DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1998-08-07
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<PAGE>
Dreyfus
General New York
Municipal Money
Market Fund
Semi-Annual
Report


May 31, 1998

<PAGE>
General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Letter to Shareholders

Dear Shareholder:

   We are pleased to report the performance for General New York Municipal Money
Market Fund for the six-month reporting period ended May 31, 1998 as shown in
the following table:
                                  ANNUALIZED           ANNUALIZED
                                    YIELD           EFFECTIVE YIELD*
                                -------------       ----------------
   Class A Shares............       2.84%                 2.88%
   Class B Shares............       2.57%                 2.60%

Money Market Overview

   Over the past several months, mixed economic signals have made it difficult
to discern the direction in which the economy is moving. Consumer spending
increased 0.5% in both April and May, fueled by both strong employment and
income growth. In addition, construction spending also rose 0.8% in April for
the fifth straight monthly increase. On the other hand, spring housing data was
mixed, with new home sales rising to record levels in April and existing-home
sales and new housing starts dropping off. The U.S. trade gap also continued to
widen, as manufacturers reported declines in exports to Asia, and tough
competition from cheaper Asian imports. With arguments to be made for both
continued growth and emerging weakness, it appears that Federal Reserve Board
monetary policy will remain on hold at least until something major happens to
sway Board members' opinions one way or another.

   Inflation has remained benign throughout the period. Incoming data from April
did show a small 0.2% increase in the Consumer Price Index, although this modest
rise was the largest in six months. With no consensus as to the direction of the
economy, the Federal Reserve Board Open Market Committee left short-term
interest rates unchanged at its May meeting; however, the decision to do so may
not have been unanimous. Those most wary of inflation may win out in upcoming
meetings if the economy does not cool on its own. Interest rates on money market
securities fluctuated modestly during the period, but remained largely
unchanged. As U.S. Treasury borrowing needs continued to reduce the supply of
money market securities, demand remained steady.

Market Environment/Portfolio Overview

   While the Fed has remained quiet over the past six months, market technicals
(i.e. supply/demand fluctuations) have played a major role in our overall
investment strategy. The municipal money market has experienced some of these
changes in seasonal cash flows and note issuance since our last report. For
example, in late December, the short-term municipal market experienced a sharp,
albeit temporary, rise in short-term rates as a result of corporate seasonal
window dressing. Dealers priced securities at attractive levels in order to
minimize their inventories, which helped to boost your Fund's yield at year end.
The situation reversed in January as assets flowed back into the tax-exempt
money funds, thereby putting downward pressure on yields. During this period,
yields on tax-exempt money market funds fluctuated in response to these supply
and demand imbalances.

   By mid-January, the market stabilized and normal trading patterns, for the
most part, returned and continued through March. In April, money funds were
tapped for income tax payments which, once again, put upward pressure on rates
as funds experienced redemptions. Supply conditions in late May reversed this
trend as municipal fund managers anticipated the effect of over $10 billion
notes leaving the market when they mature this month.

   Unlike previous summer financing periods, this year's calendar of municipal
notes appropriate for purchase for your Fund was drastically reduced by a
combination of factors. Due to the strength of local and state economies, many
issuers (a significant number of which were not New York-exempt) reduced the
amount of short-term borrowings. Additionally, many issuers came to market with
maturities outside of the 13-month maximum maturity allowable for money funds,
whereas these notes were eligible for purchase in prior years. Other issues were
converted to a synthetic structure that is not

<PAGE>
currently permitted for purchase in your Fund. The overall result was a lower
yield for those note issues that were considered appropriate investments for
your Fund. We expect to choose selectively among these issues and those to
follow in the coming weeks to structure the portfolio in an attempt to maximize
current yield while maintaining our commitment to high quality tax-exempt
investments.

