DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1996-07-29
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GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this report on the General New York
Municipal Money Market Fund. For its semi-annual reporting period ended May
31, 1996, your Fund produced an annualized yield of 2.89% for Class A shares
and an annualized yield of 2.57% for Class B shares. Income dividends of
approximately $.014 per share and $.013 per share for Class A and Class B
shares, respectively, were paid during the period. Reinvesting these
dividends and calculating the effect of compounding resulted in an annualized
effective yield of 2.92% for Class A shares, and 2.61% for Class B shares.*
These dividends were exempt from Federal and State of New York personal
income taxes, although some income may be subject to the Federal Alternative
Minimum Tax (AMT) for certain shareholders.**
THE ECONOMY
    Recent economic reports show that the economy continues to recover from
its year-end 1995 pause. Spurred by a surge in consumer and business
spending, the annualized Gross Domestic Product grew at a moderate 2.3%
during the first quarter of this year. The Index of Leading Economic
Indicators, a major forecasting index, extended its string of increases for
the third consecutive month in April, the first such three-month advance
since late 1993. Despite a sharp jump in energy prices, inflation remained in
check. For the 12 months ended in April, consumer prices rose 2.9%.
    Despite the relatively benign level of inflation, the economy's expansion
has sparked concern that the Federal Reserve Board could raise short-term
interest rates. So far, the Fed has refrained from tightening monetary
policy, apparently interpreting economic data to mean that the economy
remains on a path of moderate growth unaccompanied by a surge in inflation.
There is now a greater consensus that the Fed will tighten eventually in
order to prevent unacceptable levels of price inflation from coming on the
heels of economic growth.
MARKET/PORTFOLIO ENVIRONMENT
    If one were to trace the trend in short-term municipal rates over this
most recent semi-annual period, the direction would mirror closely the
changes in supply and demand conditions. The six-month cycle would reflect:
higher rates at year-end due to December outflows; a precipitous drop in
yields throughout January as cash returned to the market; price
weakness/higher rates in April as investors tapped their money market funds
to pay income taxes; and yield stability in May as market activity settled
into a trading range. These technical influences continue to be the overriding
factor affecting municipal money rates.
    These conditions, coupled with action(s) taken by the Federal Reserve
Board, provide the framework for our investment strategy - both on a
day-to-day basis and looking ahead over a one-year horizon. During the first
few months of 1996, as a result of uncertainty surrounding potential tax
reform, variable rate demand notes (which represent a significant portion of
your Portfolio's investments) benefited from unusually high yields. While the
concerns were only temporary, they translated for a time into a more
attractive after-tax rate of return than was available to the New York
investor on taxable instruments with similar maturities. During this period,
the purchase of attractively yielding commercial paper in the 90-day range
also allowed us to capture returns similar to those on one-year issues
without a significant extension of average maturity, enabling us to wait out
a lower yield environment in anticipation of higher rates.
    The opportunity to commit to the longer note issues has appeared in
recent weeks and should continue to be available during the summer months as
issuers return to the market with mid-year financings. We expect to take
advantage of these buying opportunities as we monitor potential Fed activity
and any other significant changes in the municipal money market. All new New
York-exempt investments will continue to meet the high credit quality
standards which we require and to provide a significant level of liquidity,
commensurate with the needs of your Fund.
    Included in this report is a series of detailed statements about your
Fund's holdings and its financial condition. We hope they are informative.
Please know that we appreciate greatly your continued confidence in the Fund
and in The Dreyfus Corporation.
                              Sincerely,

                          [Richard J. Moynihan signature logo]

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
                              The Dreyfus Corporation
June 14, 1996
New York, N.Y.

*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
**Some income may be subject to state and local taxes for non-New York
residents.
<TABLE>



GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                                                                             MAY 31, 1996 (UNAUDITED)
                                                                                                    PRINCIPAL
TAX-EXEMPT INVESTMENTS-100.0%                                                                         AMOUNT           VALUE
                                                                                                      _______         _______
<S>                                                                                                <C>             <C>
NEW YORK-95.2%
Babylon Industrial Development Agency, RRR, VRDN (Equity Babylon Project)
    3.75% (LOC; Union Bank of Switzerland) (a,b)............................                        $ 5,000,000    $ 5,000,000
Buffalo, RAN 4.20%, 7/16/96 (LOC; Landesbank Hessen) (a)....................                          9,000,000      9,008,684
Erie County, RAN 4.50%, 9/20/96 (LOC; Union Bank of Switzerland) (a)........                         27,500,000     27,552,185
Erie County Water Authority, Water Revenue, VRDN
    3.35%, Series A (Insured; AMBAC and Liquidity Facility; National Bank of Australia) (b)           9,000,000      9,000,000
Town of Islip Industrial Development Agency, IDR, VRDN
    (Brentwood Distribution Project) 3.50% (LOC; Bankers Trust) (a,b).......                          1,000,000      1,000,000
Metropolitan Transport Authority, Commuter Facilities Revenue, VRDN
    3.50% (LOC: Bank of Tokyo-Mitsubishi, Industrial Bank of Japan,
    Morgan Guaranty Trust Co., National Westminster Bank and Sumitomo Bank) (a,b)                    28,100,000     28,100,000
New York City:
    CP:
      3.35%, 8/15/96 (Insured; AMBAC and Liquidity Facility; Krediet Bank)..                         11,000,000    11,000,000
      3.35%, Series B-9, 8/15/96 (LOC; Chemical Bank) (a)...................                         11,000,000    11,000,000
      3.45%, Series H-3, 8/16/96 (Insured; FSA and Liquidity Facility; Banque Paribus)                5,800,000     5,800,000
    VRDN:
      3.50%, Series A-6 (LOC; Landesbank Hessen) (a,b)......................                         10,000,000    10,000,000
      3.65%, Series B (Insured; MBIA and SBPA; Westdeutsche Landesbank) (b).                         24,300,000    24,300,000
      3.70%, Series A-7  (LOC; Morgan Guaranty Trust Co.) (a,b).............                         7,300,000      7,300,000
New York City Housing Development Corporation, Mortgage Revenue, VRDN:
    (Multi-Family-York Avenue Development Project) 3.65% (LOC; Midland Bank) (a,b)                   8,000,000      8,000,000
    (Park Gate Tower) 3.40% (LOC; Citibank) (a,b)...........................                         2,405,000      2,405,000
    (Residential East 17th Street) 3.70%, Series A (LOC; Chemical Bank) (a,b)                        11,000,000    11,000,000
New York City Industrial Development Agency, VRDN:
    Civil Facility Revenue (Children's Oncology Society/ Ronald McDonald House)
      3.50% (LOC; Barclays Bank) (a,b)......................................                         3,000,000      3,000,000
    IDR:
      3.55%, Series E (LOC; ABN-Amro Bank) (a,b)............................                           900,000        900,000
      (Japan Airlines Co. Limited Project)
          3.75% (LOC; Morgan Guaranty Trust Co.) (a,b)......................                         17,700,000    17,700,000
      (LaGuardia Association Project) 3.70% (LOC; Banque Indosuez) (a,b)....                          8,900,000     8,900,000
New York State, CP:
    3.70%, Series R, 7/17/96 (Revolving Credit Agreement; Westdeutsche Landesbank)                    8,200,000      8,200,000
    3.70%, Series R, 8/12/96 (Revolving Credit Agreement; Westdeutsche Landesbank)                    6,200,000      6,200,000
    BAN 3.70%, Series S, 7/19/96
      (Revolving Credit Agreement; Westdeutsche Landesbank).................                          4,000,000      4,000,000
New York State Energy, Research and Development Authority:
    Electric Facilities Revenue, VRDN (Lilco Project)
      3.50%, Series B (LOC; Toronto Dominion Bank) (a,b)....................                          8,000,000      8,000,000

