DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1996-02-12
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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 annual reporting period ended November
30, 1995, your Fund produced a yield of 3.23% for Class A shares and an
annualized yield of 2.80% for Class B shares. For investors in New York City
in the highest income tax bracket, this equates to a taxable equivalent yield
of 6.10% and, annualized, 5.29%, respectively.* Income dividends of
approximately $.032 per share for Class A shares and $.006 for Class B shares
were paid during the period. Reinvesting these dividends and calculating the
effect of compounding resulted in an effective yield of 3.28% and,
annualized, 2.83%, respectively. ** These dividends were exempt from Federal,
State of New York and New York City personal income taxes, although some
income may be subject to the Federal Alternative Minimum Tax (AMT) for
certain shareholders.
THE ECONOMY
    Modest economic growth and low inflation have spurred a dramatic,
year-long rally in the bond market. Short-term rates rates have fallen as
well. The Federal Reserve Board's reduction of the Fed Funds rate confirms
what investors had already suspected: that inflation, at least for the
immediate future, is under control. Now questions abound regarding the
duration of the economic recovery and the likelihood of recession.
    The economic recovery of the 1990s was productivity-driven. Corporations
implemented extraordinary cost control measures that, while dramatically
improving bottom line earnings, now contribute to the slow rate of employment
growth. Job creation is a significant factor that affects consumer spending
and a major component of economic activity. The pace of new job creation,
currently at its slowest since World War II, is worrisome. Indeed, wages and
salaries grew at under 3% over the past year, barely keeping pace with
inflation. Still, surveys indicate that consumers remain optimistic, despite
indications that their spending is being affected by the slow growth in
disposable income. Recent reports on retail sales confirm this reticence in
spending. A consumer-led weakening of the economy could lead to further
Federal Reserve easing of monetary policy.
    It was concern about lagging economic growth that prompted the Federal
Reserve to ease the Federal Funds rate in July. The housing market and new
home construction had been helped earlier this year by low interest rates,
though both have exhibited signs of weakness recently. Another engine of
economic growth, business capital spending, has been solid. Exports represent
another bright area of the economy. Because of the new competitiveness of
American businesses abroad, the U.S. trade deficit continues to shrink.
Through September, the trade deficit with Japan narrowed for the sixth
consecutive month. Exports, while a relatively small component of overall
economic activity in this country, provide an important support for the job
market. If U.S. products lose competitiveness in world markets, foreign
orders may go elsewhere and jobs could be lost here.
MARKET ENVIRONMENT
    In addition to the impact of action taken by the Federal Reserve Board,
technical factors (i.e. supply/demand) contributed to a significant
strengthening of market conditions in late June and early July. Demand
exceeded supply during this time, and short-term yields on municipal issues
dropped accordingly.
    In the Fall, rates on short-term issues settled into a trading range.
However, a steady interchange of variable rate demand notes (VRDNs) between
corporate holders and municipal money market funds kept
rates on these securities attractive, which resulted in an inverted yield
curve (where rates on shorter maturities are higher than rates on longer
issues) through most of the season. We believe that this situation will
change dramatically in January as cashflows into municipal money market funds
increase demand for VRDNs and their rates drop.
THE PORTFOLIO
    With the inverted yield curve, daily and weekly demand notes yielded
moderately more than both commercial paper and notes through most of the
period. But since this situation is expected to change, our investment
strategy involved an attempt to lengthen the maturity, where possible, and to
lock in rates that we felt would outperform variable rate notes early in
1996.
    The commercial paper and one-year note markets provided the means for
extending maturity while attempting to maintain a competitive yield. However,
our success in achieving the desired average maturity was somewhat limited
due to a dearth of high quality issues from which to choose. As a result,
your Fund's current average maturity still leaves room to extend should we
feel a change in market or supply conditions warrants it.
    The Fund's goal - 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 - continues to guide
our portfolio decisions.
    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.
                              Very truly yours,

                          [Richard J. Moynihan signature logo]

                              Richard J. Moynihan
                              Director, Municipal Portfolio Management
December 15, 1995
New York, N.Y.

