666,563,496
Cash                                                                                  4,389,410
Interest receivable                                                                   5,032,658
Prepaid expenses                                                                         58,094
                                                                                    676,043,658
- ------------------------------------------------------------------------------------------------
Liabilities ($):
Due to The Dreyfus Corporation and affiliates                                           275,031
Due to Distributor                                                                      124,867
Payable for investment securities purchased                                          10,057,800
Accrued expenses and other liabilities                                                   59,239
                                                                                     10,516,937
- ------------------------------------------------------------------------------------------------
Net Assets ($)                                                                      665,526,721
- ------------------------------------------------------------------------------------------------
Composition of Net Assets ($):
Paid-in capital                                                                     665,539,077
Accumulated net realized gain (loss) on investments                                     (12,356)
- ------------------------------------------------------------------------------------------------
Net Assets ($)                                                                      665,526,721


<CAPTION>
- ------------------------------------------------------------------------------------------------
Net Asset Value Per Share
                                                                         Class A        Class B
- ------------------------------------------------------------------------------------------------
<S>                                                                  <C>            <C>
Net Assets ($)                                                       264,370,301    401,156,420
Shares Outstanding                                                   264,662,105    401,158,246
- ------------------------------------------------------------------------------------------------
Net Asset Value Per Share ($)                                               1.00           1.00
</TABLE>


See notes to financial statements.

                                                                    The Fund  13

<PAGE>

STATEMENT OF OPERATIONS
Six Months Ended May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------
Investment Income ($)

- --------------------------------------------------------------------------------
Interest Income                                                      10,355,577
Expenses:
Management fee--Note 2(a)                                             1,617,141
Shareholder servicing costs--Note 2(c)                                  653,274
Distribution fees (Class B)--Note 2(b)                                  382,040
Professional fees                                                        36,400
Custodian fees                                                           34,517
Registration fees                                                        34,100
Directors' fees and expenses--Note 2(d)                                  19,032
Prospectus and shareholders' reports                                      8,783
Miscellaneous                                                             8,647
Total Expenses                                                        2,793,934
Less--reduction in shareholder servicing costs due to
  undertaking--Note 2(c)                                               (141,756)
Net Expenses                                                          2,652,178
Investment Income--Net                                                7,703,399
Net Realized Gain (Loss) on Investments--Note 1(b)($)                     7,566
Net Increase in Net Assets Resulting from Operations                  7,710,965


See notes to financial statements.

14


<PAGE>

STATEMENT OF CHANGES IN NET ASSETS

<TABLE>
<CAPTION>
- ------------------------------------------------------------------------------------------------
                                                             Six Months Ended
                                                                 May 31, 1999        Year Ended
                                                                  (Unaudited) November 30, 1998
- ------------------------------------------------------------------------------------------------
<S>                                                               <C>              <C>
Operations ($):
Investment income--net                                              7,703,399        16,844,414
Net realized gain (loss) on investments                                 7,566           (17,137)
Net Increase (Decrease) in Net Assets
  Resulting from Operations                                         7,710,965        16,827,277
- ------------------------------------------------------------------------------------------------
Dividends to Shareholders from ($):
Investment income--net:
Class A shares                                                     (3,459,196)       (8,462,642)
Class B shares                                                     (4,244,203)       (8,381,772)
Net realized gain on investments:
Class A shares                                                             --            (5,225)
Class B shares                                                             --            (5,196)
Total Dividends                                                    (7,703,399)      (16,854,835)
- ------------------------------------------------------------------------------------------------
Capital Stock Transactions ($1.00 per share):
Net proceeds from shares sold:
Class A shares                                                    609,161,527     1,327,446,611
Class B shares                                                    879,344,414     1,660,435,145
Dividends reinvested:
Class A shares                                                      3,340,077         8,202,286
Class B shares                                                      4,161,202         8,193,899
Cost of shares redeemed:
Class A shares                                                   (628,531,772)   (1,328,295,655)
Class B shares                                                   (859,990,276)   (1,553,986,658)
Increase (Decrease) in Net Assets from
  Capital Stock Transactions                                        7,485,172       121,995,628
Total Increase (Decrease) in Net Assets                             7,492,738       121,968,070
- ------------------------------------------------------------------------------------------------
Net Assets ($):
Beginning of Period                                               658,033,983       536,065,913
End of Period                                                     665,526,721       658,033,983
</TABLE>


See notes to financial statements.