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                  MAY 31, 1996 (UNAUDITED)
                                                                                                    PRINCIPAL
TAX-EXEMPT INVESTMENTS (CONTINUED)                                                                    AMOUNT           VALUE
                                                                                                     _______           _______
NEW YORK (CONTINUED)
New York State Energy, Research and Development Authority (continued):
    PCR:
      Bonds (New York State Electric and Gas Corp.)
          3.65%, Series D, 12/1/96 (LOC; Union Bank of Switzerland) (a).....                     $  14,615,000    $  14,615,000
      VRDN:
          (Central Hudson Gas and Electric Project)
            3.55%, Series A (LOC; Union Bank of Switzerland) (a,b)..........                         7,800,000        7,800,000
          (Niagara Mohawk Power Corp.):
            3.70%, Series B (LOC; Toronto Dominion Bank) (a,b)..............                         3,900,000      3,900,000
            3.70%, Series C (LOC; Canadian Imperial Bank of Commerce) (a,b).                        18,400,000     18,400,000
            3.90%, Series B (LOC; Morgan Guaranty Trust Co.) (a,b)..........                         9,000,000      9,000,000
            3.90%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b)..........                        21,000,000     21,000,000
New York State Local Government Assistance Corporation, VRDN
    3.40%, Series B (LOC: Credit Suisse and Swiss Bank Corp.) (a,b).........                        41,900,000     41,900,000
New York State Medical Care Facilities Finance Agency, Revenue, VRDN
    (Pooled Equipment Loan Program):
      3.55%, Series I (LOC; Chemical Bank) (a,b)............................                          8,900,000      8,900,000
      3.55%, Series II (LOC; Chemical Bank) (a,b)...........................                         27,500,000     27,500,000
New York State Power Authority, CP 3.75%, 8/16/96 (Liquidity Facility: Bank of America,
    The Bank of New York, Bank of Nova Scotia, Bank of Tokyo-Mitsubishi,
    Chemical Bank, Citibank, Industrial Bank of Japan and Sanwa Bank).......                         20,000,000     20,000,000
North Hempstead Solid Waste Management Authority,
    Solid Waste Management Revenue, Refunding, VRDN
    3.40%, Series A (LOC; National Westminster Bank) (a,b)..................                          3,750,000      3,750,000
Onondaga County Industrial Development Agency, IDR, VRDN
    (Edgecomb Metals Co. Project) 3.50% (LOC; Banque Nationale de Paris) (a,b)                        2,000,000      2,000,000
Port Authority of New York and New Jersey, Special Obligation Revenue, VRDN
    3.60%, Series 3 (LOC; Deutsche Bank) (a,b)..............................                         11,900,000     11,900,000
Rochester, BAN 3.75%, Series I, 3/11/97.....................................                         18,000,000     18,067,454
Sachem Central School District, TAN 4.50%, 6/27/96..........................                         20,000,000     20,010,546
Smithtown Central School District, TAN 4.10%, 6/27/96.......................                          9,000,000      9,003,388
Suffolk County, TAN:
    4%, Series I, 8/15/96 (LOC: Canadian Imperial Bank of Commerce,
      National Westminster Bank and Westdeutsche Landesbank) (a)............                         15,000,000    15,021,150
    4.50%, Series II, 9/12/96 (LOC: Canadian Imperial Bank of Commerce,
      National Westminster Bank and Westdeutsche Landesbank) (a)............                         32,000,000    32,056,318
Triborough Bridge and Tunnel Authority, Special Obligation, VRDN
    3.40% (Insured; FGIC) (b)...............................................                         27,900,000    27,900,000
Westchester County, TAN 3.75%, 12/11/96.....................................                         12,000,000    12,040,246

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                MAY 31, 1996 (UNAUDITED)
                                                                                                    PRINCIPAL
TAX-EXEMPT INVESTMENTS (CONTINUED)                                                                   AMOUNT           VALUE
                                                                                                      _______         _______
NEW YORK (CONTINUED)
Yonkers Industrial Development Authority, Civic Revenue, Consumers Union Facilities,
    VRDN 3.40% (Insured; AMBAC and Liquidity Facility; Credit Local de France) (b)                  $ 3,400,000    $ 3,400,000
U.S. RELATED-4.8%
Commonwealth of Puerto Rico Government Development Bank, Refunding:
    CP 3.55%, 7/16/96.......................................................                         10,000,000    10,000,000
    VRDN 3.25% (LOC; Credit Suisse) (a,b)...................................                         18,000,000    18,000,000
                                                                                                                   ____________
TOTAL INVESTMENTS
    (cost $583,529,971).....................................................                                      $583,529,971
                                                                                                                  =============

</TABLE>

<TABLE>

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND

SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <C>      <C>
AMBAC         American Municipal Bond Assurance Corporation      PCR      Pollution Control Revenue
BAN           Bond Anticipation Notes                            RAN      Revenue Anticipation Notes
CP            Commercial Paper                                   RRR      Resources Recovery Revenue
FGIC          Financial Guaranty Insurance Company               SBPA     Standby Bond Purchase Agreement
FSA           Financial Security Assurance                       TAN      Tax Anticipation Notes
IDR           Industrial Development Revenue                     VRDN     Variable Rate Demand Notes
LOC           Letter of Credit
MBIA          Municipal Bond Investors Assurance
                 Insurance Corporation
</TABLE>