*  Tax equivalent yield is based on the highest Federal (39.6%), State of New
York (4.76%) and New York City (2.69%) income tax bracket.
**Effective and annualized effective yields are based upon dividends declared
daily and reinvested monthly.

<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                                                                                NOVEMBER 30, 1995
                                                                                                    PRINCIPAL
TAX-EXEMPT INVESTMENTS-100.0%                                                                         AMOUNT           VALUE
                                                                                                       _______        _______
<S>                                                                                             <C>             <C>
NEW YORK-96.7%
Erie County, RAN 4.50%, 9/20/96 (LOC; Union Bank of Switzerland) (a)........                     $  27,500,000  $  27,638,220
Erie County Water Authority, Water Revenue, VRDN 3.65%, Series A
    (Insured; AMBAC and Liquidity Facility; Industrial Bank of Japan) (b)...                         9,000,000      9,000,000
Town of Islip Industrial Development Agency, IDR, VRDN
    (Brentwood Distribution Project) 3.95% (LOC; Bankers Trust) (a,b).......                         1,000,000      1,000,000
Metropolitan Transport Authority, Commuter Facilities Revenue, VRDN
    3.55% (LOC: Bank of Tokyo, Industrial Bank of Japan, Mitsubishi Bank,
Morgan Bank,
    Morgan Guaranty Trust Co., National Westminster Bank and Sumitomo Bank) (a,b)                   28,100,000     28,100,000
Monroe County, RAN 4.50%, 3/14/96...........................................                         10,000,000    10,020,457
New York City, VRDN:
    3.35%, Series A-6 (LOC; Landesbank Hessen) (a,b)........................                         10,000,000    10,000,000
    3.70%, Series B (Insured; MBIA and Standby Liquidity Agreement; Rabobank) (b)                     3,600,000     3,600,000
    3.70%, Series B (Insured; MBIA and SBPA; Deutsche Landesbank) (b).......                         4,400,000      4,400,000
    3.75%, Series B-9 (Insured; FSA and Liquidity Facility; Banque Paribas) (b)                      5,800,000      5,800,000
    3.80%, Series E-6 (Insured; FGIC) (b)...................................                         7,000,000      7,000,000
    3.85%, Series A-4 (LOC; Chemical Bank) (a,b)............................                         5,200,000      5,200,000
    Refunding 3.85%, Series H (Insured; AMBAC, Liquidity Facility; Krediet Bank) (b)                11,000,000     11,000,000
New York City Housing Development Corporation, Mortgage Revenue, VRDN:
    (Multi-Family-York Avenue Development Project) 3.85% (LOC; Chemical Bank) (a,b)                  8,000,000      8,000,000
    (Park Gate Tower) 3.50% (LOC; Citibank) (a,b)...........................                         2,720,000      2,720,000
    (Residential East 17th Street) 3.80%, Series A (LOC; Chemical Bank) (a,b)                        16,600,000    16,600,000
New York City Industrial Development Agency, VRDN:
    Civil Facility Revenue (Children's Oncology Society/ Ronald McDonald
House)
      3.45% (LOC; Barclays Bank) (a,b)......................................                         3,100,000      3,100,000
    IDR:
      3.60%, Series E (LOC; ABN-Amro Bank) (a,b)............................                           900,000        900,000
      (Field Hotel Association JFK Project) 3.60% (LOC; Banque Indosuez) (a,b)                       9,400,000      9,400,000
      (Japan Airlines Co. Limited Project) 4.% (LOC; Morgan Guaranty Trust Co.) (a,b)               13,300,000     13,300,000
      (LaGuardia Association Project) 3.60% (LOC; Banque Indosuez) (a,b)....                         8,900,000      8,900,000
New York City Municipal Water Finance Authority, Water and Sewer Systems
Revenue,
    VRDN 4%, Series A (Insured; FGIC) (b)...................................                         12,500,000    12,500,000
New York State Dormitory Authority, Revenues, CP (Memorial Sloan Kettering)
    3.70%, Series D, 12/7/95 (LOC; Chemical Bank) (a).......................                         29,800,000    29,800,000
New York State Energy, Research and Development Authority:
    Electric Facilities Revenue, VRDN (Lilco Project)
      3.60%, Series B (LOC; Toronto Dominion Bank) (a,b)....................                         8,000,000      8,000,000
    PCR:
      Bonds:
          (Lilco Project) 4.70%, Series A, 3/1/96 (LOC; Deutsche Bank) (a)..                         10,000,000    10,000,000
          (New York State Electric and Gas Corp.):
            4.60%, Series D, 12/1/95 (LOC; Union Bank of Switzerland) (a)...                         11,450,000    11,450,000

