DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1999-02-05
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YEAR 2000 ISSUES (UNAUDITED)

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

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

LETTER TO SHAREHOLDERS

Dear Shareholder:

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

                                                                           YIELD                   EFFECTIVE YIELD*
                                                                          _______                   _____________
        <S>                                                                 <C>                        <C>
        Class A Shares . . . . . . . . . . . . . . . . . . . .              2.74%                      2.77%
        Class B Shares . . . . . . . . . . . . . . . . . . . .              2.44%                      2.47%
</TABLE>
ECONOMY

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

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

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

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

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

MARKET ENVIRONMENT/PORTFOLIO OVERVIEW

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

  We  attempted to extend your Fund's average maturity beyond 40 days during the
summer  months, just prior to the market strengthening. Your Fund benefited from
those  securities purchased in the one-year range at yields significantly higher
than what is currently available in the market. As the summer progressed, yields
began  to drop as they reflected the diminished supply of one-year notes. During
this  period  we  utilized  the  commercial  paper market to maintain the Fund's
average  maturity.  As year-end approaches, we will continue to search for those
longer-term  investment  opportunities  which  will  lock  in higher rates while
providing  an  attractive return to the New York tax-exempt investor. As always,
we  will  structure  the portfolio in an attempt to maximize current yield while
maintaining our commitment to high quality tax-exempt investments.

               Very truly yours,



               [Richard J. Moynihan signature]


               Richard J. Moynihan

               Director, Municipal Portfolio Management

               The Dreyfus Corporation

December 15, 1998

New York, N.Y.

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

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS                                    NOVEMBER 30, 1998

                                                                                                  Principal

Tax Exempt Investments--101.0%                                                                     Amount             Value
- -------------------------------------------------------                                         _____________     _____________
New York--98.8%
<S>                                                                                             <C>               <C>
Erie County, RAN 4%, 10/13/99 (LOC; Bank of New York). . . . . . . . . . . . . . . . . . .      $  10,000,000     $  10,084,035

Erie County Water Authority, Water Revenue, VRDN

 2.75%, Series A (Insured; AMBAC and Liquidity Facility; National Bank

  of Australia) (a)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          9,000,000         9,000,000

Hicksville Union Free School District, TAN 4%, 6/23/99 . . . . . . . . . . . . . . . . . .          8,000,000         8,017,234

Town of Islip Industrial Development Agency, IDR, VRDN

  (Brentwood Distribution Project) 3.10% (LOC; Fleet Bank) (a) . . . . . . . . . . . . . .          1,000,000         1,000,000

Long Island Power Authority, Electric Systems Revenue:

  CP 3%, Sub-Series 1, 2/9/99 (LOC: Bayerische Landesbank and Westdeutsche Landesbank) . .         10,000,000        10,000,000

  VRDN 3.25%, Sub-Series 5

    (LOC: ABN-Amro Bank and Morgan Guaranty Trust Co.) (a) . . . . . . . . . . . . . . . .          6,000,000         6,000,000

Metropolitan Transportation Authority, Transit Facilities Revenue, CP

  3.10%, Series 1, 2/9/99 (LOC: ABN-Amro Bank) . . . . . . . . . . . . . . . . . . . . . .         14,000,000        14,000,000

Municipal Assistance Corporation, VRDN

  3.20%, Sub-Series K-3, (LOC; Landesbank Hessen) (a)  . . . . . . . . . . . . . . . . . .          8,000,000         8,000,000

New York City, VRDN:

  2.90%, Series B, Subseries B-10 (LOC; Union Bank of Switzerland) (a) . . . . . . . . . .          5,000,000         5,000,000

  2.95%, Sub-Series A-6 (LOC; Landesbank Hessen) (a) . . . . . . . . . . . . . . . . . . .          8,000,000         8,000,000

  3.15%, Sub-Series A-10 (LOC; Morgan Guaranty Trust Co.) (a)  . . . . . . . . . . . . . .          3,000,000         3,000,000

  3.25%, Sub-Series E-4 (LOC; State Street Bank and Trust Co. ) (a)  . . . . . . . . . . .          4,300,000         4,300,000