                                                                    The Fund  15

<PAGE>

FINANCIAL HIGHLIGHTS

The following tables describe the performance for each share class for the
fiscal periods indicated. Certain 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              Year Ended November 30,
                                May 31, 1999   -------------------------------------------
Class A Shares                    (Unaudited)    1998     1997     1996     1995     1994
- ------------------------------------------------------------------------------------------
<S>                                  <C>      <C>      <C>      <C>      <C>      <C>
Per Share Data ($):
Net asset value,
  beginning of period                   1.00     1.00     1.00     1.00     1.00     1.00
Investment Operations:
Investment income--net                  .013     .030     .031     .029     .034     .023
Distributions:
Dividends from investment
  income--net                          (.013)   (.030)   (.031)   (.029)   (.034)   (.023)
Net asset value, end of period          1.00     1.00     1.00     1.00     1.00     1.00
- ------------------------------------------------------------------------------------------
Total Return (%)                        2.63*    3.02     3.14     2.97     3.41     2.27
- ------------------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average
  net assets                             .59*     .60      .62      .66      .66      .64
Ratio of net investment income
  to average net assets                 2.61*    2.98     3.09     2.93     3.35     2.22
- ------------------------------------------------------------------------------------------
Net Assets, end of period
  ($ x 1,000)                        264,370  280,398  273,058  256,862  294,379  294,711

<FN>
* Annualized.
</FN>
</TABLE>

See notes to financial statements.


<PAGE>
<TABLE>
<CAPTION>
- ---------------------------------------------------------------------------------------
                                     Six Months Ended        Year Ended November 30,
                                         May 31, 1999   -------------------------------
Class B Shares                             (Unaudited)    1998    1997    1996    1995*
- ---------------------------------------------------------------------------------------
<S>                                           <C>      <C>     <C>      <C>      <C>
Per Share Data ($):
Net asset value, beginning of period             1.00     1.00    1.00    1.00    1.00
Investment Operations:
Investment income--net                           .011     .026    .028    .027    .020
Distributions:
Dividends from investment income--net           (.011)   (.026)  (.028)  (.027)  (.020)
Net asset value, end of period                   1.00     1.00    1.00    1.00    1.00
- ---------------------------------------------------------------------------------------
Total Return (%)                                 2.23(b)  2.64    2.86    2.70    3.01(b)
- ---------------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average net assets           .98(b)   .96     .95     .85    1.10(b)
Ratio of net investment income
  to average net assets                          2.22(b)  2.59    2.87    2.65    2.83(b)
Decrease reflected in above expense ratios
  due to undertakings by the Manager              .07(b)   .09     .16     .29     .09(b)
- ---------------------------------------------------------------------------------------
Net Assets, end of period
  ($ x 1,000)                                 401,156  377,636 263,008  17,491   3,024
<FN>
a From March 31, 1995 (commencement of initial offering) to November 30, 1995.
b Annualized.

</TABLE>

See notes to financial statements.
</FN>
                                                                  The Fund  17



<PAGE>

NOTES TO FINANCIAL STATEMENTS (Unaudited)

NOTE 1--Significant Accounting Policies:

General Municipal Money Market Fund (the "fund") is a separate diversified
series of General Municipal Money Market 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.

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

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

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

18


<PAGE>

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 $23,241 during the period ended May 31, 1999
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 carry overs, if 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.

                                                                  The Fund  19


<PAGE>

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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

At May 31, 1999, the cost of investments for Federal income tax purposes was
substantially the same as the cost for financial reporting purposes (see the
Statement of Investments).

NOTE 2--Management Fee and Other Transactions
With Affiliates:

(a) Pursuant to a management agreement ("Agreement") with the Manager, the
management fee is computed at the annual rate of .50 of 1% of the value of the
fund's average daily net assets and is payable monthly. The Agreement provides
that if in any full fiscal year the aggregate expenses of the fund, exclusive of
taxes, brokerage, interest on borrowings and extraordinary expenses, exceed
1-1/2% of the average value of the fund's net assets, the fund may deduct from
payments to be made to the Manager, or the Manager will bear such excess
expense. During the period ended May 31, 1999, there was no expense
reimbursement pursuant to the Agreement.