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                         NOVEMBER 30, 1995
                                                                                                    PRINCIPAL
TAX-EXEMPT INVESTMENTS (CONTINUED)                                                                    AMOUNT          VALUE
                                                                                                      _______         _______
NEW YORK (CONTINUED)
New York State Energy, Research and Development Authority (continued):
    PCR (continued):
      Bonds (continued):
          (New York State Electric and Gas Corp.) (continued):
            4.65%, 3/15/96 (LOC; JP Morgan) (a)............................                       $  12,000,000   $12,000,000
            VRDN 3.70%, Series D (LOC; Union Bank of Switzerland) (a,b).....                         14,400,000    14,400,000
      VRDN:
          (Central Hudson Gas and Electric Project)
            3.80%, Series A (LOC; Union Bank of Switzerland) (a,b)..........                         3,800,000      3,800,000
          (Niagara Mohawk Power Corp.):
            3.80%, Series B (LOC; Toronto Dominion Bank) (a,b)..............                         3,900,000      3,900,000
            3.80%, Series C (LOC; Canadian Imperial Bank of Commerce) (a,b).                         18,400,000    18,400,000
            3.95%, Series A (LOC; Toronto Dominion Bank) (a,b)..............                         21,800,000    21,800,000
            4.05%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b)..........                         21,000,000    21,000,000
New York State Local Government Assistance Corporation, VRDN
    3.50%, Series B (LOC: Credit Suisse and Swiss Bank Corp.) (a,b).........                         42,600,000    42,600,000
New York State Medical Care Facilities Finance Agency, Revenue, VRDN
    (Pooled Equipment Loan Program):
      3.55%, Series II (LOC; Chemical Bank) (a,b)...........................                         9,400,000      9,400,000
      3.65%, Series I (LOC; Chemical Bank) (a,b)............................                         27,500,000    27,500,000
New York State Power Authority, CP 3.70%, 12/13/95 (Liquidity Facility:
    Bank of America, The Bank of New York, Bank of Nova Scotia, Chemical Bank,
    Citibank, Industrial Bank of Japan, Mitsubishi Bank and Sanwa Bank).....                         20,000,000    20,000,000
New York State Thruway Authority, General Revenues, VRDN
    3.80% (Insured; FGIC and Liquidity Facility) (b)........................                         11,200,000    11,200,000
Niagara County, BAN 5.50%, 1/25/96..........................................                         8,900,000      8,905,740
North Hempstead Solid Waste Management Authority,
    Solid Waste Management Revenue, Refunding, VRDN
    3.50%, Series A (LOC; National Westminster Bank) (a,b)..................                         11,050,000    11,050,000
Onondaga County Industrial Development Agency, IDR, VRDN
    (Edgecomb Metals Co. Project) 3.95% (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
    3.45%, Series 3 (LOC; Deutsche Bank) (a,b)..............................                         11,900,000    11,900,000
Rochester, BAN 4.75%, 3/12/96...............................................                         11,000,000    11,022,555
Sachem Central School District, TAN 4.50%, 6/27/96..........................                         20,000,000    20,084,771
Smithtown Central School District, TAN 4.10%, 6/27/96.......................                         9,000,000      9,027,233
Suffolk County, TAN 4.50%, 9/12/96 (LOC: Canadian Imperial Bank of Commerce,
    National Westminster and West Landesbank) (a)...........................                         32,000,000    32,156,379
Triborough Bridge and Tunnel Authority, Special Obligation, VRDN
    3.50% (Insured; FGIC) (b)...............................................                         22,900,000    22,900,000