  3.30%, Sub-Series A-7 (LOC; Morgan Guaranty Trust Co. ) (a)  . . . . . . . . . . . . . .         14,900,000        14,900,000

  3.30%, Series B, Sub-Series B-3 (Insured; MBIA and Liquidity Facility; Bank of

    Nova Scotia) (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          5,900,000         5,900,000

  3.30%, Sub-Series E-3 (LOC; Morgan Guaranty Trust Co.) (a) . . . . . . . . . . . . . . .         19,500,000        19,500,000

  3.30%, Sub-Series E-5 (LOC; Morgan Guaranty Trust Co.) (a) . . . . . . . . . . . . . . .         18,600,000        18,600,000

  3.35%, Sub-Series A-4 (LOC; Chase Manhattan Bank) (a)  . . . . . . . . . . . . . . . . .          3,850,000         3,850,000

New York City Health and Hospital Corporation, Health Systems Revenue, VRDN

  2.95%, Series A (LOC; Morgan Guaranty Trust Co.) (a) . . . . . . . . . . . . . . . . . .          9,900,000         9,900,000

New York City Housing Development Corporation, VRDN:

  MFMR (York Avenue Development Project) 3.15% (LOC; Midland Bank) (a) . . . . . . . . . .          8,000,000         8,000,000

  Multi-Family Rental Housing Revenue (Monterey) 3%, Series A (LOC; FNMA) (a)  . . . . . .         10,000,000        10,000,000

New York City Municipal Water Finance Authority, CP

 3%, Series 1, 3/18/99 (LOC: Bank of Nova Scotia, Commerzbank and

  Toronto-Dominion Bank) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         20,000,000        20,000,000

New York City Trust, Cultural Resource Revenue, Refunding, VRDN

 (American Museum of Natural History)

  2.75%, Series A (Insured; MBIA and Liquidity Facility; Credit Suisse) (a)  . . . . . . .          3,000,000         3,000,000

New York State Energy Research and Development Authority:

 Electric Facilities Revenue, VRDN (LILCO Project)

  3%, Series B (LOC; Toronto-Dominion Bank) (a)  . . . . . . . . . . . . . . . . . . . . .          8,000,000         8,000,000

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        NOVEMBER 30, 1998


                                                                                                  Principal

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

New York (continued)

New York State Energy Research and Development Authority (continued):

 PCR:

    (LILCO Project) 3.58%, Series A, 3/1/99 (LOC; Deutsche Bank) . . . . . . . . . . . . .      $  15,470,000     $  15,470,000

    (New York State Electric and Gas Corp.)

       3.80%, Series D, 12/1/98 (LOC; Union Bank of Switzerland) . . . . . . . . . . . . .          8,325,000         8,325,000

  VRDN:

    (Central Hudson Gas and Electric Project)

       3.25%, Series A (LOC; Union Bank of Switzerland) (a)  . . . . . . . . . . . . . . .          7,800,000         7,800,000

    (Niagara Mohawk Power Corp.)

       3.35%, Series B (LOC; Toronto-Dominion Bank) (a)  . . . . . . . . . . . . . . . . .          4,500,000         4,500,000

       3.35%, Series C (LOC; Canadian Imperial Bank of Commerce) (a) . . . . . . . . . . .         11,000,000        11,000,000

New York State Housing Finance Agency, Revenue, VRDN:

  (Normandie Court I Project) 2.85% (LOC; Landesbank Hessen) (a) . . . . . . . . . . . . .          8,000,000         8,000,000

  Contract Obligation 2.90%, Series A (LOC; Commerzbank) (a) . . . . . . . . . . . . . . .         14,400,000        14,400,000

New York State Local Government Assistance Corporation, VRDN:

  2.90%, Series A (LOC: Credit Suisse and Union Bank of Switzerland) (a) . . . . . . . . .         28,000,000        28,000,000

  2.90%, Series F (LOC; Toronto-Dominion Bank) (a) . . . . . . . . . . . . . . . . . . . .         10,200,000        10,200,000