   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 greatly appreciate your continued confidence in this Fund and in The
Dreyfus Corporation.
                                     Very truly yours,

                                     /s/ Richard J. Moynihan

                                     Richard J. Moynihan
                                     Director, Municipal Portfolio Management
                                     The Dreyfus Corporation
June 18, 1998
New York, N.Y.

* Annualized effective yield is based upon dividends declared daily and
  reinvested monthly.

<PAGE>
General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Investments                                May 31, 1998 (Unaudited)

<TABLE>
<CAPTION>

                                                                                     Principal
Tax Exempt Investments--100.0%                                                         Amount           Value
- ---------------------------------------------------------------------------------  -------------   ------------
<S>                                                                                <C>             <C>
Buffalo, RAN 4.40%, 8/5/98 (LOC; Landesbank Hessen) (a)........................    $  9,000,000    $  9,009,070
Erie County, RAN 4.50%, Series A, 6/25/98 (LOC; Union Bank of Switzerland) (a).       9,000,000       9,003,988
Erie County Water Authority, Water Revenue, VRDN
  3.90%, 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%, 6/26/98.........................................      11,750,000      11,751,314
Town of Islip Industrial Development Agency, IDR, VRDN
  (Brentwood Distribution Project) 3.70% (LOC; Fleet Bank) (a,b)...............       1,000,000       1,000,000
Long Island Power Authority, Electric Systems Revenue:
  CP 3.75%, 8/19/98 (LOC: Bayerische Landesbank and Westdeutsche Landesbank) (a)     10,000,000      10,000,000
  VRDN 3.95%, Series 6, Subseries 3B (LOC: ABN-Amro Bank and
    Morgan Guaranty Trust Co.) (a,b)...........................................       5,000,000       5,000,000
Longwood Central School District, TAN 4.35%, 6/30/98...........................      10,000,000      10,003,052
Municipal Assistance Corporation, CP:
  3.65%, Series 2, 7/16/98 (LOC; Landesbank Hessen) (a)........................      12,000,000      12,000,000
  3.45%, Series 2, 7/20/98 (LOC; Landesbank Hessen) (a)........................      13,000,000      13,000,000
New York City, VRDN:
  3.90%, Series A-6 (LOC; Landesbank Hessen) (a,b).............................      10,000,000      10,000,000
  4%, Series E-3 (LOC; Morgan Guaranty Trust Co.) (a,b)........................      18,900,000      18,900,000
  4.10%, Series C (LOC; Morgan Guaranty Trust Co.) (a,b).......................       7,600,000       7,600,000
New York City Health and Hospital Corporation, Revenue, Health Systems
  Revenue, VRDN 3.90%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b).........       9,900,000       9,900,000
New York City Housing Development Corporation, VRDN:
  Mortgage Revenue:
    (Multi-Family-York Avenue Development Project) 3.90%
      (LOC; Midland Bank) (a,b)................................................       8,000,000       8,000,000
    (Park Gate Tower) 3.55%, Series 1 (LOC; Citibank) (a,b)....................       2,175,000       2,175,000
    (Residential-East 17th St) 4.05%, Series A
      (LOC; Chase Manhattan Bank) (a,b)........................................       6,000,000       6,000,000
  Multi-Family Rental Housing Revenue (Monterey) 3.70%, Series A
    (LOC; FNMA) (a,b)..........................................................      10,000,000      10,000,000
New York City Industrial Development Agency, VRDN:
    Civil Facility Revenue (Children's Oncology Society/Ronald McDonald House)
      3.80% (LOC; Barclays Bank) (a,b).........................................       2,700,000       2,700,000
  IDR:
    (Field Hotel Association JFK Project) 3.95%
      (LOC; Credit Agricole-Indosuez) (a,b)....................................       5,000,000       5,000,000
    (La Guardia Association Project) 3.95% (LOC; Credit Agricole-Indosuez) (a,b)      8,900,000       8,900,000
New York City Municipal Water Finance Authority, Water and Sewer System
  Revenue, VRDN:
  3.95%, Series G (Insured; FGIC and Liquidity Facility; FGIC) (b).............       3,600,000       3,600,000
  4%, Series C (Insured; FGIC and Liquidity Facility; FGIC) (b)................       8,800,000       8,800,000
New York City Trust, Cultural Resource Revenue, Refunding, VRDN
  (American Museum of Natural History)
  3.90%, Series A (Insured; MBIA and Liquidity Facility; Credit Suisse) (b)....       3,000,000       3,000,000
New York State, CP 3.50%, 7/13/98 (Liquidity Facility; Westdeutsche Landesbank)       9,200,000       9,200,000
New York State Dormitory Authority, Revenues, CP (Memorial Sloan Kettering)
  3.55%, Series A, 8/14/98 (LOC; Chase Manhattan Bank) (a).....................      14,900,000      14,900,000