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                        NOVEMBER 30, 1995
                                                                                                     PRINCIPAL
TAX-EXEMPT INVESTMENTS (CONTINUED)                                                                     AMOUNT           VALUE
                                                                                                       _______          _______
NEW YORK (CONTINUED)
Westchester County, TAN 5%, 12/14/95........................................                      $  15,000,000    $ 15,002,585
Yonkers Industrial Development Authority, Civic Revenue, Consumers Union
Facilities,
    VRDN 3.45% (Insured; AMBAC and Liquidity Facility; Credit Local de France) (b)                    3,400,000      3,400,000
U.S. RELATED-3.3%
Commonwealth of Puerto Rico Government Development Bank, Refunding, VRDN
    3.30% (LOC; Credit Suisse) (a,b)........................................                         21,000,000    21,000,000
                                                                                                                       ______-
TOTAL INVESTMENTS
    (cost $631,877,940).....................................................                                      $631,877,940
                                                                                                                       =======
</TABLE>
<TABLE>
<CAPTION>
SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <S>      <C>
AMBAC         American Municipal Bond Assurance Corporation      MBIA     Municipal Bond Investors Assurance
BAN           Bond Anticipation Notes                                         Insurance Corporation
CP            Commercial Paper                                   PCR      Pollution Control Revenue
FGIC          Financial Guaranty Insurance Company               RAN      Revenue Anticipation Notes
FSA           Financial Security Assurance                       SBPA     Standby Bond Purchase Agreement
IDR           Industrial Development Revenue                     TAN      Tax Anticipation Notes
LOC           Letter of Credit                                   VRDN     Variable Rate Demand Notes
</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)               94.1%
AAA/AA (e)                         Aaa/Aa (e)                     AAA/AA (e)                          .5
Not Rated (f)                      Not Rated (f)                  Not Rated (f)                      5.4
                                                                                                    ___-
                                                                                                   100.0%
                                                                                                   =====
</TABLE>
NOTES TO STATEMENT OF INVESTMENTS:
(a)    Secured by letters of credit. At November 30, 1995, 70.3% of the
Fund's net assets are backed by letters of credit issued by domestic banks,
foreign banks and brokerage firms, of which Chemical Bank provided letters of
credit to 15.2% of the Fund's net assets.
(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 notes to financial statements.

<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES                                                NOVEMBER 30, 1995
<S>                                                                                                <C>            <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                      $631,877,940
    Interest receivable.....................................................                                         4,585,602
    Prepaid expenses........................................................                                            21,731
                                                                                                                       -------
                                                                                                                   636,485,273
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                       $289,145
    Due to Custodian........................................................                         45,023
    Accrued expenses and other liabilities..................................                         137,856           472,024
                                                                                                       -----           -------
NET ASSETS  ................................................................                                      $636,013,249
                                                                                                                       =======
REPRESENTED BY:
    Paid-in capital.........................................................                                      $636,080,742
    Accumulated net realized (loss) on investments..........................                                           (67,493)
                                                                                                                       -------
NET ASSETS at value.........................................................                                      $636,013,249
                                                                                                                       =======
Shares of Beneficial Interest outstanding:
    Class A Shares
      (unlimited number of $.001 par value shares authorized)...............                                       636,080,642
                                                                                                                       =======
    Class B Shares
      (unlimited number of $.001 par value shares authorized)...............                                               101
                                                                                                                       =======
NET ASSET VALUE per share:
    Class A Shares
      ($636,013,148 / 636,080,642 shares)...................................                                             $1.00
                                                                                                                       =======
    Class B Shares
      ($101 / 101 shares)...................................................                                             $1.00
                                                                                                                       =======




