DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1997-08-01
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<PAGE>

Dreyfus
General New York
Municipal
Money Market Fund
Semi-Annual
Report

May 31, 1997


<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Letter to Shareholders

Dear Shareholder:

     We are pleased to report the performance of General New York Municipal
Money Market Fund for its six-month reporting period ended May 31, 1997 as
shown in the following table:

<TABLE>
<CAPTION>

                                                                                            Annualized
                                                             Annualized Yield            Effective Yield*
                                                             ----------------            ---------------
<S>                                                                <C>                         <C>
     Class A Shares...................................             2.86%                       2.89%
     Class B Shares...................................             2.59%                       2.62%

</TABLE>

Money Market Overview

     Despite the predictions of many analysts who believed growth was slowing
at last, the U.S. economy remained upward bound throughout the period. In fact,
after posting a 3.8% gain during the fourth quarter of 1996, real Gross
Domestic Product (GDP) reached a zenith of 5.6% during the first three months
of 1997, a level not attained in a decade. Most recently, the widely watched
index of the National Association of Purchasing Management jumped to 57.1% in
May from 54.2% in April. The apparent pickup in manufacturing overshadowed two
Commerce Department reports that had pointed to a second-quarter slowdown in
national economic activity. Those April reports showed consumer spending edging
up just 0.1% -- the smallest increase since last September -- and personal
income posting a similarly small gain of only 0.1%.

     Alongside the news of surprisingly strong economic growth came another
surprise: inflation remained very low. The latest supporting evidence was a
drop in producer prices for April. At the same time, April's unemployment rate
hit 4.9%, the lowest level in 23 years. The Employment Cost Index also showed
minimal price pressure registering just 0.6% for the first quarter of 1997, a
reduction from its 0.8% rise during the last quarter of 1996. Prior to the
release of these rather reassuring statistics, the Federal Reserve Board (Fed)
had increased overnight bank lending rates one quarter of a percentage point at
its March 25 Federal Open Market Committee meeting. While many expected this to
be the first in a series of moves, the Fed left rates alone in May, leaving
market participants guessing about what will happen when the Fed meets again in
July.

Market Environment/Portfolio

     Each year, as summer approaches, the short-term municipal market
experiences volatility that is reflective of the changing patterns of supply
and demand conditions during the period. These market "technicals" require
adjustments to portfolio strategy in anticipation of conditions such as: an
increase in available securities due to fund redemptions (April tax season), a
dearth of supply of high quality issues (end of June maturities), and
substantial new money market issuance (mid-July financings). Our portfolio
adjustments attempt to structure your Fund in such a way as to take advantage
of these changing conditions in an effort to enhance your Fund's return while
maintaining our commitment to high quality holdings.

     In response to the expected changes in both cash flow and supply
conditions, we began preparations for extending your Fund's average maturity in
early June. By creating a calendar of upcoming New York issues and by
subjecting each new issue to rigorous in-house credit review, we were
positioned to take advantage of those notes which we believe would be
attractive holdings for your Fund. We expect to continue to purchase notes
selectively through the summer months in

<PAGE>

seeking to maximize your Fund's current yield. As we endeavor to accomplish
this, we will continue to commit to those New York tax-exempt issues which meet
our high quality investment guidelines and which provide the appropriate level
of liquidity for your Fund's needs. Additionally, we will monitor those
conditions which affect our marketplace and adjust our investment policy where
necessary to pursue competitive returns.

     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

                                       Director, Municipal Portfolio Management
                                       The Dreyfus Corporation

June 17, 1997
New York, N.Y.

* Annualized effective yield takes into account the effect of compounding and
is based upon dividends declared daily and reinvested monthly.