(b) Under the Distribution Plan with respect to Class B ("Class B Distribution
Plan"), adopted pursuant to Rule 12b-1 under the Act, Class B shares directly
bear the costs of preparing, printing and distributing prospectuses and
statements of additional information and of implementing and operating the Class
B Distribution Plan. In addition, Class B shares reimburse the Distributor for
payments made to third parties for distributing their shares at an annual rate
of .20 of 1% of the value of the average daily net assets of Class B. During the
period ended May 31, 1999, Class B shares were charged $382,040 pursuant to the
Class B Distribution Plan.

20



<PAGE>

(c) Under the Shareholder Services Plan with respect to Class A ("Class A
Shareholder Services Plan"), Class A shares reimburse Dreyfus Service
Corporation, a wholly-owned subsidiary of the Manager, an amount not to exceed
an annual rate of .25 of 1% of the value of the average daily net assets of
Class A for certain allocated expenses of providing personal services and/or
maintaining shareholder accounts. The services provided may include personal
services relating to shareholder accounts, such as answering shareholder
inquiries regarding Class A shares and providing reports and other information,
and services related to the maintenance of shareholder accounts. During the
period ended May 31, 1999, Class A shares were charged $39,042 pursuant to the
Class A Shareholder Services Plan.

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

The Manager had undertaken from December 1, 1998 through May 31, 1999, that if
the aggregate expenses of Class B shares, exclusive of taxes, brokerage,
interest on borrowings and extraordinary expenses, exceeded .98 of 1% of the
average daily net assets of Class B, the Manager will reimburse the expenses of
the fund under the Class B Shareholder Services Plan to the extent of any excess
expense and up to the full fee payable under such Plan. During the period ended
May 31, 1999, Class B shares were charged $573,061 of which $141,756 was
reimbursed by the Manager.

                                                                    The Fund  21


<PAGE>

NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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, 1999, the fund was charged $18,557 pursuant to the transfer agency
agreement.

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

22

<PAGE>


<PAGE>

NOTES


<PAGE>

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
90 Washington Street
New York, NY 10286

Transfer Agent &
Dividend Disbursing Agent

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

Distributor

Premier Mutual Fund Services, Inc.
60 State Street
Boston, MA 02109



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) 1999, Dreyfus Service Corporation     918/697SA995

General Minnesota
Municipal Money
Market Fund

SEMIANNUAL REPORT
May 31, 1999

<PAGE>

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

Year 2000 Issues (Unaudited)

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

<PAGE>

                                   Contents

                                   THE FUND

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

                              2     Letter from the President

                              3     Discussion of Fund Performance

                              6     Statement of Investments

                              9     Statement of Assets and Liabilities

                             10     Statement of Operations

                             11     Statement of Changes in Net Assets

                             12     Financial Highlights

                             14     Notes to Financial Statements

                                    FOR MORE INFORMATION

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

                                    Back Cover

<PAGE>

          General Minnesota
Municipal Money Market Fund     The 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, 1998 through
May 31, 1999. 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, Karen Hand.

Yields on both taxable and tax-exempt money market securities generally declined
early in the reporting period in the wake of the Federal Reserve Board's
decision in the fall of 1998 to ease monetary policy. While the U.S. economy has
continued to grow, the Federal Reserve was concerned about persistent economic
weakness abroad. Their adoption of lower short-term interest rates was intended
to stimulate not just domestic economic growth, but the economies of other
nations as well.

Despite lower nominal interest rates for tax-exempt money market instruments,
very low inflation continued to support attractive real returns, which are
nominal yields less the rate of inflation.

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 14, 1999

2

<PAGE>
DISCUSSION OF FUND PERFORMANCE

Karen Hand, Portfolio Manager

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

For the six-month period ended May 31, 1999, General Minnesota Municipal Money
Market Fund produced an annualized, tax-exempt yield of 2.56% for Class A shares
and 2.41% for Class B shares. After taking into account the effect of
compounding, the fund's Class A shares provided an annualized effective yield of
2.59% while the fund's Class B shares produced an annualized effective yield of
2.44%.(1)

For the six-month period ended May 31, 1999, the fund's Class A shares and Class
B shares provided total returns of 1.28% and 1.21%,(2) respectively, compared to
the Lipper Other States Tax-Exempt Money Market Funds category average total
return of 1.30% for the same time period.(3)

What is the fund's investment approach?