<TABLE>

SUMMARY OF COMBINED RATINGS (UNAUDITED)
FITCH (C)              OR          MOODY'S             OR         STANDARD & POOR'S                      PERCENTAGE OF VALUE
_____                              _____                          _________________                      ____________________
<S>                                <C>                            <C>                                       <C>
F1+/F1                             VMIG1/MIG1,P1 (d)              SP1+/SP1,A1+/A1 (d)                       96.6%
AAA/AA (e)                         Aaa/Aa (e)                     AAA/AA (e)                                 3.1
Not Rated (f)                      Not Rated (f)                  Not Rated (f)                               .3
                                                                                                           ______
                                                                                                           100.0%
                                                                                                          =========
</TABLE>

NOTES TO STATEMENT OF INVESTMENTS:
    (a)  Secured by letters of credit. At May 31, 1996, 67.2% of the Fund's
    net assets are backed by letters of credit issued by domestic banks, and
    foreign banks.
    (b)  Securities payable on demand. The interest rate, which is subject to
    change, is based upon bank prime rates or an index of market interest
    rates.
    (c)  Fitch currently provides creditworthiness information for a limited
    number of investments.
    (d)  P1 and A1 are the highest ratings assigned tax-exempt commercial
    paper by Moody's and Standard & Poor's, respectively.
    (e)  Notes which are not F, MIG or SP rated are represented by bond
    ratings of the issuers.
    (f)  Securities which, while not rated by Fitch, Moody's or Standard &
    Poor's have been determined by the Fund's Board of Trustees to be of
    comparable quality to those rated securities in which the Fund may
    invest.








See independent accountants' review report and notes to financial statements.
<TABLE>

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES                                                             MAY 31, 1996 (UNAUDITED)
<S>                                                                                          <C>                  <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                       $583,529,971
    Interest receivable.....................................................                                          5,600,177
    Prepaid expenses........................................................                                            123,874
                                                                                                                    ___________
                                                                                                                    589,254,022
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                 $   312,994
    Due to Distributor......................................................                      48,691
    Due to Custodian........................................................                   1,154,694
    Accrued expenses and other liabilities..................................                      124,120             1,640,499
                                                                                               __________           ___________
NET ASSETS..................................................................                                       $587,613,523
                                                                                                                   ============
REPRESENTED BY:
    Paid-in capital.........................................................                                        $587,681,016
    Accumulated net realized (loss) on investments..........................                                            (67,493)
                                                                                                                    ___________
NET ASSETS at value.........................................................                                        $587,613,523
                                                                                                                   ============
Shares of Beneficial Interest outstanding:
    Class A Shares
      (unlimited number of $.001 par value shares authorized)...............                                         557,398,204
                                                                                                                   ============
    Class B Shares
      (unlimited number of $.001 par value shares authorized)...............                                         30,282,812
                                                                                                                   ============
NET ASSET VALUE per share:
    Class A Shares
      ($557,330,711 / 557,398,204 shares)...................................                                              $1.00
                                                                                                                          =====
    Class B Shares
      ($30,282,812 / 30,282,812 shares).....................................                                              $1.00
                                                                                                                          =====


</TABLE>





See independent accountants' review report and notes to financial
investments.
<TABLE>

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF OPERATIONS                                                               SIX MONTHS ENDED MAY 31, 1996 (UNAUDITED)
<S>                                                                                              <C>                 <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                         $10,929,761
    EXPENSES:
      Management fee-Note 2(a)..............................................                     $1,528,628
      Shareholder servicing costs-Note 2(c).................................                        467,291
      Distribution fees (Class B shares)-Note 2(b)..........................                         15,136
      Custodian fees........................................................                         28,572
      Professional fees.....................................................                         24,557
      Registration fees.....................................................                         14,166
      Trustees' fees and expenses-Note 2(d).................................                         14,115
      Prospectus and shareholders' reports..................................                         10,167
      Miscellaneous.........................................................                         11,616
                                                                                                 ___________
            TOTAL EXPENSES..................................................                      2,114,248
      Less-reduction in shareholder servicing costs due to
          undertaking-Note 2(c).............................................                         11,669
                                                                                                 ___________
            NET EXPENSES....................................................                                           2,102,579
                                                                                                                      __________
INVESTMENT INCOME-NET, representing net increase in net assets
    resulting from operations...............................................                                        $  8,827,182
                                                                                                                   =============


</TABLE>











See independent accountants' review report and notes to financial statements.
<TABLE>