<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Investments                                May 31, 1997 (Unaudited)

<TABLE>
<CAPTION>

                                                                                  Principal
Tax Exempt Investments--100.0%                                                     Amount             Value
- -----------------------------------------------------------------------------    ----------       ------------

<S>                                                                              <C>              <C>
New York--97.2%
Buffalo, RAN 4.215%, 7/15/97 (LOC; Landesbank Hessen) (a)....................    $16,000,000      $  16,012,305
East Northport Union Free School District, TAN 4.50%, 6/30/97................     10,400,000         10,404,450
Erie County Water Authority, Water Revenue, VRDN
  3.80%, Series A (Insured; AMBAC and Liquidity Facility; National Bank
  of Australia) (b)..........................................................      9,000,000          9,000,000
Half Hallow Hills Central School District, TAN
  (Huntington and Babylon) 4.25%, 6/27/97....................................     13,050,000         13,052,678
Town of Islip Industrial Development Agency, IDR, VRDN
  (Brentwood Distribution Project) 3.85% (LOC; Bankers Trust) (a,b)..........      1,000,000          1,000,000
Metropolitan Transport Authority, Commuter Facilities Revenue, VRDN
  3.95% (LOC: Bank of Tokyo-Mitsubishi, Industrial Bank of Japan, JP Morgan,
  Morgan Guaranty Trust Co., National Westminster Bank and
  Sumitomo Bank) (a,b).......................................................     27,700,000         27,700,000
New York City:
  CP:
    3.45%, 7/22/97 (Insured; AMBAC and Liquidity Facility; Krediet Bank).....     12,000,000         12,000,000
    3.45%, 7/22/97 (LOC; Chase Manhattan Bank) (a)...........................     11,000,000         11,000,000
  VRDN:
    3.90%, Series A-6 (LOC; Landesbank Hessen) (a,b).........................     10,000,000         10,000,000
    4.05%, Series E-2 (LOC; Morgan Guaranty Trust Co.) (a,b).................      9,700,000          9,700,000
New York City Health and Hospital Corporation, Health Systems Revenue, VRDN
  3.80%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b).....................     10,000,000         10,000,000
New York City Housing Development Corporation, Mortgage Revenue, VRDN:
  Multi-Family-York Avenue Development Project) 3.90% (LOC; Midland Bank) (a,b)    8,000,000          8,000,000
  (Park Gate Tower) 4% (LOC; Citibank) (a,b).................................      2,285,000          2,285,000
New York City Industrial Development Agency, VRDN:
  Civil Facility Revenue (Children's Oncology Society/ Ronald McDonald House)
    3.70% (LOC; Barclays Bank) (a,b).........................................      2,900,000          2,900,000
    IDR (La Guardia Association Project) 4% (LOC; Banque Indosuez) (a,b).....      8,900,000          8,900,000
New York City Municipal Assistance Corporation:
  3.80%, Series 2, 8/20/97 (LOC; Landesbank Hessen) (a)......................     10,000,000         10,000,000
  3.80%, Series 2, 8/21/97 (LOC; Landesbank Hessen) (a)......................     13,000,000         13,000,000
New York City Municipal Water Finance Authority, Water and Sewer System, VRDN
  4.20%, Series A (Insured; FGIC and Liquidity Facility; FGIC)...............     11,400,000         11,400,000

</TABLE>

<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Investments (continued)                    May 31, 1997 (Unaudited)