Our goal is to seek a high level of federal and Minnesota tax-exempt income
while maintaining a stable $1.00 share price. We also seek to provide a
competitive total return, and we attempt to be especially vigilant in our
efforts to preserve capital.

To achieve these objectives, 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 interest rate trends and
supply-and-demand changes in Minnesota's short-term municipal marketplace.

For example, if we expect supply to increase temporarily when many
municipalities issue short-term debt at once -- as they tend to in July, for
example -- we may reduce the portfolio's average maturity to make

                                                                      The Fund 3

<PAGE>
DISCUSSION OF FUND PERFORMANCE (continued)

cash available for the purchase of higher-yielding securities. That's because
yields tend to rise if many issuers are competing for investor interest. If we
expect demand to surge at a time when we anticipate little issuance and,
therefore, lower yields -- as often happens in January -- we may increase the
portfolio's average maturity prior to that time to maintain current yields for
as long as possible. Overall, we try to maintain an average maturity that
reflects our view of short-term interest rate trends, note issuance and
anticipated cash flows.

What other factors influenced the fund's performance?

Although the fund, by definition, contains primarily securities from Minnesota
issuers, the entire U.S. fixed-income marketplace was influenced just prior to
the reporting period by economic events overseas. When the Asian currency and
credit crisis threatened Latin America last summer and fall, the Federal Reserve
Board and other central banks reduced key short-term interest rates. This move
was intended to help boost economic activity by making borrowing less expensive
for corporations. An additional consequence was lower yields on money market
securities.

Despite economic weakness in some overseas markets, the U.S. and Minnesota
economies remained strong. Because municipalities have enjoyed higher tax
revenues during this period of economic prosperity, many have had less need to
borrow. As a result, fewer tax-exempt money market securities were issued in
Minnesota than in the same six-month period one year ago. Yet, demand from
investors seeking to minimize their income tax liabilities remained high. This
imbalance helped push short-term tax-exempt yields down further during the
final months of 1998. Tax-exempt yields have remained relatively stable so far
in 1999.

4

<PAGE>
What is the fund's current strategy?

We have continued to focus on high-quality money market instruments from a wide
array of tax-exempt issuers. Some of the most frequently used instruments
include Variable Rate Demand Notes (VRDNs), which are issued by investment banks
through the securitization of longer-term municipal bonds. With a put feature of
either one or seven days attached to each VRDN, we believe that VRDNs afford a
high degree of liquidity as well as high quality to the Portfolio. Accordingly,
as of May 31, 1999, approximately 60% of the portfolio was composed of VRDNs.
The remaining 40% was comprised of municipal notes as well as smaller, non-rated
short-term debt issues from Minnesota school districts, housing projects and the
state's general obligation securities that have been deemed equivalent to the
highest credit agency ratings by Dreyfus credit analysts.

June 14, 1999

[FN]
1 Annualized effective yield is based upon dividends declared daily and
  reinvested monthly. Past performance is no guarantee of future results.
  Yields fluctuate. An investment in the fund is not insured or guaranteed by
  the FDIC or any other government agency. 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.
2 Total return includes reinvestment of dividends. Return figures provided
  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 returns would have been
  lower. Income may be subject to state and local income taxes for non-Minnesota
  residents, and some income may be subject to the Federal Alternative Minimum
  Tax (AMT) for certain shareholders.
3 Source: Lipper Analytical Services, Inc.
</FN>

                                                                      The Fund 5

<PAGE>
<TABLE>
STATEMENT OF INVESTMENTS
May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------
                                                          Principal
Tax Exempt Investments--100.3%                           Amount ($)   Value ($)
- --------------------------------------------------------------------------------
<S>                                                         <C>         <C>