</TABLE>

<PAGE>
General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Investments (continued)                    May 31, 1998 (Unaudited)

<TABLE>
<CAPTION>

                                                                                     Principal
Tax Exempt Investments (continued)                                                    Amount           Value
- ---------------------------------------------------------------------------------  -------------   ------------
<S>                                                                                <C>             <C>
New York State Energy, Research and Development Authority:
  Electric Facilities Revenue, VRDN  (LILCO Project)
    4.05%, Series B (LOC; Toronto-Dominion Bank) (a,b).........................    $  8,000,000    $  8,000,000
  PCR:
    (LILCO Project) 3.58%, Series A, 3/1/99 (LOC; Deutsche Bank) (a)...........      15,470,000      15,470,000
    (New York State Electric and Gas Corp.)
      3.80%, Series D, 12/1/98 (LOC; Union Bank of Switzerland) (a)............       8,325,000       8,325,000
    VRDN:
      (Central Hudson Gas and Electric Project)
        3.75%, Series A (LOC; Union Bank of Switzerland) (a,b).................       7,800,000       7,800,000
      (Niagara Mohawk Power Corp.)
        4.05%, Series B (LOC; Toronto-Dominion Bank) (a,b).....................       4,500,000       4,500,000
New York State Housing Finance Agency, Revenue, VRDN:
  Contract Obligation 3.85%, Series A (LOC; Commerzbank) (a,b).................      14,400,000      14,400,000
  (Normandie Court I Project)
    3.90% (LOC; Landesbank Hessen) (a,b).......................................       8,000,000       8,000,000
New York State Local Government Assistance Corporation, VRDN:
  3.85%, Series A (LOC: Credit Suisse and Union Bank of Switzerland) (a,b).....      17,000,000      17,000,000
  3.85%, Series B (LOC; Krediet Bank) (a,b)....................................      30,700,000      30,700,000
New York State Medical Care Facilities Finance Agency, Revenue, VRDN (Pooled
  Equipment Loan Program):
    3.80%, Series I (LOC; Chase Manhattan Bank) (a,b)..........................      17,500,000      17,500,000
    3.95%, Series II (LOC; Chase Manhattan Bank) (a,b).........................       6,470,000       6,470,000
New York State Power Authority:
  CP 3.75%, 7/22/98 (Liquidity: Bank of Nova Scotia, Commerzbank, Credit Locale
    de France, Landesbank Hessen, Morgan Guaranty Trust Co. and
      Toronto-Dominion Bank)...................................................      19,100,000      19,100,000
  Revenue, General Purpose Junior Lein
    3.60%, 9/1/98 (Liquidity Facility: Bank of America, Bank of Tokyo-Mitsubishi,
    Morgan Guaranty Trust Co. and Sumitomo Bank)...............................      12,545,000      12,545,000
Onondaga County Industrial Development Agency, IDR, VRDN (Edgecomb Metals Co. Project)
  3.70% (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
  (Versatile Structure):
    3.95%, Series 4 (LOC; Landesbank Hessen) (a,b).............................      10,000,000      10,000,000
    3.95%, Series 6 (Liquidity; Bank of Nova Scotia) (b).......................       7,000,000       7,000,000
Suffolk County, TAN:
  4.25%, 8/13/98 (LOC: Canadian Imperial Bank of Commerce,
    National Westminster Bank and Westdeutsche Landesbank) (a).................      15,000,000      15,017,677
  4.25%, Series II, 9/10/98 (LOC: Canadian Imperial Bank of Commerce,
    National Westminster Bank and Westdeutsche Landesbank) (a).................      16,000,000      16,017,020
Triborough Bridge and Tunnel Authority, Special Obligation, VRDN
  3.90% (Insured; FGIC and Liquidity Facility; FGIC) (b).......................      22,300,000      22,300,000