<TABLE>
<CAPTION>

                                                                                  Principal
Tax Exempt Investments (Continued)                                                  Amount             Value
- -----------------------------------------------------------------------------    ----------       ------------
<S>                                                                              <C>              <C>
New York (continued)
New York State, CP:
  3.60%, 7/9/97 (Liquidity Facility; Westdeutsche Landesbank)..............    $10,000,000      $  10,000,000
  3.80%, 8/7/97 (Liquidity Facility; Westdeutsche Landesbank)..............      7,000,000          7,000,000
  3.80%, Series S, 8/14/97 (Liquidity Facility; Westdeutsche Landesbank)...     27,000,000         27,000,000
New York State Dormitory Authority, Revenues, VRDN
  (Oxford University Press Inc.) 4.15% (LOC; Landesbank Hessen) (a,b)......     10,700,000         10,700,000
New York State Energy, Research and Development Authority:
  Electric Facilities Revenue, VRDN  (LILCO Project)
    3.90%, Series B (LOC; Toronto-Dominion Bank) (a,b).....................      8,000,000          8,000,000
    PCR:
      Bonds:
          (LILCO Project)
            3.60%, Series B, 3/1/98 (LOC; Deutsche Bank) (a)...............      5,470,000          5,470,000
           (New York State Electric and Gas Corp.)
             3.60%, Series D, 12/1/97 (LOC; Union Bank of Switzerland) (a).     10,000,000         10,000,000
        VRDN:
           (Central Hudson Gas and Electric Project)
             3.90%, Series A (LOC; Union Bank of Switzerland) (a,b)........      7,800,000          7,800,000
           (Niagara Mohawk Power Corp.):
             4.20%, Series A (LOC; Toronto-Dominion Bank) (a,b)............      3,400,000          3,400,000
             4.25%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b)........      3,700,000          3,700,000
New York State Housing Finance Agency, Revenue, VRDN (Normandie Court I Project)
  3.90% (LOC; Landesbank Hessen) (a,b).....................................      8,100,000          8,100,000
New York State Local Government Assistance Corporation, VRDN:
  3.80%, Series A (LOC: Credit Suisse and Union Bank of Switzerland) (a,b).      2,000,000          2,000,000
  3.80%, Series B (LOC; Credit Suisse) (a,b)...............................     41,200,000         41,200,000
New York State Medical Care Facilities Finance Agency, Revenue, VRDN
  (Pooled Equipment Loan Program):
    3.90%, Series I (LOC; Chase Manhattan Bank) (a,b)......................     17,500,000         17,500,000
    3.90%, Series II (LOC; Chase Manhattan Bank) (a,b).....................      7,970,000          7,970,000
New York State Power Authority:
  CP 3.80%, 7/23/97 (LOC: Bank of America, The Bank of New York,
    Bank of Nova Scotia, Bank of Tokyo-Mitsubishi, Chase Manhattan Bank,
    Citibank, Industrial Bank of Japan and Sanwa Bank) (a).................     20,000,000         20,000,000

</TABLE>

<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Investments (continued)                    May 31, 1997 (Unaudited)

<TABLE>
<CAPTION>

                                                                                  Principal
Tax Exempt Investments (Continued)                                                  Amount             Value
- -----------------------------------------------------------------------------    ----------       ------------
<S>                                                                              <C>              <C>
New York (continued)
New York State Power Authority (continued):
  Revenue, General Purpose Junior Lein
    3.50%, 9/1/97 (Liquidity Facility: Bank of America, Bank of
      Tokyo-Mitsubishi, Morgan Guaranty Trust Co. and Sumitomo Bank).........    $11,500,000      $  11,500,000
Onondaga County Industrial Development Agency, IDR, VRDN
  (Edgecomb Metals Co. Project) 3.85% (LOC; Banque Nationale de Paris) (a,b)       2,000,000          2,000,000
Patchogue-Medford Union Free School District, TAN 4.50%, 6/26/97.............     10,000,000         10,003,975
Rochester, BAN:
  4%, Series I, 3/10/98......................................................     25,000,000         25,055,780
  4.25%, Series III, 10/30/97................................................     15,000,000         15,026,943
Rockland County, RAN 4.25%, 4/15/98..........................................      9,000,000          9,030,191
Sachem Central School District, TAN 4.50%, 6/26/97...........................      7,000,000          7,002,535
Suffolk County, TAN
  4%, Series I, 8/14/97 (LOC: Canadian Imperial Bank of Commerce,
  National Westminster Bank and Westdeutsche Landesbank) (a).................     24,000,000         24,033,712
Three Village Central School District, TAN 4.25%, 6/30/97....................      9,500,000          9,502,179
Triborough Bridge and Tunnel Authority, Special Obligation, VRDN
  3.85% (Insured; FGIC and Liquidity Facility; FGIC) (b).....................     25,700,000         25,700,000
Yonkers Industrial Development Authority, Civic Revenue, Consumers Union
  Facilities, VRDN 3.70% (Insured; AMBAC and Liquidity Facility; Credit
  Local de France) (b).......................................................      3,400,000          3,400,000