Ankoa County, G.O. Notes 3.60%, Series C, 5/1/2000          340,000     340,000
Becker, PCR, Refunding, CP (Northern State Power Co.)
  2.90%, Series B, 7/16/99 (Corp. Guaranty;
  Northern State Power Co.)                               2,000,000   2,000,000
Beltrami County, Environmental Control Revenue,
  VRDN (Northwood Panelboard Co. Project)
  3.35% (LOC; Union Bank of Switzerland)(a)               1,000,000   1,000,000
Bemidji Independent School District Number 31,
  Refunding 4.50%, 2/1/2000                                 200,000     201,828
Cloquet, Industrial Facilities Revenue, VRDN
  (Potlatch Corp. Project) 3.50%, Series C
  (LOC; Credit Suisse)(a)                                 3,000,000   3,000,000
Coon Rapids, G.O. Notes 3.10%, Series A, 2/1/2000           195,000     194,868
Cottage Grove, Environmental Control Revenue, VRDN
  (Minnesota Mining and Manufacturing)
  3.726% (Corp. Guaranty; Minnesota Mining and
  Manufacturing)(a)                                         500,000     500,000
Dakota County Housing and Redevelopment Authority, MFMR,
  Refunding, VRDN (Southview Gables Apartment Project)
  3.30% (Corp. Guaranty; Northwestern Mutual Life)(a)     1,500,000   1,500,000
Duluth, Tax Increment:
  G.O. Notes, 3.30%, Series B, 2/1/2000                     200,000     200,000
  Revenue, VRDN (Lake Superior Paper)
    3.20% (LOC; Wachovia Bank of Georgia)(a)              1,500,000   1,500,000
Eden Prairie, Commercial Development Revenue, Refunding,
  VRDN (Lakeview Business Center)
  3.45% (LOC; Firstar Bank of Milwaukee)(a)               1,400,000   1,400,000
Edina Independent School District Number 273, G.O. Notes
  4%, Series B, 2/1/2000                                  1,000,000   1,006,542
Golden Valley, IDR, VRDN (Unicare Homes Project)
  3.55% (LOC; Banque Paribas)(a)                          1,000,000   1,000,000
Hennepin County, G.O. Notes 4%, Series B, 12/1/1999         600,000     602,939
Metropolitan Council, Minneapolis-St. Paul Metropolitan
  Area, G.O. Notes, Refunding
  4.40%, 12/1/1999                                          400,000     402,631
Minneapolis, G.O. Notes, Refunding  4.50%, 3/1/2000       1,100,000   1,112,117
Minneapolis Community Development Agency, PCR, VRDN
  (Northern State Power Co. Project)
  3.35% (Corp. Guaranty; Northern State Power Corp.)(a)   1,000,000   1,000,000
Minnesota School District Tax and Aid Anticipation
  Borrowing Program, COP 3.625%, Series B, 8/27/1999        500,000     500,000
Minnesota Higher Education Coordinating Board,
  Student Loan Program, Revenue, VRDN
  3.40%, Series B  (LOC; Norwest Bank of Minnesota)(a)    3,000,000   3,000,000

6

<PAGE>

- --------------------------------------------------------------------------------
                                                          Principal
Tax Exempt Investments (continued)                       Amount ($)   Value ($)
- --------------------------------------------------------------------------------
Minnesota Housing Finance Agency, Single Family Mortgage
  3.70% Series H, 8/9/1999                                  500,000     500,000
New Hope Utility, G.O. Notes, 3.25%, Series A, 2/1/2000     200,000     200,000
Prior Lake Independent School District Number 719
  3.10%, 3/24/2000                                          400,000     400,150
Roseville Tax Increment, G.O. Notes 4%, 3/1/2000          1,000,000   1,006,720
St. Paul Housing and Redevelopment Authority, Revenue,
  VRDN (District Cooling) 3.45%, Series L
  (LOC; Credit Locale de France)(a)                       1,000,000   1,000,000
St. Paul Independent School District Number 625,
  G.O. Notes
  4.25%, Series B, 2/1/2000                                 700,000     704,307
St. Paul Port Authority, IDR, VRDN (Ideal Printers Inc.)
  3.45%, Series A (Corp. Guaranty; Marshall and Isley
  Corp.)(a)                                               1,140,000   1,140,000
St. Paul Special Assessment, G.O. Notes 4%, Series C,
  4/1/2000                                                  560,000     563,638
Wadena, IDR, VRDN (Homecrest Industry Inc. Project)
  3.50% (LOC; U.S. Bank of Minneapolis)(a)                3,000,000   3,000,000
State of Minnesota:
  5%, Series A, 6/30/1999 (Insured; AMBAC)                  500,000     500,773
  G.O. Notes:
    5%, 8/1/1999                                            750,000     752,421
    6.60%, 8/1/1999                                         200,000     201,193
  Prerefunded 6.60%, 8/1/1999                             1,000,000   1,004,861
- --------------------------------------------------------------------------------
Total Investments (cost $31,434,963)                         100.3%  31,434,988