</TABLE>

<PAGE>
General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Investments (continued)                    May 31, 1998 (Unaudited)

<TABLE>
<CAPTION>

                                                                                     Principal
Tax Exempt Investments (continued)                                                    Amount           Value
- ---------------------------------------------------------------------------------  -------------   ------------
<S>                                                                                <C>             <C>
Yonkers Industrial Development Authority, Civic Revenue, Consumers Union
  Facilities, VRDN 3.80% (Insured; AMBAC and Liquidity Facility: Credit Local de
  France and Union Bank of Switzerland) (b)....................................    $  3,400,000    $  3,400,000
                                                                                                   ------------
TOTAL INVESTMENTS
  (cost $463,987,121)..........................................................                    $463,987,121
                                                                                                   ============

</TABLE>

Summary of Abbreviations
- --------------------------------------------------------------------------------

<TABLE>

<S>        <C>                                              <C>        <C>
AMBAC      American Municipal Bond Assurance Corporation    MBIA       Municipal Bond Investors Assurance
CP         Commercial Paper                                              Insurance Corporation
FGIC       Financial Guaranty Insurance Company             PCR        Pollution Control Revenue
FNMA       Federal National Mortgage Association            RAN        Revenue Anticipation Notes
IDR        Industrial Development Revenue                   TAN        Tax Anticipation Notes
LOC        Letter of Credit                                 VRDN       Variable Rate Demand Notes

</TABLE>

Summary of Combined Ratings
- --------------------------------------------------------------------------------

<TABLE>

<S>                            <C>                            <C>                       <C>
Fitch (c)          or          Moody's           or           Standard & Poor's         Percentage of Value
- ------                         --------                       ----------------           -----------------
F1+/F1                         VMIG1/MIG1,P1 (d)              SP1+/SP1,A1+/A1 (d)                 88.3%
AAA/AA (e)                     Aaa/Aa (e)                     AAA/AA (e)                            .4
Not Rated (f)                  Not Rated (f)                  Not Rated (f)                       11.3%
                                                                                                 -----
                                                                                                 100.0%
                                                                                                 -----
                                                                                                 -----

<FN>
Notes to Statement of Investments:
- --------------------------------------------------------------------------------
(a) Secured by letters of credit. At May 31, 1998, 73.8% of the Fund's net
    assets are backed by letters of credit issued by domestic banks, foreign
    banks and government agencies of which Landesbank Hessen provided letters
    of credit to 13.3% 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 Manager to be of comparable quality to those
    rated securities in which the Fund may invest.

</FN>
</TABLE>

                       See notes to financial statements.

<PAGE>
General New York Municipal Money Market Fund
- --------------------------------------------------------------------------------
Statement of Assets and Liabilities                     May 31, 1998 (Unaudited)

<TABLE>
<CAPTION>

                                                                                              Cost           Value
                                                                                          ------------    ------------
<S>                           <C>                                                         <C>             <C>
ASSETS:                       Investments in securities--See Statement of Investments     $461,287,121    $461,287,121
                              Cash.............................................                                654,836
                              Interest receivable..............................                              3,902,172
                              Receivable for investment securities sold........                              1,000,427
                              Prepaid expenses.................................                                 54,193
                                                                                                          ------------
                                                                                                           466,898,749
                                                                                                          ------------