U.S. Related--2.8%

Commonwealth of Puerto Rico Government Development Bank, Refunding, CP
  3.30%, 6/13/97.............................................................     15,000,000         15,000,000
                                                                                                  -------------
TOTAL INVESTMENTS
  (cost $533,449,748)........................................................                      $533,449,748
                                                                                                   ============
</TABLE>





<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------


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

<S>        <C>                                              <C>        <C>

AMBAC      American Municipal Bond Assurance Corporation    LOC        Letter of Credit
BAN        Bond Anticipation Notes                          PCR        Pollution Control Revenue
CP         Commercial Paper                                 RAN        Revenue Anticipation Notes
FGIC       Financial Guaranty Insurance Company             TAN        Tax Anticipation Notes
IDR        Industrial Development Revenue                   VRDN       Variable Rate Demand Notes

</TABLE>


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

<TABLE>
<CAPTION>

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)               90.4%
AAA/AA (e)                     Aaa/Aa (e)                     AAA/AA (e)                         2.1
Not Rated (f)                  Not Rated (f)                  Not Rated (f)                      7.5
                                                                                              -------
                                                                                               100.0%
                                                                                              =======
</TABLE>

Notes to Statement of Investments:
- --------------------------------------------------------------------------------
(a) Secured by letters of credit. At May 31, 1997, 57.0% of the Fund's net
assets are backed by letters of credit issued by domestic banks, foreign banks
and brokerage firms of which Landesbank Hessen is provided letters of credit to
12.8% 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 and Standard & Poor's
have been determined by the Manager to be of comparable quality to those rated
securities in which the Fund may invest.


                       See notes to financial statements.


<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Assets and Liabilities                     May 31, 1997 (Unaudited)
<TABLE>
<CAPTION>

                                                                                                    Cost            Value
                                                                                               -------------    -------------
<S>                                                                                             <C>              <C>
ASSETS:                       Investments in securities--See Statement of Investments..         $533,449,748    $533,449,748
                              Interest receivable......................................                            5,116,999
                              Prepaid expenses.........................................                               43,129
                                                                                                                ------------
                                                                                                                 538,609,876
                                                                                                                ------------

LIABILITIES:                  Due to The Dreyfus Corporation and affiliates............                              264,848
                              Due to Distributor.......................................                                2,703
                              Cash overdraft due to Custodian..........................                            7,526,646
                              Accrued expenses.........................................                              178,835
                                                                                                                ------------
                                                                                                                   7,973,032
                                                                                                                ------------

NET ASSETS.............................................................................                         $530,636,844
                                                                                                                ============

REPRESENTED BY:               Paid-in capital..........................................                         $530,697,981
                              Accumulated net realized gain (loss) on investments                                    (61,137)
                                                                                                                ------------

NET ASSETS.............................................................................                         $530,636,844
                                                                                                                ============

</TABLE>


                            NET ASSET VALUE PER SHARE
<TABLE>
<CAPTION>

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

<S>                                                                                             <C>              <C>
Net Assets............................................................................          $494,777,423     $35,859,421
Shares Outstanding....................................................................           494,839,064      35,858,917


NET ASSET VALUE PER SHARE.............................................................                 $1.00           $1.00
                                                                                                       =====           =====

</TABLE>


                       See notes to financial statements.



