DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 2000-08-07
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General New York
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

                            11   Statement of Assets and Liabilities

                            12   Statement of Operations

                            13   Statement of Changes in Net Assets

                            14   Financial Highlights

                            16   Notes to Financial Statements

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

                                 Back Cover

                                                                       The Fund

                                                               General New York

                                                    Municipal Money Market Fund

LETTER FROM THE PRESIDENT

Dear Shareholder:

We  are pleased to present this semiannual report for General New York 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, Scott Sprauer.

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 New York Municipal Money Market Fund.

Sincerely,


/s/Stephen E. Canter
Stephen E. Canter
President and Chief Investment Officer
The Dreyfus Corporation
June    15,    2000




DISCUSSION OF FUND PERFORMANCE

Scott Sprauer, Portfolio Manager

How did General New York 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  3.10%, and Class B shares provided a 2.81% annualized
yield.  Taking into account the effects of compounding, the fund's Class A and B
shares  provided  annualized  effective yields of 3.14% and 2.84%, respectively,
during    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, New York state
and  New  York City personal income taxes as 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  New  York issuers. 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.

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 matu-

                                                                      The Fund 3


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

rity  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,  rising  interest rates and a declining supply of newly issued
securities.

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  has  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 New York
and  its municipalities enjoyed higher tax revenues during the reporting period.
This  reduced  their  need  to  borrow  and  resulted  in  a  reduced  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 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.

4

In  the  face  of these uncertainties, we have recently adjusted the portfolio's
average  weighted  maturity  so that it is longer than other New York tax-exempt
money  market  funds.  This maturity management strategy was designed to help us
lock  in  then  current  yields.  In  addition, we have used municipal notes and
commercial  paper  opportunistically  to capture higher yielding securities that
may   be   the   result   of   temporary   imbalances  in  supply  and  demand.

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 commercial paper to lock
in  higher  yields as they became available. Of course, portfolio composition is
subject to change over 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-NEW YORK
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 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. YIELDS PROVIDED FOR THE FUND'S 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 THE EXPENSES NOT BEEN ABSORBED, THE FUND'S CLASS B
YIELDS WOULD HAVE BEEN LOWER. WITHOUT THE FUND'S EXPENSE ABSORPTION, THE FUND'S
CLASS B SHARES WOULD HAVE PRODUCED AN ANNUALIZED NET YIELD OF 2.71% AND AN
ANNUALIZED EFFECTIVE NET YIELD OF 2.75%.

                                                             The Fund 5

STATEMENT OF INVESTMENTS

May 31, 2000 (Unaudited)
<TABLE>

STATEMENT OF INVESTMENTS

                                                                                              Principal
TAX EXEMPT INVESTMENTS--99.1%                                                                Amount ($)                Value ($)
------------------------------------------------------------------------------------------------------------------------------------
<S>                                                                                           <C>                       <C>

Beacon City School District, RAN 4.75%, 10/27/2000                                            4,000,000                4,006,326

Connetquot Central School District, TAN 3.80%, 6/29/2000                                      9,000,000                9,002,993

Erie County Water Authority, Water Revenue, VRDN

  3.75%, Series A (Insured; AMBAC and Liquidity Facility;

   National Bank of Australia)                                                                9,000,000  (a)           9,000,000

Town of Islip Industrial Development Agency, IDR, VRDN

   (Brentwood Distribution Co.) 4.35% (LOC; Fleet National Bank)                              1,000,000  (a)           1,000,000

Jefferson County, BAN 4.75%, 4/27/2001                                                        4,500,000                4,515,949

Long Island Power Authority, Electric Systems Revenue:

  CP:

    4.30%, Sub-Series 3, 8/22/2000

         (LOC: Bayerische Landesbank and Westdeutsche

         Landesbank)                                                                         10,950,000               10,950,000

      4.75%, Series 3, 9/11/2000

         (LOC: Bayerische Landesbank and Westdeutsche

         Landesbank)                                                                         16,500,000               16,500,000

      4.75%, Sub-Series 3, 9/20/2000

         (LOC: Bayerische Landesbank and Westdeutsche

         Landesbank)                                                                         10,000,000               10,000,000

      4.30%, Series 4, Sub-Series 4, 10/11/2000

         (LOC: Bayerische Landesbank and Westdeutsche

         Landesbank)                                                                          3,600,000                3,600,000

      4.50%, Series 4, Sub-Series 4, 10/11/2000

         (LOC: Bayerische Landesbank and Westdeutsche

         Landesbank)                                                                         10,000,000               10,000,000