LIABILITIES:                  Due to The Dreyfus Corporation and affiliates....                                196,898
                              Due to Distributor...............................                                  2,917
                              Accrued expenses.................................                                 81,762
                                                                                                          ------------
                                                                                                               281,577
                                                                                                          ------------

NET ASSETS.....................................................................                           $466,617,172
                                                                                                          ------------
                                                                                                          ------------

REPRESENTED BY:               Paid-in capital..................................                           $466,681,600
                              Accumulated net realized gain (loss) on investments                              (64,428)
                                                                                                          ------------
NET ASSETS.....................................................................                           $466,617,172
                                                                                                          ------------
                                                                                                          ------------

                            NET ASSET VALUE PER SHARE
                            -------------------------

                                                                                             Class A         Class B
                                                                                          ------------    ------------
Net Assets.....................................................................           $424,071,393     $42,545,779
Shares Outstanding.............................................................            424,136,124      42,545,476
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, 1998 (Unaudited)

<TABLE>

INVESTMENT INCOME

<S>                           <C>                                                       <C>                   <C>
INCOME                        Interest Income............................                                     $8,484,759

EXPENSES:                     Management fee--Note 2(a)..................               $1,195,227
                              Shareholder servicing costs--Note 2(c).....                  446,044
                              Distribution fees (Class B)--Note 2(b).....                   45,819
                              Custodian fees.............................                   24,660
                              Professional fees..........................                   23,796
                              Registration fees..........................                   18,304
                              Trustees' fees and expenses--Note 2(d).....                   11,542
                              Prospectus and shareholders' reports.......                    9,872
                              Miscellaneous..............................                    5,666
                                                                                        ----------
                                Total Expenses...........................                1,780,930

                              Less--reduction in shareholder servicing costs due to
                                undertaking--Note 2(c)...................                  (22,232)
                                                                                        ----------
                                Net Expenses...........................                                      1,758,698
                                                                                                              ----------

INVESTMENT INCOME--NET...................................................                                      6,726,061

NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--Note 1(b)........                                          1,958
                                                                                                              ----------

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS.....................                                     $6,728,019
                                                                                                              ==========

</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, 1998         Year Ended
                                                                              (Unaudited)      November 30, 1997
                                                                           ----------------   ------------------
<S>                                                                        <C>                <C>
OPERATIONS:
   Investment income--net................................................. $  6,726,061       $   15,160,748
   Net realized gain (loss) on investments................................        1,958                1,107
   Net unrealized appreciation (depreciation) on investments..............           --               (1,333)
                                                                           ------------       --------------

         Net Increase (Decrease) in Net Assets Resulting from Operations..    6,728,019           15,160,522
                                                                           ------------       --------------
DIVIDENDS TO SHAREHOLDERS FROM:
   Investment income--net:
      Class A shares......................................................   (6,137,120)         (14,099,515)
      Class B shares......................................................     (588,941)          (1,061,233)
                                                                           ------------       --------------
         Total Dividends..................................................   (6,726,061)         (15,160,748)
                                                                           ------------       --------------
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
Net proceeds from shares sold:
      Class A shares......................................................  573,813,848        1,232,077,695
      Class B shares......................................................   52,134,865           88,699,944
   Dividends reinvested:
      Class A shares......................................................    5,920,045           13,492,714
      Class B shares......................................................      585,760            1,060,123
   Cost of shares redeemed:
      Class A shares...................................................... (596,414,283)      (1,312,357,416)
      Class B shares......................................................  (52,343,892)         (83,789,854)
                                                                           ------------       --------------
         Increase (Decrease) in Net Assets from Beneficial Interest
           Transactions...................................................  (16,303,657)         (60,816,794)
                                                                           ------------       --------------
            Total Increase (Decrease) in Net Assets.......................  (16,301,699)         (60,817,020)

NET ASSETS:
   Beginning of Period....................................................  482,918,871          543,735,891
                                                                           ------------       --------------
   End of Period.......................................................... $466,617,172       $  482,918,871
                                                                           ============       ==============

</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 the Fund's financial statements.