Liabilities, Less Cash and Receivables                         (.3%)    (78,721)

Net Assets                                                   100.0%  31,356,267

                                                                      The Fund 7

</TABLE>
<PAGE>
STATEMENT OF INVESTMENTS (continued)
- --------------------------------------------------------------------------------
Summary of Abbreviations

AMBAC   American Municipal Bond          LOC          Letter of Credit
          Assurance Corporation          MFMR         Multi-Family Mortgage
CP      Commerical Paper                                Revenue
COP     Certificate of Participation     PCR          Pollution Control Revenue
GO      General Obligation               VRDN         Variable Rate Demand Notes
IDR     Industrial Development Revenue
- --------------------------------------------------------------------------------


- --------------------------------------------------------------------------------
Summary of Combined Ratings

Fitch             or      Moody's        or    Standard & Poor's     Value (%)
- --------------------------------------------------------------------------------
F1+/F1                    VMIG1/MIG1, P1       SP1+/SP1,A1+/A1            67.1
AAA/AA(b)                 Aaa/Aa(b)            AAA/AA(b)                  21.8
Not Rated(c)              Not Rated(c)         Not Rated(c)               11.1
                                                                         100.0

[FN]
a Securities payable on demand. Variable interest rate--subject to periodic
  change.
b Notes which are not F, MIG or SP rated are represented by bond ratings of
  the issuers.
c Securities which, while not rated by Fitch, Moody's and Standard & Poor's
  have been determined by the Manager to be of comparable quality to those
  rated securities in which the fund may invest.

See notes to financial statements.
</FN>

8

<PAGE>

STATEMENT OF ASSETS AND LIABILITIES
May 31, 1999 (Unaudited)

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

                                                             Cost         Value
- --------------------------------------------------------------------------------
Assets ($):
Investments in securities--See Statement of
  Investments                                          31,434,963    31,434,988
Cash                                                                     26,024
Interest receivable                                                     237,620
Prepaid expenses                                                         30,993
                                                                     31,729,625
- --------------------------------------------------------------------------------
Liabilities ($):
Due to The Dreyfus Corporation and affiliates                            13,194
Payable for investment securities purchased                             340,510
Accrued expenses                                                         19,654
                                                                        373,358
- --------------------------------------------------------------------------------
Net Assets ($)                                                       31,356,267
- --------------------------------------------------------------------------------
Composition of Net Assets ($):
Paid-in capital                                                      31,356,242
Accumulated net unrealized appreciation (depreciation)
  on investments                                                             25
- --------------------------------------------------------------------------------
Net Assets ($)                                                       31,356,241


- --------------------------------------------------------------------------------
Net Asset Value Per Share
                                                         Class A        Class B
- --------------------------------------------------------------------------------
Net Assets ($)                                           104,895     31,251,372
Shares Outstanding                                       104,895     31,251,347
- --------------------------------------------------------------------------------
Net Asset Value Per Share ($)                               1.00           1.00

See notes to financial statements.

                                                                      The Fund 9

<PAGE>

STATEMENT OF OPERATIONS
Six Months Ended May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------
Investment Income ($)
- --------------------------------------------------------------------------------
Income:
Interest Income                                                       521,458
Expenses:
Management fee--Note 2(a)                                              81,551
Shareholder servicing costs--Note 2(c)                                 48,529
Distribution fees (Class B)--Note 2(b)                                 32,304
Registration fees                                                      26,926
Professional fees                                                      10,238
Prospectus and shareholders' reports                                    6,565
Custodian fees                                                          1,690
Directors' fees and expenses-Note 2(d)                                    872
Miscellaneous                                                           2,181
Total Expenses                                                        210,856
Less--reduction in management fee and shareholder servicing
  costs due to undertakings--Note 2(a,c)                              (80,481)
Net Expenses                                                          130,375
Investment Income--Net                                                391,083
- --------------------------------------------------------------------------------
Net Unrealized Gain (Loss) on Investments                                 (25)
Net Increase in Net Assets Resulting from Operations                  391,108

See notes to financial statements.