      4.60%, Sub-Series 4, 10/12/2000

         (LOC: Bayerische Landesbank and Westdeutsche

         Landesbank)                                                                         11,000,000               11,000,000

   VRDN 3.75%, Series 7, Sub-Series 7-A

      (Insured; MBIA and Liquidity Facility; Credit Suisse)                                  10,000,000  (a)          10,000,000

Mahopac Central School District 4.50%, Series A, 9/1/2000                                     1,575,000                1,576,616

Metropolitan Transportation Authority, Transit Facilities

  Revenue, Series 1, CP:

      4.05%, Sub-Series B, 9/1/2000 (LOC; ABN-Amro Bank)                                     10,000,000               10,000,000

      4.50%, 9/11/2000 (LOC; ABN-Amro Bank)                                                  11,000,000               11,000,000

      4.40%, 11/8/2000 (LOC; ABN-Amro Bank)                                                   3,000,000                3,000,000

New York City:

  CP 4.45%, Series H-3, 11/15/2000 (Insured; FSA and

      Liquidity Facility; State Street Bank and Trust Co.)                                    4,500,000                4,500,000

   VRDN:

      4.30%, Sub-Series A-4, (LOC; Chase Manhattan Bank)                                      1,900,000  (a)           1,900,000

      4.30%, Series B, Sub-Series B-6

         (Insured; MBIA and Liquidity Facility; Bank of Nova Scotia)                          3,800,000  (a)           3,800,000


6

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

New York City (continued):

  VRDN (continued):

    4.30%, Sub-Series E-4

         (LOC; State Street Bank and Trust Co.)                                               9,700,000  (a)           9,700,000

      4.40%, Series B, Sub-Series B-3

         (Insured; MBIA and Liquidity Facility; Bank of Nova Scotia)                          5,000,000  (a)           5,000,000

New York City Housing Development Corporation, VRDN:

  Multi-Family Rental Housing Revenue (Monterey)

      3.90%, Series A (LOC; FNMA)                                                            10,000,000  (a)          10,000,000

   Multi-Family Revenue (West 54th Street Development Project)

      3.80%, Series A (LOC; Key Bank)                                                        18,300,000  (a)          18,300,000

New York City Industrial Development Agency,

  Special Facility Revenue VRDN

   (Korean Air Lines Co.) 4.05%, Series C (LOC; Citibank)                                     7,000,000  (a)           7,000,000

New York City Municipal Water Finance Authority,

  Water and Sewer System Revenue, VRDN:

      4.30%, Series G (Insured; FGIC and Liquidity Facility; FGIC)                            2,500,000  (a)           2,500,000

      4.40%, Series C (Insured; FGIC and Liquidity Facility; FGIC)                            8,900,000  (a)           8,900,000

New York City Transitional Finance Authority, Revenue:

   BAN 4.75%, Series 3, 11/1/2000                                                            15,000,000               15,021,175

   VRDN, Future Tax Secured:

      3.85%, Series A-2 (Liquidity Facility; Bank of Nova Scotia)                            20,000,000  (a)          20,000,000

      4.35%, Sub-Series B-1 (Liquidity Facility;

         Morgan Guaranty Trust Co.)                                                           2,600,000  (a)           2,600,000

New York City Trust, Cultural Resource Revenue, Refunding,

  VRDN (American Museum of Natural History)

  3.75%, Series A (Insured; MBIA and Liquidity Facility;

   Credit Suisse)                                                                             3,000,000  (a)           3,000,000

New York State Dorm Authority, Revenues, VRDN:

  (Memorial Sloan Kettering Hospital) 4.35%, Series A

      (LOC; Chase Manhattan Bank)                                                             8,400,000  (a)           8,400,000

   (Miriam Osborn Memorial Home)

      4.15%, Series B (LOC; Manufacturers and Traders Bank)                                  10,000,000  (a)          10,000,000

   (Oxford University Press Inc.)

      4.40% (LOC; Landesbank Hessen)                                                         10,000,000  (a)          10,000,000

New York State Energy, Research and Development Authority,

  PCR:

    (New York State Electric and Gas):

         3.90%, Series D, 12/1/2000 (LOC; Fleet National Bank)                               11,700,000               11,700,000

         VRDN, Refunding 4.30%, Series D (LOC; Bank One Corp.)                                3,000,000  (a)           3,000,000

      (Niagara Mohawk Power Corp.) VRDN:

         4.40%, Series A (LOC; Toronto-Dominion Bank)                                        12,600,000  (a)          12,600,000

         4.50%, Series A (LOC; Morgan Guaranty Trust Co.)                                     8,200,000  (a)           8,200,000