  2.95%, Series B (LOC; Krediet Bank) (a)  . . . . . . . . . . . . . . . . . . . . . . . .         30,700,000        30,700,000

New York State Medical Care Facilities Finance Agency, Revenue, VRDN

 (Pooled Equipment Loan Program):

    3.10%, Series I (LOC; Chase Manhattan Bank) (a)  . . . . . . . . . . . . . . . . . . .         10,500,000        10,500,000

    3.10%, Series II (LOC; Chase Manhattan Bank) (a) . . . . . . . . . . . . . . . . . . .          5,870,000         5,870,000

New York State Power Authority, CP:

 3%, 12/2/98 (Liquidity: Bank of Nova Scotia, Commerzbank, Credit Locale

    de France, Landesbank Hessen, Morgan Guaranty Trust Co. and Toronto-Dominion Bank) . .         19,100,000        19,100,000

  3.20%, 12/3/98 (Liquidity: Bank of Nova Scotia, Commerzbank, Credit Locale

    de France, Landesbank Hessen, Morgan Guaranty Trust Co. and Toronto-Dominion Bank) . .          7,700,000         7,700,000

Onondaga County Industrial Development Agency, IDR, VRDN (Edgecomb Metals Co.
Project)

  3.10% (LOC; Banque Nationale de Paris) (a) . . . . . . . . . . . . . . . . . . . . . . .          2,000,000         2,000,000

Oyster Bay, BAN 4%, 10/1/99. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          7,000,000         7,036,655

Port Authority of New York and New Jersey, Special Obligation Revenue, VRDN

 (Versatile Structure):

    3.25%, Series 2 (LOC; Morgan Guaranty Trust Co.) (a) . . . . . . . . . . . . . . . . .         15,000,000        15,000,000

    3.35%, Series 6 (Liquidity; Bank of Nova Scotia) (a) . . . . . . . . . . . . . . . . .          2,600,000         2,600,000

    3.40%, Series 6 (Liquidity; Bank of Nova Scotia) (a) . . . . . . . . . . . . . . . . .            100,000           100,000

Sachem Central School District, TAN 4%, 6/25/99. . . . . . . . . . . . . . . . . . . . . .          7,500,000         7,513,496

Three Village Central School District, TAN (Brookhaven and Smithtown)

  4%, 6/30/99  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          8,500,000         8,518,960

Westchester County Health Care Corporation, CP

  3%, Series 1, 12/7/98  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         11,000,000        11,000,000

Yonkers Industrial Development Authority, Civic Revenue, Consumers Union
Facilities,

  VRDN 2.85% (Insured; AMBAC and Liquidity Facility; Credit Locale de France) (a)  . . . .          3,300,000         3,300,000

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF INVESTMENTS (CONTINUED)                        NOVEMBER 30, 1998


                                                                                                  Principal

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

U.S. Related--2.2%

Commonwealth of Puerto Rico, TRAN 3.50%, Series A, 7/30/99 . . . . . . . . . . . . . . . .      $  10,000,000     $  10,042,000

                                                                                                                  _____________

TOTAL INVESTMENTS (cost $456,727,380). . . . . . . . . . . . . . . . . . . . . . . . . . .             101.0%      $456,727,380
                                                                                                    =========      ============


LIABILITIES, LESS CASH AND RECEIVABLES . . . . . . . . . . . . . . . . . . . . . . . . . .              (1.0%)     $ (4,676,277)
                                                                                                     =========     =============

NET ASSETS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .             100.0%      $452,051,103
                                                                                                     ========      ============
</TABLE>
<TABLE>
<CAPTION>

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------


Summary of Abbreviations
- -----------------------------------------------------------------------------
<S>         <C>                                                     <C>         <C>
AMBAC       American Municipal Bond Assurance Corporation           MFMR        Multi-Family Mortgage Revenue

BAN         Bond Anticipation Notes                                 PCR         Pollution Control Revenue

CP          Commercial Paper                                        RAN         Revenue Anticipation Notes

FNMA        Federal National Mortgage Association                   TAN         Tax Anticipation Notes

IDR         Industrial Development Revenue                          TRAN        Tax and Revenue Anticipation Notes