10

<PAGE>
STATEMENT OF CHANGES IN NET ASSETS

- --------------------------------------------------------------------------------
                                           Six Months Ended
                                               May 31, 1999          Year Ended
                                                 (Unaudited)  November 30, 1998*
- --------------------------------------------------------------------------------
Operations ($):
Investment income--net                              391,083             347,474
Net unrealized appreciation (depreciation)
  on investments                                         25                  --
Net Increase (Decrease) in Net Assets
  Resulting from Operations                         391,108             347,474
- --------------------------------------------------------------------------------
Dividends to Shareholders from ($):
Investment income--net:
Class A shares                                       (4,301)            (14,199)
Class B shares                                     (386,782)           (333,275)
Total Dividends                                    (391,083)          ( 347,474)
- --------------------------------------------------------------------------------
Capital Stock Transactions ($1.00 per share):
Net proceeds from shares sold:
Class A shares                                        3,000           1,000,000
Class B shares                                   38,595,163          44,810,839
Dividends reinvested:
Class A shares                                        4,289              14,128
Class B shares                                      378,379             326,009
Cost of Shares redeemed:
Class A shares                                     (916,522)                 --
Class B shares                                  (35,881,890)        (16,977,153)
Increase (Decrease) in Net Assets from
  Capital Stock Transactions                      2,182,419          29,173,823
Total Increase (Decrease) in Net Assets           2,182,444          29,173,823
- --------------------------------------------------------------------------------
Net Assets ($):
Beginning of Period                              29,173,823                  --
End of Period                                    31,356,267          29,173,823

* From June 1, 1998 (commencement of operations) to November 30, 1998.
See notes to financial statements.

                                                                     The Fund 11

<PAGE>

FINANCIAL HIGHLIGHTS

The following tables describe the performance for each share class for the
fiscal periods indicated. Certain 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.

- --------------------------------------------------------------------------------
                                        Six Months Ended
                                            May 31, 1999            Year Ended
Class A Shares                               (Unaudited)   November 30, 1998(a)
- --------------------------------------------------------------------------------
Per Share Data ($):
Net asset value, beginning of period                 1.00                  1.00
Investment Operations:
Investment income-net                                .013                  .014
Distributions:
Dividends from investment income-net                (.013)                (.014)
Net asset value, end of period                       1.00                  1.00
- --------------------------------------------------------------------------------
Total Return (%)b                                    2.57                  2.81
- --------------------------------------------------------------------------------
Ratios/Supplemental Data ($):
Ratio of expenses to average net assets(b)            .65                   .65
Ratio of net investment income
  to average net assets(b)                           2.73                  2.80
Decrease reflected in above expense ratios
  due to undertakings by the Manager(b)               .16                   .76
- --------------------------------------------------------------------------------
Net Assets, end of period ($ X 1,000)                 105                 1,014

[FN]
a From June 1, 1998 (commencement of operations) to November 30, 1998.
b Annualized.
See notes to financial statements.
</FN>

12

<PAGE>

- --------------------------------------------------------------------------------
                                         Six Months Ended
                                             May 31, 1999            Year Ended
Class B Shares                                 (Unaudited)  November 30, 1998(a)
- --------------------------------------------------------------------------------
Per Share Data ($):
Net asset value, beginning of period                 1.00                  1.00
Investment Operations:
Investment income-net                                .012                  .013
Distributions:
Dividends from investment income-net                (.012)                (.013)
Net asset value, end of period                       1.00                  1.00
- --------------------------------------------------------------------------------
Total Return (%)b                                    2.43                  2.67
- --------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average net assets(b)            .80                   .80
Ratio of net investment income
  to average net assetsb                             2.39                  2.63
Decrease reflected in above expense ratios
  due to undertakings by the Manager(b)               .50                   .87
- --------------------------------------------------------------------------------
Net Assets, end of period ($ X 1,000)              31,251                28,160

[FN]
a From June 1, 1998 (commencement of operations) to November 30, 1998.
b Annualized.
See notes to financial statements.
</FN>
                                                                     The Fund 13

<PAGE>
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.