         4.50%, Series B (LOC; Morgan Guaranty Trust Co.)                                    23,200,000  (a)          23,200,000

                                                                                                     The Fund 7

STATEMENT OF INVESTMENTS (Unaudited) (CONTINUED)

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

New York State Environmental Quality

  3.90%, Series G, 10/5/2000 (LOC; Westdeutsche

   Landesbank)                                                                               15,000,000               15,000,000

New York State Housing Finance Agency, Revenue, VRDN:

   3.80%, Series A (LOC; FNMA)                                                               10,000,000  (a)          10,000,000

   (Normandie Court I Project) 3.70% (LOC; Landesbank Hessen)                                 7,900,000  (a)           7,900,000

   Service Contract Obligation 3.80%, Series A

      (LOC; Commerzbank)                                                                     14,400,000  (a)          14,400,000

New York State Local Government Assistance Corporation, VRDN:

  3.75%, Series B (LOC: Bayerische Landesbank and

      Westdeutsche Landesbank)                                                                9,700,000  (a)           9,700,000

   3.75%, Series F (LOC; Toronto-Dominion Bank)                                               9,200,000  (a)           9,200,000

New York State Medical Care Facilities Finance Agency, Revenue,

  VRDN (Pooled Equipment Loan Program):

      3.80%, Series II-A (LOC; Chase Manhattan Bank)                                          3,970,000  (a)           3,970,000

      3.95%, Series I (LOC; Chase Manhattan Bank)                                             1,100,000  (a)           1,100,000

New York State Power Authority, CP 4.40%, Series 2, 7/25/2000

  (Liquidity Facility: The Bank of New York, Bank of Nova Scotia,

  Bayerische Landesbank, Chase Manhattan Bank, Commerzbank,

  Credit Local de France, First Union National

  Bank of North Carolina, Landesbank Hessen, Morgan Guaranty

   Trust Co. and State Street Bank and Trust Co.)                                             9,000,000                9,000,000

New York State Thruway Authority, Revenue, CP

  4.35%, Series 1, 11/8/2000

   (Liquidity Facility; Landesbank Hessen)                                                    5,000,000                5,000,000

Newark Central School District, BAN 4.50%, 1/26/2001                                          9,000,000                9,011,225

Niagara County Industrial Development Agency, SWDR,

  Refunding, VRDN (American Refunding Fuel Co.)

    3.80%, Series C (LOC; Chase Manhattan Bank)                                              15,000,000  (a)          15,000,000

Norwich, BAN 4.625%, 3/29/2001                                                                2,000,000                2,003,076

Onondaga County Industrial Development Agency, IDR, VRDN

   (Edgecomb Metals Co. Project) 4.25% (LOC; Wells Fargo Bank)                                2,000,000  (a)           2,000,000

Port Authority of New York and New Jersey, Special Obligation

  Revenue, VRDN (Versatile Structure)

    4.45%, Series 6 (Liquidity Facility; Bank of Nova Scotia)                                11,250,000  (a)          11,250,000

Richfield Springs Central School District, BAN 4.50%, 2/23/2001                               4,000,000                4,006,011

Rochester, BAN 4.50%, 3/7/2001                                                                5,000,000                5,010,999

Sachem Central School District, TAN (Holbrook) 4%, 6/29/2000                                  8,000,000                8,003,257

Smithtown Central School District, TAN 4%, 6/26/2000                                         12,500,000               12,505,363

West Genesee Central School District, BAN 4.75%, 4/20/2001                                    2,500,000                2,507,832

8


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

Yonkers Industrial Development Agency, Civic Facilities Revenue,

  Consumer Union Facilities, VRDN 3.90% (Insured; AMBAC

   and Liquidity Facility; Credit Local de France)                                            3,200,000  (a)           3,200,000
-----------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $484,240,822)                                                             99.1%              484,240,822

CASH AND RECEIVABLES (NET)                                                                          .9%                4,331,272

NET ASSETS                                                                                       100.0%              488,572,094

                                                                                                     The Fund 9

STATEMENT OF INVESTMENTS (Unaudited) (CONTINUED)

Summary of Abbreviations


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

BAN                       Bond Anticipation Notes                MBIA                      Municipal Bond
                                                                                           Investors Assurance
                                                                                           Insurance Corporation

CP                        Commercial Paper                       PCR                       Pollution Control Revenue

FGIC                      Financial Guaranty Insurance           RAN                       Revenue Anticipation Notes
                             Company

FNMA                      Federal National Mortgage              SWDR                      Solid Waste Disposal Revenue
                             Association

FSA                       Financial Security Assurance           TAN                       Tax Anticipation Notes

IDR                       Industrial Development Revenue         VRDN                      Variable Rate Demand Notes




Summary of Combined Ratings (Unaudited)


</TABLE>
<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)                                         2.5
Not Rated(c)                     Not Rated(c)                    Not Rated(c)                                      6.7

                                                                                                                 100.0
</TABLE>


(A)  SECURITIES PAYABLE ON DEMAND. VARIABLE INTEREST RATE--SUBJECT TO PERIODIC
     CHANGE.