LOC         Letter of Credit                                        VRDN        Variable Rate Demand Notes

MBIA        Municipal Bond Investors Assurance
            Insurance Corporation

</TABLE>
<TABLE>
<CAPTION>


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

Fitch                or            Moody's             or            Standard & Poor's              Percentage of Value
_______                            ________                          _________________              ___________________
<S>                                <C>                               <C>                                  <C>
F1+/F1                             VMIG1/MIG1, P1                    SP1+/SP1, A1+/A1                     96.3%

AAA/AA (b)                         Aaa/Aa (b)                        AAA/AA (b)                             .4

Not Rated (c)                      Not Rated (c)                     Not Rated (c)                         3.3
                                                                                                       _______

                                                                                                         100.0%
                                                                                                       ========
</TABLE>

Notes to Statement of Investments:
- -----------------------------------------------------------------------------

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

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

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

                      SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------
<TABLE>
<CAPTION>
STATEMENT OF ASSETS AND LIABILITIES                         NOVEMBER 30, 1998

                                                                                                     Cost             Value
                                                                                                _____________     _____________
<S>                              <C>                                                             <C>               <C>
ASSETS:                          Investments in securities--See Statement of Investments . .     $456,727,380      $456,727,380

                                 Cash  . . . . . . . . . . . . . . . . . . . . . . . . . .                            3,746,232

                                 Interest receivable . . . . . . . . . . . . . . . . . . .                            1,877,362

                                                                                                                  _____________

                                                                                                                    462,350,974

                                                                                                                  _____________

LIABILITIES:                     Due to The Dreyfus Corporation and affiliates . . . . . .                              198,555

                                 Due to Distributor  . . . . . . . . . . . . . . . . . . .                                  242

                                 Payable for investment securities purchased . . . . . . .                           10,042,000

                                 Accrued expenses  . . . . . . . . . . . . . . . . . . . .                               59,074
                                                                                                                _____________

                                                                                                                     10,299,871
                                                                                                                  _____________

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $452,051,103
                                                                                                                  =============


REPRESENTED BY:                  Paid-in capital . . . . . . . . . . . . . . . . . . . . .                         $452,117,342

                                 Accumulated net realized gain (loss) on investments . . .                              (66,239)
                                                                                                                  -------------

NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                         $452,051,103
                                                                                                                  =============

                                                  NET ASSET VALUE PER SHARE
                              ___________________________________________________________________

                                                                                                   Class A           Class B
                                                                                                _____________     _____________

Net Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $405,054,015     $  46,997,088

Shares Outstanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        405,120,373        46,996,969

NET ASSET VALUE PER SHARE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .              $1.00             $1.00
                                                                                                        =====             =====
                      SEE NOTES TO FINANCIAL STATEMENTS.


GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF OPERATIONS                          YEAR ENDED NOVEMBER 30, 1998

INVESTMENT INCOME

INCOME                           Interest Income . . . . . . . . . . . . . . . . . . . . .                          $16,200,617

EXPENSES:                        Management fee--Note 2(a) . . . . . . . . . . . . . . . .       $  2,369,250

                                 Shareholder servicing costs--Note 2(c)  . . . . . . . . .            763,000

                                 Distribution fees (Class B)--Note 2(b)  . . . . . . . . .             93,487

                                 Custodian fees  . . . . . . . . . . . . . . . . . . . . .             48,897

                                 Registration fees . . . . . . . . . . . . . . . . . . . .             39,680

                                 Professional fees . . . . . . . . . . . . . . . . . . . .             36,245

                                 Trustees' fees and expenses--Note 2(d)  . . . . . . . . .             25,164

                                 Prospectus and shareholders' reports  . . . . . . . . . .             19,339

                                 Miscellaneous . . . . . . . . . . . . . . . . . . . . . .             12,640

                                                                                                 ____________

                                        Total Expenses . . . . . . . . . . . . . . . . . .          3,407,702

                                 Less--reduction in shareholder servicing costs due to

                                    undertaking--Note 2(c) . . . . . . . . . . . . . . . .            (38,784)