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                         YEAR ENDED            SIX MONTHS ENDED
                                                                                         NOVEMBER 30,            MAY 31, 1996
                                                                                            1995                 (UNAUDITED)
                                                                                         ________                ___________
<S>                                                                             <C>                              <C>
OPERATIONS:
    Investment income-net.............................................          $      21,275,753                $  8,827,182
    Net realized (loss) on investments................................                    (18,598)                      __
                                                                                         ________                ___________
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........                 21,257,155                   8,827,182
                                                                                         ________                ___________
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares..................................................                (21,275,753)                (8,635,767)
      Class B shares..................................................                          __                  (191,415)
                                                                                         ________                ___________
          TOTAL DIVIDENDS.............................................                (21,275,753)                (8,827,182)
                                                                                         ________                ___________
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares..................................................              1,207,959,406                 596,899,255
      Class B shares..................................................                        101                  47,114,245
    Dividends reinvested:
      Class A shares..................................................                 20,215,913                   8,166,918
      Class B shares..................................................                          __                    191,415
    Cost of shares redeemed:
      Class A shares..................................................            (1,282,061,656)                 (683,748,609)
      Class B shares..................................................                        __                   (17,022,950)
                                                                                         ________                ___________
          (DECREASE) IN NET ASSETS FROM BENEFICIAL INTEREST TRANSACTIONS             (53,886,236)                  (48,399,726)
                                                                                         ________                ___________
            TOTAL (DECREASE) IN NET ASSETS............................               (53,904,834)                  (48,399,726)
NET ASSETS:
    Beginning of period...............................................                689,918,083                  636,013,249
                                                                                         ________                ___________
    End of period.....................................................             $  636,013,249                $ 587,613,523
                                                                                   ==============                ==============

</TABLE>






See independent accountants' review report and notes to financial statements.

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.
<TABLE>


                                                                                     CLASS A SHARES
                                               ________________________________________________________________________________
                                                                                                              SIX MONTHS ENDED
                                                                   YEAR ENDED NOVEMBER 30,                       MAY 31, 1996
                                               ___________________________________________________________
PER SHARE DATA:                                    1991        1992        1993         1994        1995          (UNAUDITED)
                                                  ______      ______      ______       ______      ______         __________
<S>                                               <C>        <C>         <C>          <C>         <C>              <C>
    Net asset value, beginning of period..        $  1.00    $  1.00     $  1.00      $  1.00     $  1.00          $  1.00
                                                  ______      ______      ______       ______      ______          ________
    INVESTMENT OPERATIONS;
    Investment income-net.................           .044       .028       .020         .023         .032             .015
                                                  ______      ______      ______       ______      ______          ________
    DISTRIBUTIONS;
    Dividends from investment income-net..         (.044)      (.028)     (.020)        (.023)     (.032)           (.015)
                                                  ______      ______      ______       ______      ______          ________
    Net asset value, end of period........        $  1.00    $  1.00     $  1.00      $  1.00      $  1.00          $  1.00
                                                  =======    =======     ========     ========     =======          =========
TOTAL INVESTMENT RETURN...................          4.45%       2.78%      2.00%        2.34%      3.28%               2.91%*
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets.         .09%        .25%       .32%         .34%        .58%               .68%*
    Ratio of net investment income to
      average net assets..................          4.44%       2.99%      1.98%        2.33%      3.23%               2.89%*
    Decrease reflected in above expense
      ratios due to undertakings by
      the Manager                                    .55%       .38%        .35%        .32%         .05%                 -
    Net Assets, end of period (000's Omitted)    $586,933    $630,899    $612,441    $689,918    $636,013             $557,331
*  Annualized.





</TABLE>




See independent accountants' review report and 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.
<TABLE>


                                                                                                CLASS B SHARES
                                                                                     _______________________________________
                                                                                     YEAR ENDED           SIX MONTHS ENDED
                                                                                    NOVEMBER 30,             MAY 31, 1996
                                                                                      1995(1)                 (UNAUDITED)
                                                                                     _______                  ___________
<S>                                                                                  <C>                       <C>
PER SHARE DATA:
    Net asset value, beginning of period....................................         $  1.00                   $  1.00
                                                                                      _______                   _______
    INVESTMENT OPERATIONS;
    Investment income-net...................................................            .006                      .013
                                                                                      _______                   _______
    DISTRIBUTIONS;
    Dividends from investment income-net....................................          (.006)                     (.013)
                                                                                      _______                   _______
    Net asset value, end of period..........................................        $  1.00                    $  1.00
                                                                                    ========                  =========
TOTAL INVESTMENT RETURN.....................................................         2.82%(2)                  2.59%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets.................................         1.04%(2)                   .95%(2)
    Ratio of net investment income to average net assets....................         3.64%(2)                  2.52%(2)
    Decrease reflected in above expense ratios due to
      undertakings by the Manager...........................................            -                       .15%(2)
    Net Assets, end of period (000's Omitted)...............................            -                      $30,283
(1)    From September 8, 1995 (commencement of initial offering) to
       November 30, 1995.
(2)    Annualized.