<TABLE>
<CAPTION>

                                                                         Class A Shares
                                                -----------------------------------------------------------------
                                                Six Months Ended               Year Ended November 30,
                                                  May 31, 1998      ---------------------------------------------
PER SHARE DATA:                                    (Unaudited)       1997      1996      1995     1994      1993
                                                   -----------      ------    ------    ------   ------    ------
<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           .029      .028      .032     .023      .020
                                                     -----          -----     -----     -----    -----     -----
   Distributions:
   Dividends from investment income--net......       (.014)         (.029)    (.028)    (.032)   (.023)    (.020)
                                                     -----          -----     -----     -----    -----     -----
   Net asset value, end of period.............       $1.00          $1.00     $1.00     $1.00    $1.00     $1.00
                                                     -----          -----     -----     -----    -----     -----
                                                     -----          -----     -----     -----    -----     -----
TOTAL INVESTMENT RETURN.......................        2.85%*         2.98%     2.84%     3.28%    2.34%     2.00%
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets....         .71%*          .66%      .68%      .58%     .34%      .32%
   Ratio of net investment income
      to average net assets...................        2.84%*         2.94%     2.80%     3.23%    2.33%     1.98%
   Decrease reflected in above expense ratios
      due to undertakings by the Manager......          --             --        --       .05%     .32%      .35%
   Net Assets, end of period (000's Omitted)..    $424,071       $440,750  $507,537  $636,013 $689,918  $612,441

<FN>
- --------------------
* Annualized.

</FN>
</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 the Fund's financial statements.

<TABLE>
<CAPTION>

                                                                               Class B Shares
                                                            ---------------------------------------------------
                                                            Six Months Ended       Year Ended November 30,
                                                              May 31, 1998     --------------------------------
PER SHARE DATA:                                                (Unaudited)      1997        1996        1995(1)
                                                             ---------------   -------    --------     --------
<S>                                                            <C>           <C>        <C>            <C>
   Net asset value, beginning of period....................      $1.00         $1.00      $1.00        $1.00
                                                                 -----         -----      -----        -----
   Investment Operations:
   Investment income--net..................................       .013          .027       .025         .006
                                                                 -----         -----      -----        -----
   Distributions:
   Dividends from investment income--net...................      (.013)        (.027)     (.025)       (.006)
                                                                 -----         -----      -----        -----
   Net asset value, end of period..........................      $1.00         $1.00      $1.00        $1.00
                                                                 -----         -----      -----        -----
                                                                 -----         -----      -----        -----
TOTAL INVESTMENT RETURN....................................       2.59%(2)      2.68%      2.55%        2.82%(2)
RATIOS/SUPPLEMENTAL DATA:
   Ratio of expenses to average net assets.................        .95%(2)       .95%       .95%        1.04%(2)
   Ratio of net investment income
      to average net assets................................       2.57%(2)      2.64%      2.47%        3.64%(2)
   Decrease reflected in above expense ratios
      due to undertakings by the Manager...................        .10%          .08%       .16%         --
   Net Assets, end of period (000's Omitted)...............    $42,546       $42,169    $36,199          --

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

</FN>
</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 A shares and Class B
shares are identical except for the services offered to and the expenses borne
by each class and certain voting rights. Class B shares are subject to a
Distribution Plan adopted pursuant to Rule 12b-1 under the Act and, in addition,
Class B shares are charged directly for sub-accounting services provided by
Service Agents (a securities dealer, financial institution or other industry
professional) at an annual rate of .05% of the value of the average daily net
assets of Class B shares.

   It is the Fund's policy to maintain a continuous net asset value per share of
$1.00; the Fund has adopted certain investment, portfolio valuation and dividend
and distribution policies to enable it to do so. There is no assurance, however,
that the Fund will be able to maintain a stable net asset value per share of
$1.00.