                                                                                                 ____________

                                        Net Expenses . . . . . . . . . . . . . . . . . . .                            3,368,918
                                                                                                                   ____________

INVESTMENT INCOME--NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                           12,831,699
                                                                                                                   ============
NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b) . . . . . . . . . . . ..                                  147
                                                                                                                   ____________

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS . . . . . . . . . . . . . . . . . . .                          $12,831,846
                                                                                                                   ____________

                      SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

STATEMENT OF CHANGES IN NET ASSETS

                                                                                             Year Ended          Year Ended

                                                                                         November 30, 1998   November 30, 1997
                                                                                        ___________________  ___________________

OPERATIONS:

  Investment income--net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    $    12,831,699      $  15,160,748

  Net realized gain (loss) on investments  . . . . . . . . . . . . . . . . . . . . . .                147              1,107

  Net unrealized appreciation (depreciation) on investments  . . . . . . . . . . . . .         -----                  (1,333)
                                                                                           ______________     ______________

         Net Increase (Decrease) in Net Assets Resulting from Operations . . . . . . .         12,831,846         15,160,522

                                                                                           ______________     ______________

DIVIDENDS TO SHAREHOLDERS FROM:

 Investment income--net:

    Class A shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        (11,691,987)       (14,099,515)

    Class B shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         (1,139,712)        (1,061,233)
                                                                                           ______________     ______________

         Total Dividends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        (12,831,699)       (15,160,748)
                                                                                           ______________     ______________

BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):

 Net proceeds from shares sold:

    Class A shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      1,060,136,234  1,232,077,695

    Class B shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        107,077,205  88,699,944

  Dividends reinvested:

    Class A shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         11,286,121  13,492,714

    Class B shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          1,135,035  1,060,123

  Cost of shares redeemed:

    Class A shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     (1,107,118,496)    (1,312,357,416)

    Class B shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       (103,384,014)       (83,789,854)
                                                                                           ______________     ______________

       Increase (Decrease) in Net Assets from Beneficial Interest Transactions . . . .        (30,867,915)       (60,816,794)
                                                                                           ______________     ______________

         Total Increase (Decrease) in Net Assets . . . . . . . . . . . . . . . . . . .        (30,867,768)       (60,817,020)

NET ASSETS:

  Beginning of Period  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        482,918,871        543,735,891
                                                                                           ______________     ______________

  End of Period  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     $  452,051,103     $  482,918,871
                                                                                           ==============     ==============
</TABLE>

                      SEE NOTES TO FINANCIAL STATEMENTS.
<TABLE>
<CAPTION>

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS

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


                                                                                         Class A Shares

                                                                      ______________________________________________________

                                                                                    Year Ended November 30,
                                                                      ______________________________________________________

PER SHARE DATA:                                                    1998          1997         1996         1995         1994
                                                                    ______       ______       ______        ______       ______
   <S>                                                             <C>          <C>          <C>           <C>          <C>
   Net asset value, beginning of period  . . . . . . . . . .       $  1.00      $  1.00      $  1.00       $  1.00      $  1.00
                                                                   _______      _______      _______       _______      _______

   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . .          .027         .029         .028          .032         .023
                                                                    ______       ______       ______        ______       ______

   Distributions:

   Dividends from investment income--net . . . . . . . . . .         (.027)       (.029)       (.028)        (.032)       (.023)
                                                                    ______       ______       ______        ______       ______

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

TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . .          2.77%        2.98%        2.84%         3.28%        2.34%

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . .           .68%         .66%         .68%          .58%         .34%

   Ratio of net investment income

       to average net assets . . . . . . . . . . . . . . . .          2.74%        2.94%        2.80%         3.23%        2.33%

   Decrease reflected in above expense ratios

       due to undertakings by the Manager  . . . . . . . . .            --           --           --           .05%         .32%

   Net Assets, end of period (000's Omitted) . . . . . . . .      $405,054    $ 440,750    $ 507,537      $636,013     $689,918
</TABLE>
<TABLE>
<CAPTION>

                      SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

FINANCIAL HIGHLIGHTS (CONTINUED)