</TABLE>








See independent accountants' review report and notes to financial statements.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
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 ("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 ("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") acts as the
distributor of the Fund's shares, which are sold to the public without a
sales charge. Class A shares and Class B shares are identical except as to
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 at an
annual rate of .05% of the value of the average daily net assets of Class B.
    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 of $1.00.
    (A) PORTFOLIO VALUATION: Investments 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.
    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. 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 Internal
Revenue 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 $67,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1995. If not
applied, $9,000 of the carryover expires in fiscal 1998, $40,000 expires in
fiscal 2002 and $18,000 expires in fiscal 2003.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

    At May 31, 1996, 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 for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses, exceed 1 1/2% of the average value of the Fund's net
assets for any full fiscal year. There was no reimbursement for the six
months ended May 31, 1996.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, the Fund
directly bears 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, the Fund reimburses the
Distributor for payments made to third parties for distributing the Fund's
Class B shares at an aggregate annual rate of .20 of 1% of the value of the
average daily net assets of Class B. During the six months ended May 31,
1996, $15,136 was charged to the Fund pursuant to the Class B Distribution
Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan, with respect to
Class A ("Class A Shareholder Services Plan"), the Fund reimburses 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 Fund's 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 the Fund and providing reports
and other information, and services related to the maintenance of shareholder
accounts. During the six months ended May 31, 1996, the Fund was charged an
aggregate of $282,997 pursuant to the Class A Shareholder Services Plan.
    Pursuant to the Fund's Shareholder Services Plan, with respect to Class B
("Class B Shareholder Services Plan"), effective September 8, 1995, the Fund
pays 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 the
Fund and providing reports and other information, and services related to the
maintenance of shareholder accounts. The Distributor may make payments to
Service Agents (a securities dealer, financial institution or other industry
professional) in respect of their services. The Distributor determines the
amounts to be paid to Service Agents.
    The Manager has undertaken, through November 30, 1996, that if the
aggregate expenses of Class B of the Fund, (excluding certain expenses as
described above) exceed .95 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 relating to Class B to the extent of
any excess expense and up to the full fee payable under such Plan. During the
six months ended May 31, 1996, the Fund was charged an aggregate of $18,920,
all of which $11,669 was reimbursed by the Manager.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
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. Such
compensation amounted to $88,401 for the six months ended May 31, 1996.
    (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
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF TRUSTEES
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
    We have reviewed the accompanying statement of assets and liabilities of
General New York Municipal Money Market Fund, including the statement of
investments, as of May 31, 1996, and the related statements of operations and
changes in net assets and financial highlights for the six month period ended
May 31, 1996. These financial statements and financial highlights are the
responsibility of the Fund's management.
    We conducted our review in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures
to financial data, and making inquiries of persons responsible for financial
and accounting matters. It is substantially less in scope than an audit
conducted in accordance with generally accepted auditing standards, which
will be performed for the full year with the objective of expressing an
opinion regarding the financial statements and financial highlights taken as
a whole. Accordingly, we do not express such an opinion.
    Based on our review, we are not aware of any material modifications that
should be made to the interim financial statements and financial highlights
referred to above for them to be in conformity with generally accepted
accounting principles.
    We have previously audited, in accordance with generally accepted
auditing standards, the statement of changes in net assets for the year ended
November 30, 1995 and financial highlights for each of the five years in the
period ended November 30, 1995 and in our report dated January 8, 1996, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.

                          [Ernst & Young LLP signature logo]

New York, New York
July 5, 1996


[Dreyfus lion "d" logo]
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.
One American Express Plaza
Providence, RI 02903




Further information is contained
in the Prospectus, which must
precede or accompany this report.




Printed in U.S.A.                        574/700SA965
[Dreyfus logo]
General New York
Municipal
Money Market Fund
Semi-Annual
Report
May 31, 1996










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