(B)  NOTES WHICH ARE NOT F, MIG OR SP RATED ARE REPRESENTED BY BOND RATINGS OF
     THE ISSUERS.

(C)  SECURITIES WHICH, WHILE NOT RATED BY FITCH, MOODY'S AND STANDARD & POOR'S
     HAVE BEEN DETERMINED BY THE MANAGER TO BE OF COMPARABLE QUALITY TO THOSE
     RATED SECURITIES IN WHICH THE FUND MAY INVEST.

(D)  AT MAY 31, 2000, THE FUND HAD $128,050,000 (26.2% OF NET ASSETS) INVESTED
     IN SECURITIES WHOSE PAYMENT OF PRINCIPAL AND INTEREST IS DEPENDENT UPON
     REVENUES GENERATED FROM UTILITY-ELECTRIC PROJECTS.

SEE NOTES TO FINANCIAL STATEMENTS.
[/TABLE]


10

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2000 (Unaudited)

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

ASSETS ($):

Investments in securities--See Statement of
Investments                                           484,240,822   484,240,822

Cash                                                                  1,188,334

Interest receivable                                                   3,352,173

Prepaid expenses                                                         57,799

                                                                    488,839,128
--------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                           218,960

Accrued expenses                                                         48,074

                                                                        267,034
--------------------------------------------------------------------------------

NET ASSETS ($)                                                      488,572,094
--------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                     488,630,422

Accumulated net realized gain (loss) on investments                    (58,328)
--------------------------------------------------------------------------------

NET ASSETS ($)                                                      488,572,094

NET ASSET VALUE PER SHARE

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

Net Assets ($)                                        377,839,177   110,732,917

Shares Outstanding                                    377,905,535   110,732,798
--------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                                1.00          1.00

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund 11

STATEMENT OF OPERATIONS

Six Months Ended May 31, 2000 (Unaudited)

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

INVESTMENT INCOME ($):

INTEREST INCOME                                                      8,936,497

EXPENSES:

Management fee--Note 2(a)                                            1,175,783

Shareholder servicing costs--Note 2(c)                                 401,813

Distribution fees (Class B)--Note 2(b)                                  99,332

Prospectus and shareholders' reports                                    35,810

Professional fees                                                       31,540

Custodian fees                                                          23,996

Registration fees                                                       17,034

Trustees' fees and expenses--Note 2(d)                                  13,292

Miscellaneous                                                            6,597

TOTAL EXPENSES                                                       1,805,197

Less--reduction in management fee
  due to undertaking--Note 2(a)                                       (47,728)

NET EXPENSES                                                         1,757,469

INVESTMENT INCOME--NET, REPRESENTING NET INCREASE IN NET ASSETS
  RESULTING FROM OPERATIONS                                          7,179,028

SEE NOTES TO FINANCIAL STATEMENTS.


12

STATEMENT OF CHANGES IN NET ASSETS

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

OPERATIONS ($):

INVESTMENT INCOME--NET, REPRESENTING NET
   INCREASE IN NET ASSETS
        RESULTING FROM OPERATIONS               7,179,028           10,589,082
--------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A Shares                                (5,769,357)          (9,378,973)

Class B Shares                                (1,409,671)          (1,210,109)

TOTAL DIVIDENDS                               (7,179,028)         (10,589,082)
--------------------------------------------------------------------------------

BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share)

Net proceeds from shares sold:

Class A Shares                                427,356,665          919,904,202

Class B Shares                                201,461,593          184,564,048

Dividends reinvested:

Class A Shares                                  5,558,217            9,041,654

Class B Shares                                  1,387,032            1,209,242

Cost of shares redeemed:

Class A Shares                              (433,191,191)        (955,884,385)

Class B Shares                              (185,402,569)        (139,483,517)

INCREASE (DECREASE) IN NET ASSETS FROM
   BENEFICIAL INTEREST TRANSACTIONS           17,169,747           19,351,244

TOTAL INCREASE (DECREASE) IN NET ASSETS       17,169,747           19,351,244
--------------------------------------------------------------------------------