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

                                                                                                Class B Shares
                                                                                   __________________________________________

                                                                                            Year Ended November 30,
                                                                                   __________________________________________

PER SHARE DATA:                                                                   1998         1997          1996        1995(1)
                                                                                 ______       ______        ______       ______
   <S>                                                                          <C>          <C>           <C>          <C>
   Net asset value, beginning of period  . . . . . . . . . . . . . . . .        $  1.00      $  1.00       $  1.00      $  1.00
                                                                                 ______       ______        ______       ______

   Investment Operations:

   Investment income--net  . . . . . . . . . . . . . . . . . . . . . . .           .024         .027          .025         .006
                                                                                 ______       ______        ______       ______


   Distributions:

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

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

TOTAL INVESTMENT RETURN. . . . . . . . . . . . . . . . . . . . . . . . .           2.47%        2.68%         2.55%        2.82%(2)

RATIOS/SUPPLEMENTAL DATA:

   Ratio of expenses to average net assets . . . . . . . . . . . . . . .            .98%         .95%          .95%        1.04%(2)

   Ratio of net investment income

       to average net assets . . . . . . . . . . . . . . . . . . . . . .           2.44%        2.64%         2.47%        3.64%(2)

   Decrease reflected in above expense ratios

       due to undertakings by the Manager  . . . . . . . . . . . . . . .            .08%         .08%          .16%          --

   Net Assets, end of period (000's Omitted) . . . . . . . . . . . . . .        $46,997      $42,169       $36,199           --
- -----------------------------
</TABLE>

(1)  From September 8, 1995 (commencement of initial offering) to
     November 30, 1995.

(2)  Annualized.

                      SEE NOTES TO FINANCIAL STATEMENTS.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS

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.

   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  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.

   (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  $32,465 during the period ended
November  30,  1998  based  on  available  cash balances left on deposit. Income
earned under this arrangement is included in interest income.

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

   (C)  DIVIDENDS  TO  SHAREHOLDERS:  It  is  the  policy of the Fund to declare
dividends  daily  from  investment  income-net. Such dividends are paid monthly.
Dividends  from  net  realized  capital  gain  are  normally  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  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, 1998. If not
applied, $40,000 expires in fiscal 2002 and $18,000 expires in fiscal 2003.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

At November 30, 1998, the cost of investments for Federal income tax purposes
was substantially the same as the cost for financial reporting purposes (see the
Statement of Investments).

NOTE 2--MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:

   (A)  Pursuant  to  a management agreement ("Agreement") with the Manager, the
management  fee  is computed at the annual rate of .50 of 1% of the value of the
Fund's  average daily net assets and is payable monthly. The Agreement provides
that  if  in  any  full  fiscal year the aggregate expenses, exclusive of taxes,
brokerage,  interest  on borrowings and extraordinary expenses, exceed 1 1/2% 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. During the
period  November  30,  1998,  there was no expense reimbursement pursuant to the
Agreement.

   (B)  Under  the  Distribution  Plan  with  respect  to  Class  B  ("Class  B
Distribution  Plan"), adopted  pursuant  to  Rule  12b-1 under the Act, Class B
shares directly  bear  the  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 November 30, 1998, Class B shares were
charged $93,487 pursuant to the Distribution Plan.

   (C)  Under  the  Shareholder  Services Plan with respect to Class A ("Class A
Shareholder Services Plan"), Class  A  shares  reimburse  Dreyfus  Service
Corporation,  a  wholly-owned subsidiary of the Manager, an amount not to exceed
an  annual  rate  of  .25  of 1% of the value of the average daily net assets of
Class  A  for  certain  allocated expenses of providing personal services and/or
maintaining  shareholder  accounts.  The  services provided may include personal
services  relating  to  shareholder  accounts,  such  as  answering  shareholder
inquiries  regarding Class A shares and providing reports and other information,
and  services  related  to  the  maintenance of shareholder accounts. During the
period ended November 30, 1998, Class A shares were charged $412,841 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 through November 30, 1998, that if the aggregate
expenses  of  Class  B  shares,  exclusive  of  taxes,  brokerage,  interest  on
borrowings  and  extraordinary  expenses, exceeded .98 of 1% of the value of the
average  daily net assets of Class B, the Manager will reimburse the expenses of
the Fund under the Class B Shareholder Services Plan to the extent of any excess
expense  and up to the full fee payable under such Plan. During the period ended
November  30,  1998,  Class B shares were charged $140,231, of which $38,784 was
reimbursed by the Manager.