   The Fund's financial statements are prepared in accordance with generally
accepted accounting principles which may require the use of management estimates
and assumptions. Actual results could differ from those estimates.

   (A) PORTFOLIO VALUATION: Investments in securities are valued at amortized
cost, which has been determined by the Fund's Board of Trustees to represent the
fair value of the Fund's investments.

   (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities transactions
are recorded on a trade date basis. Interest income, adjusted for amortization
of premiums and original issue discounts on investments, is earned from
settlement date and recognized on the accrual basis. Realized gain and loss from
securities transactions are recorded on the identified cost basis. Cost of
investments represents amortized cost. Under the terms of the custodian
agreement, the Fund received net earnings credits of $16,301 during the period
ended May 31, 1998 based on available cash balances left on deposit. Income
earned under this arrangement is included in interest income.

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

   (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends daily from investment income-net. Such dividends are paid monthly.
Dividends from net realized capital gain are normally declared and paid
annually, but the Fund may make distributions on a more frequent basis to comply
with the distribution requirements of the Internal Revenue Code. 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.


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

   The Fund has an unused capital loss carryover of approximately $66,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1997. If not
applied, $8,000 of the carryover expires in fiscal 1998, $40,000 expires in
fiscal 2002 and $18,000 expires in fiscal 2003.

   At May 31, 1998, the cost of investments for Federal income tax purposes was
substantially the same as the cost for financial reporting purposes (see the
Statement of Investments).

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

   (A) Pursuant to a management agreement ("Agreement") with the Manager, the
management fee is computed at the annual rate of .50 of 1% of the value of the
Fund's average daily net assets and is payable monthly. The Agreement provides
that if in any full fiscal year the aggregate expenses, exclusive of taxes,
brokerage, interest on borrowings and extraordinary expenses, exceed 1 1/2% of
the value of the Fund's average net assets, the Fund may deduct from payments to
be made to the Manager, or the Manager will bear such excess expense. During the
period May 31, 1998, there was no expense reimbursement pursuant to the
Agreement.

   (B) Under the Distribution Plan with respect to Class B ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1 under the Act, Class B
shares directly bear the cost of preparing, printing and distributing
prospectuses and statements of additional information and of implementing and
operating the Class B Distribution Plan. In addition, Class B shares reimburse
the Distributor for payments made to third parties for distributing their shares
at an annual rate of .20 of 1% of the value of the average daily net assets of
Class B shares. During the period ended May 31, 1998, Class B shares were
charged $45,819 pursuant to the Distribution Plan.

   (C) Under the Shareholder Services Plan with respect to Class A ("Class A
Shareholder Services Plan"), Class A shares reimburse Dreyfus Service
Corporation, a wholly-owned subsidiary of the Manager, an amount not to exceed
an annual rate of .25 of 1% of the value of the average daily net 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 Class A shares and providing reports and other information,
and services related to the maintenance of shareholder accounts. During the
period ended May 31, 1998, Class A shares were charged $269,371 pursuant to the
Shareholder Services Plan.

   Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), Class B shares pay the Distributor, at an annual
rate of .25 of 1% of the value of the average daily net assets of Class B shares
for servicing shareholder accounts. The services provided may include personal
services relating to shareholder accounts, such as answering shareholder
inquiries regarding Class B shares and providing reports and other information,
and services related to the maintenance of shareholder accounts. The Distributor
may make payments to Service in respect of their services. The Distributor
determines the amounts to be paid to Service Agents.

   The Manager had undertaken, through May 31, 1998, that if the aggregate
expenses of Class B shares, 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 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, 1998, Class B shares were charged $68,728, of which $22,232
was reimbursed by the Manager.


<PAGE>
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. During the period
ended May 31, 1998, the Fund was charged $71,968 pursuant to the transfer agency
agreement.

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


<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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