See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF OPERATIONS                                                                            YEAR ENDED NOVEMBER 30, 1995
<S>                                                                                               <C>                <C>
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                         $25,080,118
    EXPENSES:
      Management fee-Note 2(a)..............................................                      $3,294,375
      Shareholder servicing costs-Note 2(c).................................                         705,352
      Custodian fees........................................................                          53,580
      Professional fees.....................................................                          39,823
      Trustees' fees and expenses-Note 2(d).................................                          23,286
      Prospectus and shareholders' reports..................................                          18,007
      Registration fees.....................................................                           7,762
      Miscellaneous.........................................................                          19,770
                                                                                                       _____
            TOTAL EXPENSES..................................................                       4,161,955
      Less-reduction in management fee due to
          undertakings-Note 2(a)............................................                         357,590
                                                                                                       _____
            NET EXPENSES....................................................                                          3,804,365
                                                                                                                         ______
INVESTMENT INCOME-NET.......................................................                                         21,275,753
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                            (18,598)
                                                                                                                         ______
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                        $21,257,155
                                                                                                                       =======



See notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                                 YEAR ENDED NOVEMBER 30,
                                                                                     ------------------------------------------
                                                                                       1994                             1995
                                                                                     ---------                        ---------
<S>                                                                              <C>                              <C>
OPERATIONS:
    Investment income-net................................................        $ 15,380,550                     $  21,275,753
    Net realized (loss) on investments...................................             (39,573)                          (18,598)
                                                                                     ---------                        ---------
          NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS...........          15,340,977                        21,257,155
                                                                                     ---------                        ---------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A shares.....................................................         (15,380,550)                      (21,275,753)
                                                                                     ---------                        ---------
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A shares.....................................................         1,264,417,458                    1,207,959,406
      Class B shares.....................................................           __                                       101
    Dividends reinvested;
      Class A shares.....................................................        14,609,328                          20,215,913
    Cost of shares redeemed;
      Class A shares.....................................................        (1,201,510,009)                (1,282,061,656)
                                                                                     ---------                        ---------
          INCREASE (DECREASE) IN NET ASSETS FROM BENEFICIAL
            INTEREST TRANSACTIONS........................................            77,516,777                    (53,886,236)
                                                                                     ---------                        ----------
            TOTAL INCREASE (DECREASE) IN NET ASSETS......................            77,477,204                    (53,904,834)
NET ASSETS:
    Beginning of year....................................................           612,440,879                     689,918,083
                                                                                     ---------                        ---------
    End of year..........................................................      $   689,918,083                  $   636,013,249
                                                                                     =========                        =========




See notes to financial statements.
</TABLE>
<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 year indicated. This
information has been derived from the Fund's financial statements.