<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Operations                Six Months Ended May 31, 1997 (Unaudited)

<TABLE>


<S>                           <C>                                                              <C>              <C>

INVESTMENT INCOME

INCOME                        Interest Income..................................                                 $9,433,148


EXPENSES:                     Management fee--Note 2(a)........................                $1,332,617
                              Shareholder servicing costs--Note 2(c)...........                   434,757
                              Distribution fees (Class B)--Note 2(b)...........                    38,455
                              Custodian fees...................................                    27,027
                              Professional fees................................                    21,468
                              Trustees' fees and expenses--Note 2(d)...........                    13,718
                              Prospectus and shareholders' reports.............                    10,158
                              Registration fees................................                     7,604
                              Miscellaneous....................................                     9,015
                                                                                               ----------
                                   Total Expenses..............................                 1,894,819

                              Less--reduction in shareholder servicing costs due to
                                undertaking--Note 2(c).........................                   (19,084)
                                                                                               ----------
                                   Net Expenses................................                                  1,875,735
                                                                                                                ----------

INVESTMENT INCOME--NET.........................................................                                  7,557,413

REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b):

                              Net realized gain (loss) on investments..........                $    6,356

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

NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS.........................                                      5,023
                                                                                                                ----------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS...........................                                 $7,562,436
                                                                                                                ==========
</TABLE>


                       See notes to financial statements.


<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Changes in Net Assets
<TABLE>
<CAPTION>

                                                                                        Six Months Ended
                                                                                          May 31, 1997        Year Ended
                                                                                           (Unaudited)     November 30, 1996
                                                                                         ----------------  -----------------
<S>                                                                                          <C>              <C>
OPERATIONS:
  Investment income--net...................................................                  $  7,557,413    $  16,442,912
  Net realized gain (loss) on investments..................................                         6,356           --
  Net unrealized appreciation (depreciation) on investments................                        (1,333)           1,333
                                                                                            -------------   --------------
      Net Increase (Decrease) in Net Assets Resulting from Operations......                     7,562,436       16,444,245
                                                                                            -------------   --------------

DIVIDENDS TO SHAREHOLDERS FROM:
  Investment income--net:
    Class A shares.........................................................                    (7,061,951)     (15,817,725)
    Class B shares.........................................................                      (495,462)        (625,187)
                                                                                            -------------   --------------
      Total Dividends......................................................                    (7,557,413)     (16,442,912)
                                                                                            -------------   --------------
BENEFICIAL INTEREST TRANSACTIONS:
  Net proceeds from shares sold:
    Class A shares.........................................................                   649,195,080    1,178,019,825
    Class B shares.........................................................                    38,429,906       92,365,836
  Dividends reinvested:
    Class A shares.........................................................                     6,741,087       15,007,966
    Class B shares.........................................................                       494,466          625,187
  Cost of shares redeemed:
    Class A shares.........................................................                  (668,700,627)  (1,321,504,908)
    Class B shares.........................................................                   (39,263,982)     (56,792,597)
                                                                                            -------------   --------------
      Increase (Decrease) in Net Assets from Beneficial Interest Transactions                 (13,104,070)     (92,278,691)
                                                                                            -------------   --------------
        Total Increase (Decrease) in Net Assets............................                   (13,099,047)     (92,277,358)

NET ASSETS:

  Beginning of Period......................................................                   543,735,891      636,013,249
                                                                                            -------------   --------------
  End of Period............................................................                 $ 530,636,844   $  543,735,891
                                                                                            -------------   --------------
                                                                                            -------------   --------------

</TABLE>

                       See notes to financial statements.