NET ASSETS ($):

Beginning of Period                           471,402,347          452,051,103

END OF PERIOD                                 488,572,094          471,402,347

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund 13

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>

                                         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          .024          .027          .029           .028          .032

Distributions:

Dividends from investment
   income--net                                      (.016)        (.024)        (.027)         (.029)        (.028)        (.032)

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

TOTAL RETURN (%)                                      3.11(a)      2.45          2.77           2.98           2.84          3.28
------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average
   net assets                                         .68(a)        .68           .68            .66           .68           .58

Ratio of net investment income
   to average net assets                             3.10(a)       2.42          2.74           2.94          2.80          3.23

Decrease reflected in above expense
   ratios due to undertakings by
   The Dreyfus Corporation                              --            --          --            --             --           .05
------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period
   ($ x 1,000)                                     377,839       378,115      405,054        440,750       507,537       636,013

(A) ANNUALIZED.


SEE NOTES TO FINANCIAL STATEMENTS.

14


                                         Six Months Ended
                                             May 31, 2000                                  Year Ended November 30,
                                                                    ----------------------------------------------------------------
CLASS B SHARES                                 (Unaudited)          1999          1998          1997          1996        1995(a)
------------------------------------------------------------------------------------------------------------------------------------

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          .021          .024          .027           .025          .006

Distributions:

Dividends from investment
   income--net                                       (.014)        (.021)        (.024)         (.027)        (.025)        (.006)

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

TOTAL RETURN (%)                                      2.83(b)       2.12          2.47           2.68          2.55          2.82(b)
------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average
   net assets                                          .98(b)        .98           .98            .95           .95          1.04(b)

Ratio of net investment income
   to average net assets                              2.83(b)       2.14          2.44           2.64          2.47          3.64(b)

Decrease reflected in above expense
   ratios due to undertakings by
   The Dreyfus Corporation                             .10(b)        .10           .08            .08           .16            --
------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period
   ($ x 1,000)                                      110,733       93,287        46,997         42,169        36,199            --

(A) FROM SEPTEMBER 8, 1995 (COMMENCEMENT OF INITIAL OFFERING) TO NOVEMBER 30, 1995.

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.
</TABLE>

                                                             The Fund 15

NOTES TO FINANCIAL STATEMENTS (Unaudited)

NOTE 1--Significant Accounting Policies:

General  New  York  Municipal Money Market Fund (the "fund") is registered under
the Investment Company Act of 1940, as amended (the "Act"), as a non-diversified
open-end  management  investment  company. The fund's investment objective is to
maximize  current  income  exempt from Federal, New York State and New York City
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  wholly-owned  subsidiary  of  Mellon  Financial  Corporation.

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
an  unlimited  number  of  $.001  par  value  shares in the following classes of
shares:  Class  A  and  Class B. 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.

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.

16

(a) Portfolio valuation: Investments in securities are valued at amortized cost,
which  has been determined by the fund's Board of Trustees 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 $18,593 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, 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, 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 17

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

The fund has an unused capital loss carryover of approximately $58,000 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,
$39,000  of  the  carryover expires in fiscal 2002 and $19,000 expires in fiscal
2003.

During  the  period  ended  May  31,  2000, the fund reclassified $7,911 between
accumulated  net  realized gain (loss) on investments and paid-in capital due to
the  expiration  of  capital  loss carryovers. The results of operations and net
assets were not affected by the reclassification.

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, exclusive of taxes,
brokerage  fees, interest on borrowings and extraordinary expenses, exceed 11/2%
of the value of the fund's average 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 .98 of 1% for Class
B  shares, of the value of the fund's average daily net assets. The reduction in
management  fee,  pursuant  to  the  undertaking  amounted to $47,728 during the
period ended May 31, 2000.


(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  cost  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 shares.
During  the  period  ended  May  31,  2000,  Class B shares were charged $99,332
pursuant to the Distribution Plan, of which $54,028 was paid to DSC.

18

(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 $169,056 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.  During the
period  ended May 31,  2000,  Class B shares  were  charged  $148,998,  of which
$81,042 was paid to DSC.


                                                                     The Fund 19

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, 2000, the fund was charged $51,051 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 fund an annual fee
of  $2,500  and an attendance fee of $250 per meeting. The Chairman of the Board
received  an additional 25% of such compensation. Subject to the fund's Director
Emeritus Program Guidelines, Emeritus Boards members, if any, receive 50% of the
fund's annual retainer fee and per meeting fee paid at the time the Board member
achieved emeritus status.

20
                                                           For More Information

                        General New York 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                                   574SA005





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