                                                                    CLASS A SHARES                              CLASS B SHARES
                                                 ----------------------------------------------------               --------
                                                                                                                   YEAR ENDED
                                                                YEAR ENDED NOVEMBER 30,                           NOVEMBER 30,
                                                 ----------------------------------------------------
PER SHARE DATA:                                    1991       1992       1993       1994       1995                  1995(1)
                                                   ____       ____       ____       ____       _____                ________
    <S>                                          <C>         <C>       <C>         <C>        <C>                    <C>
    Net asset value, beginning of year..         $   1.00    $ 1.00    $  1.00     $ 1.00     $ 1.00                 $ 1.00
                                                   ____       ____       ____       ____       _____                  ____
    INVESTMENT OPERATIONS:
    Investment income-net...............          .0436      .0275      .0198      .0232      .0323                  .0064
    Net realized and unrealized gain (loss)
      on investments....................             -        .0001        -      (.0001)        -                      -
                                                   ____       ____       ____       ____       _____                  ____
      TOTAL FROM INVESTMENT OPERATIONS..          .0436      .0276      .0198      .0231      .0323                  .0064
                                                   ____       ____       ____       ____       _____                  ____
    DISTRIBUTIONS;
    Dividends from investment income-net         (.0436)     (.0275)   (.0198)     (.0232)    (.0323)                (.0064)
                                                   ____       ____       ____       ____       _____                  ____
    Net asset value, end of year........           $ 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%                 2.82%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets       .09%        .25%       .32%      .34%         .58%                1.04%(2)
    Ratio of net investment income to average
      net assets........................           4.44%      2.99%      1.98%      2.33%      3.23%                3.64%(2)
    Decrease reflected in above expense ratios
      due to undertakings by the Manager            .55%      .38%       .35%       .32%        .05%                    -
    Net Assets, end of year (000's Omitted)      $586,933   $630,899   $612,441   $689,918   $636,013                   -
    (1)  From September 8, 1995 (commencement of initial offering) to November 30, 1995.
    (2)  Annualized.


See notes to financial statements.
</TABLE>

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a non-diversified open-end management investment company. 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. The Distributor,
located at One Exchange Place, Boston, Massachusetts 02109, is a wholly-owned
subsidiary of FDI Distribution Services, Inc., a provider of mutual fund
administration services, which in turn is a wholly-owned subsidiary of FDI
Holdings, Inc., the parent company of which is Boston Institutional Group,
Inc. The Dreyfus Corporation ("Manager") serves as the Fund's investment
adviser. The Manager is a direct subsidiary of Mellon Bank, N.A.
    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.
    On July 19, 1995, the Fund's Board of Trustees approved an amendment to
the Fund's Charter to provide for the issuance of additional shares of the
Fund. The amendment was approved by Fund shareholders on September 1, 1994.
Pursuant to the amendment, the Fund's existing authorized shares were
classified as Class A shares and one billion newly authorized shares of
Common Stock of the Fund, par value $.01 per share, were classified as Class
B shares. The Fund began offering both Class A and Class B shares on
September 8, 1995. 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.
    (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.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, which can
distribute tax exempt dividends, by complying with the applicable provisions
of the 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.
    At November 30, 1995, 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 average
daily value of the Fund's 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. The Manager had undertaken from December 1,
1994 to May 26, 1995 to reduce the management fee paid by the Fund to the
extent that the Fund's aggregate expenses (exclusive of certain expenses as
described above) exceeded specified annual percentages of the Fund's average
daily net assets. The reduction in management fee, pursuant to the
undertakings, amounted to $357,590 for the year ended November 30, 1995.
    Effective December 1, 1995, Dreyfus Transfer, Inc., a wholly-owned
subsidiary of the Manager serves as the Fund's Transfer and Dividend
Disbursing Agent.
    (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, effective
September 8, 1995, the Fund directly bears the costs of preparing, printing
and distributing prospectuses and statements of additional information and of
implementing and operating the Class B Distribution Plan. In addition, 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
the value of the average daily net assets of Class B. From September 8, 1995
through November 30, 1995, there was no amount 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 year ended November 30, 1995, the Fund was charged an
aggregate of $342,271 pursuant to the Class A Shareholder Services Plan.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
    Under the 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 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 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. From September 8,
1995 through November 30, 1995, there was no amount charged to the Fund
pursuant to the Class B Shareholder Services Plan.
    (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, 1995, 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. Our procedures included confirmation of
securities owned as of November 30, 1995 by correspondence with the custodian.
 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,
1995, 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 and Young LLP signature logo]

New York, New York
January 8, 1996


GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
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, 1995 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).


[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.                       574/700AR9511
[Dreyfus logo]
General New York
Municipal
Money Market Fund
Annual Report
November 30, 1995



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