The Fund compensates Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,   under  a  transfer  agency  agreement  for  providing  personnel  and
facilities  to  perform transfer agency services for the Fund. During the period
ended  November 30, 1998, the Fund was charged $139,632 pursuant to the transfer
agency agreement.

   (D)  Each  trustee  who  is  not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $250 per
meeting.  The  Chairman  of  the  Board  receives  an  additional  25%  of  such
compensation.


GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
- -----------------------------------------------------------------------------

REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS

SHAREHOLDERS AND BOARD OF TRUSTEES

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND

   We  have  audited  the  accompanying  statement  of assets and liabilities of
General  New  York  Municipal  Money  Market  Fund,  including  the statement of
investments,  as  of  November 30, 1998, and the related statement of operations
for  the year then ended, the statement of changes in net assets for each of the
two  years  in  the  period then ended, and financial highlights for each of the
years indicated therein. These financial statements and financial highlights are
the responsibility of the Fund's management. Our responsibility is to express an
opinion  on  these  financial  statements  and financial highlights based on our
audits.

   We  conducted  our  audits  in  accordance  with  generally accepted auditing
standards.  Those standards require that we plan and perform the audit to obtain
reasonable  assurance  about  whether  the  financial  statements  and financial
highlights  are free of material misstatement. An audit includes examining, on a
test  basis,  evidence  supporting  the amounts and disclosures in the financial
statements  and  financial  highlights.  Our procedures included confirmation of
securities  owned  as  of November 30, 1998 by correspondence with the custodian
and brokers. An audit also includes assessing the accounting principles used and
significant  estimates  made  by  management,  as well as evaluating the overall
financial   statement  presentation.  We  believe  that  our  audits  provide  a
reasonable basis for our opinion.

In our opinion, the financial statements and financial highlights referred to
above  present  fairly,  in  all  material  respects,  the financial position of
General  New  York Municipal Money Market Fund at November 30, 1998, the results
of  its  operations  for  the year then ended, the changes in its net assets for
each of the two years in the period then ended, and the financial highlights for
each  of  the  indicated years, in conformity with generally accepted accounting
principles.

                                              [ERNST & YOUNG LLP SIGNATURE LOGO]



New York, New York
January 4, 1999

IMPORTANT TAX INFORMATION (UNAUDITED)

   In  accordance  with  Federal  tax  law,  the  Fund hereby designates all the
dividends  paid from investment income-net during the fiscal year ended November
30, 1998 as "exempt-interest dividends" (not subject to regular Federal and, for
individuals  who  are  New  York  residents,  New  York  State and New York City
personal income taxes).


                                   [reg.tm logo]

                                   (reg.tm)

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

90 Washington Street

New York, NY 10286

TRANSFER AGENT &

DIVIDEND DISBURSING AGENT

Dreyfus Transfer, Inc.

P.O. Box 9671

Providence, RI 02940










Printed in U.S.A.                                             574AR9811

General New York

Municipal Money

Market Fund

Annual Report

November 30, 1998







                                    February 5, 1999





Office of Records
Securities and Exchange Commission
Judiciary Plaza
450 Fifth Street, N.W.
Washington, D.C. 20549

Re:  General New York Municipal Money Market Fund
     File No. 811-4870

Gentlemen:

     Transmitted for filing is one (1) copy of the Annual Report to Shareholders
for the above-referenced Fund as of November 30, 1998 filed pursuant to the
provisions of Section 30 of the Investment Company Act of 1940, as amended.

                                    Very truly yours,




                                    Gina M. Martone

GMM:kwm
Enclosure

Copy for filing to:
National Association of Securities Dealers, Inc.
Attn: Advertising Department




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