At May 31, 1999, MBC Investments Corp., an indirect subsidiary of Mellon Bank
Corporation, held 101,858 Class A shares.

Premier Mutual Fund Services, Inc. (the "Distributor") is the distributor of the
fund's shares, which are sold to the public without a sales load. The fund is
authorized to issue 4 billion shares of $.01 par value Common Stock. The fund is
currently authorized to issue two classes of shares: Class A (2 billion shares
authorized) and Class B (2 billion shares authorized). Class A shares and Class
B shares are identical except for the services offered to and the expenses borne
by each class and certain voting rights. Class B shares are subject to a
Distribution Plan adopted pursuant to Rule 12b-1 under the Act and, in addition,
Class B shares are charged directly for sub-accounting services provided by
Service Agents (a securities dealer, financial institution or other industry
professional) at an annual rate of .05% of the value of the average daily net
assets of Class B shares.

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

It is the fund's policy to maintain a continuous net asset value per share of
$1.00; the fund has adopted certain investment, portfolio valuation

14

<PAGE>
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 $2,366 during the period ended May 31, 1999
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, if any, are normally declared and paid annually,
but the fund may make distributions on a more frequent basis to comply with the
distribution requirements of the Internal Revenue Code of 1986, as amended (the
"Code"). To the extent that net realized capital gain can be offset by capital
loss carryovers, if any, it is the policy of the fund not to distribute such
gain.

                                                                     The Fund 15

<PAGE>
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

(d) Federal income taxes: It is the policy of the fund to continue to qualify as
a regulated investment company, which can distribute tax exempt dividends, by
complying with the applicable provisions of the Code, and to make distributions
of income and net realized capital gain sufficient to relieve it from
substantially all Federal income and excise taxes.

At May 31, 1999, the cost of investments for Federal income tax purposes was
substantially the same as the cost for financial reporting purposes (see the
Statement of Investments).

NOTE 2--Management Fee and Other Transactions
With Affiliates:

(a) Pursuant to a management agreement ("Agreement") with the Manager, the
management fee is computed at the annual rate of .50 of 1% of the value of the
fund's average daily net assets and is payable monthly. The Agreement provides
that if in any full fiscal year the aggregate expenses of the fund, exclusive of
taxes, brokerage, interest on borrowings and extraordinary expenses, exceed
1-1/2% of the average value of the fund's net assets, the fund may deduct from
payments to be made to the Manager, or the Manager will bear such excess
expense. The Manager had undertaken through May 31, 1999 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) exceed an annual
rate of .65 of 1% of the value of the fund's average daily net assets. The
expense reimbursement pursuant to the undertaking amounted to $32,022 during the
period ended May 31, 1999.

(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%

16

<PAGE>
of the value of the average daily net assets of Class B. During the period
ended May 31, 1999, Class B shares were charged $32,304 pursuant to the
Distribution Plan.

(c) Under the Shareholder Services Plan with respect to Class A ("Class A
Shareholder Services Plan"), Class A shares reimburse Dreyfus Service
Corporation, a wholly-owned subsidiary of the Manager, an amount not to exceed
an annual rate of .25 of 1% of the value of the average daily net assets of
Class A for certain allocated expenses of providing personal services and/or
maintaining shareholder accounts. The services provided may include personal
services relating to shareholder accounts, such as answering shareholder
inquiries regarding Class A shares and providing reports and other information,
and services related to the maintenance of shareholder accounts.

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

The Manager had undertaken through May 31, 1999, that if the aggregate expenses
of Class B shares, exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses, exceed .80 of 1% of the average daily net assets of
Class B, the Manager will reimburse the expenses of the fund under the Class B
Shareholder Services Plan to the extent of any excess expense and up to the full
fee payable under such Plan. During the period ended May 31, 1999, Class B
shares were charged $48,459 all of which was reimbursed by the Manager.

                                                                     The Fund 17

<PAGE>
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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, 1999, the fund was charged $37 pursuant to the transfer agency
agreement.

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

18

<PAGE>
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
                     90 Washington Street
                     New York, NY 10286

                     Transfer Agent &
                     Dividend Disbursing Agent

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

                     Distributor

                     Premier Mutual Fund Services, Inc.
                     60 State Street
                     Boston, MA 02109


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) 1999 Dreyfus Service Corporation  917/706SA995




















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