<PAGE>

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 information provided in the Fund's financial statements.
<TABLE>
<CAPTION>

                                                                       Class A Shares
                                            ---------------------------------------------------------------------------
                                               Six Months Ended                   Year Ended November 30,
                                                 May 31, 1997     ----------------------------------------------------
PER SHARE DATA:                                  (Unaudited)      1996        1995       1994        1993        1992
                                               ---------------  --------    --------   ---------   --------    ------
<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...............           .014           .028        .032       .023        .020        .028
                                                  -----          -----       -----      -----       -----       -----
   Distributions:

   Dividends from investment income--net          (.014)         (.028)      (.032)     (.023)      (.020)      (.028)
                                                  -----          -----       -----      -----       -----       -----
   Net asset value, end of period......           $1.00          $1.00       $1.00      $1.00       $1.00       $1.00
                                                  -----          -----       -----      -----       -----       -----
                                                  -----          -----       -----      -----       -----       -----
TOTAL INVESTMENT RETURN................            2.87%(1)       2.84%       3.28%      2.34%       2.00%       2.78%
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets          .68%(1)        .68%        .58%       .34%        .32%        .25%
   Ratio of net investment income
     to average net assets.............            2.86%(1)       2.80%       3.23%      2.33%       1.98%       2.99%
   Decrease reflected in above expense ratios
     due to undertakings by the Manager             --             --          .05%       .32%        .35%        .38%
   Net Assets, end of period (000's Omitted).. $494,778       $507,537    $636,013   $689,918    $612,441    $630,899

<FN>
- --------------------------------------
(1) Annualized.
</TABLE>

                       See notes to financial statements.


<PAGE>

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 information provided in the Fund's financial
statements.
<TABLE>
<CAPTION>

                                                                                      Class B Shares
                                                                 -----------------------------------------------------
                                                                   Six Months Ended       Year Ended November 30,
                                                                    May 31, 1997        ------------------------------
PER SHARE DATA:                                                     (Unaudited)           1996             1995(1)
                                                                   ---------------      ---------         ---------
<S>                                                                      <C>              <C>               <C>
   Net asset value, beginning of period...................               $1.00            $1.00             $1.00
                                                                         -----           ------            ------
   Investment Operations:

   Investment income--net..................................               .013             .025              .006
                                                                         -----           ------            ------
   Distributions:

   Dividends from investment income--net...................              (.013)           (.025)            (.006)
                                                                         -----           ------            ------
   Net asset value, end of period.........................               $1.00            $1.00             $1.00
                                                                         =====           ======            ======

TOTAL INVESTMENT RETURN...................................                2.61%(2)         2.55%             2.82%(2)
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets................                 .95%(2)          .95%             1.04%(2)
   Ratio of net investment income
      to average net assets...............................                2.58%(2)         2.47%             3.64%(2)
   Decrease reflected in above expense ratios
      due to undertakings by the Manager..................                 .10%(2)          .16%               --
   Net Assets, end of period (000's Omitted)..............              35,859          $36,199                --


<FN>
- --------------------------------------------------------------------------------
(1) From September 8, 1995 (commencement of initial offering) to November 30,
    1995.
(2) Annualized.
</TABLE>

                       See notes to financial statements.


<PAGE>

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") 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 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 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 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.

     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. 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, 1996. 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 May 31, 1997, 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).



<PAGE>

General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

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

     (a) Pursuant to a management 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 11/2% of the average value of
the Fund's net assets for any full fiscal year, the Fund may deduct from
payments to be made to the Manager, or the Manager will bear such excess
expense. There was no reimbursement during the period ended May 31, 1997.

     (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 period ended May 31, 1997, $38,455 was charged to the
Fund Pursuant to the Class B Distribution Plan.

     (c) Under the 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 of 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 period ended May
31, 1997, the Fund was charged an aggregate of $231,622 pursuant to the Class A
Shareholder Services Plan.

     Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), 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 June 30, 1997, that if the aggregate
expenses of Class B of the Fund, exclusive of taxes, brokerage, interest on
borrowings and extraordinary expenses, 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 period ended May 31, 1997, $48,069 was charged to the Fund pursuant
to the Class B Shareholder Services Plan, of which $19,084 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. Such compensation
amounted to $92,114 during the period ended May 31, 1997.

     (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.

<PAGE>

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


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