DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1994-01-25
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President's Letter

Dear Shareholder:

     We are pleased to provide you with this annual report for the
General New York Municipal Money Market Fund. For the period ended
November 30, 1993, the yield provided by your Fund was 1.98%.  After
taking into account the effect of compounding, the effective yield was
2.00%.* Dividends of approximately $.02 per share paid during the period
were exempt from Federal, New York State and New York City personal
income taxes.** Throughout the period your Fund continued to provide an
attractive after-tax return relative to its short-term taxable
alternatives for the New York investor.
     Since our last report, inflation has remained at relatively low
levels and any increase in economic and credit demand growth has been
modest. Recent indicators that revealed economic strength do not appear
strong enough to result in any immediate tightening action by the
Federal Reserve Board.  Economic growth, however, is projected to pick
up in early 1994 and it may influence the Federal Reserve to implement a
more restrictive monetary policy. As a result, short-term yields may
rise, but we expect supply and demand factors in the municipal money
market to be the overriding influence on tax exempt money market rates.
Over the past several months, many issuers returned to the marketplace
with their traditional annual financings -- the most recent example
being a $1.4 billion State of New Jersey Tax Revenue Anticipation Note
issue that was well received.  During times when issuance of this type
outpaced demand, yields rose on municipal notes, creating opportunities
for attractive purchases for your Fund's portfolio.  At these times,
high-quality securities were added to the portfolio in an effort to
enhance the Fund's yield.  In addition, we expected technical factors
(supply/demand) in the municipal note market to cause rates on notes to
rise temporarily at year end. Traditionally, this occurs as individuals
and corporations tap their money funds to meet seasonal needs. This
attractive rate environment should provide a temporary boost in yields
at year end, and indeed, it did.
     We have included a current Statement of Investments and recent
financial statements for your review. We look forward to serving your
investment needs in the future.

Very truly yours,

Signature

Richard J. Moynihan
President

January 3, 1994
New York, N.Y.


GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
<TABLE>
<CAPTION>

STATEMENT OF INVESTMENTS                                                                         NOVEMBER 30, 1993

TAX EXEMPT INVESTMENTS-100.0%                                                          PRINCIPAL
                                                                                         AMOUNT            VALUE
                                                                                       ---------         -------

NEW YORK-94.3%
<S>                                                                                 <C>               <C>
Babylon Industrial Development Agency, RRR, VRDN (Equity Babylon Project)
  1.80% (LOC; Union Bank of Switzerland) (a,b)...............................       $  5,000,000      $  5,000,000
Erie County:
  RAN 3.30%, 8/5/94 (LOC; Mitsubishi Bank) (b)...............................         15,200,000        15,219,852
  TAN 2.45%, 12/30/93 (LOC; Mitsubishi Bank) (b).............................          7,150,000         7,150,000
Erie County Water Authority, Water Revenue, VRDN 2.15%, Series A
  (Insured; AMBAC and Liquidity Facility; Industrial Bank of Japan) (a)......          9,000,000         9,000,000
Fulton County Industrial Development Agency, Revenue, VRDN
  (SLM Action Sports Project) 2.425% (LOC; Royal Bank of Canada) (a,b).......          1,800,000         1,800,000
Half Hollow Hills Central School District, Huntington and Babylon, TAN
  3%, 6/24/94................................................................         13,000,000        13,042,746
Town of Islip Industrial Development Agency, IDR, VRDN
  (Brentwood District Co.) 2.675% (LOC; Bankers Trust) (a,b).................          3,000,000         3,000,000
Metropolitan Transport Authority, Commuter Facilities Revenue, VRDN
  2.05% (LOC: Bank of Tokyo, Industrial Bank of Japan, Mitsubishi Bank,
  Morgan Bank, National Westminster Bank and Sumitomo Bank) (a,b)............         28,800,000        28,800,000
Monroe County, BAN:
  2.75%, 12/17/93............................................................          6,500,000         6,501,260
  3%, 6/10/94................................................................          5,000,000         5,011,465
City of New York:
  RAN 3.50%, 6/30/94.........................................................         30,000,000        30,102,072
  TAN 3.125%, Series A, 4/8/94...............................................         10,000,000        10,017,887
  VRDN:
    GO Notes:
      1.90%, Series D (Insured; FGIC and Liquidity Facility; GE Capital) (a).          7,900,000         7,900,000
      2%, Series A-4 (LOC; Chemical Bank) (a,b)..............................          9,100,000         9,100,000
      2%, Series C-3 (LOC; Industrial Bank of Japan) (a,b)...................          4,300,000         4,300,000
      2%, Series C-4 (LOC; Fuji Bank) (a,b)..................................         10,100,000        10,100,000
      2%, Series C-5 (LOC; Sumitomo Bank) (a,b)..............................         16,100,000        16,100,000
      2%, Series D (SBPA; Citibank) (a)......................................         18,100,000        18,100,000
      2%, Series E (LOC; Industrial Bank of Japan) (a,b).....................          4,800,000         4,800,000
      2.10%, Series A-7 (LOC; Morgan Guaranty Trust) (a,b)...................          8,100,000         8,100,000
      2.15%, Series A-10 (LOC; Sumitomo Bank) (a,b)..........................          6,000,000         6,000,000
    Trust Cultural Resource Revenue (Solomon R. Guggenheim) 1.85%, Series B
      (LOC; Swiss Bank Corp.) (a,b)..........................................          9,750,000         9,750,000
New York City Housing Development Corp., Mortgage Revenue, VRDN
  (Park Gate Tower) 2.20% (LOC; Citibank) (a,b)..............................          2,835,000         2,835,000
New York City Industrial Development Agency, VRDN:
    Civil Facility Revenue (Children's Oncology Society)
      2.20% (LOC; Barclays Bank) (a,b).......................................          3,900,000         3,900,000
  IDR:
    2.20%, Series E (LOC; ABN-Amro Bank) (a,b)...............................            950,000           950,000
    (Field Hotel Association JFK Project) 2.15% (LOC; Banque Indosuez) (a,b).          4,000,000         4,000,000
    (Nobart-New York Inc. Project) 2.80% (LOC; Dai-Ichi Kangyo Bank) (a,b)...          2,900,000         2,900,000
New York City Municipal Water Finance Authority, Water and Sewer
  Systems Revenue:
    BAN 2.75%, Series A, 4/15/94.............................................         12,000,000        12,015,198
    VRDN 1.85%, Series C (Insured; FGIC) (a).................................          2,000,000         2,000,000
New York State:
  CP 2.50%, 12/6/93 (Line of Credit; Daiwa Bank).............................          9,000,000         9,000,000
  TRAN 2.75%, 12/31/93.......................................................         20,000,000        20,009,272
New York State Dormitory Authority, Revenue, CP
  (Sloan Kettering Memorial Hospital)
    2.30%, Series 89A, 12/17/93 (LOC; Fuji Bank) (a,b).......................          5,000,000         5,000,000
New York State Energy, Research and Development Authority:
  PCR:
    Bonds:
      (Lilco Project)
        2.50%, Series B, 3/1/94 (LOC; Deutsche Bank) (b).....................          5,450,000         5,450,000
      (New York State Electric and Gas):
        2.90%, Series D, 12/1/93 (LOC; Union Bank of Switzerland) (b)........            555,000           555,000
        2.75%, Series 85A, 3/1/94 (LOC; Union Bank of Switzerland) (b).......          7,000,000         7,000,000
        2.50%, Series 85A, 3/15/94 (LOC; Morgan Guaranty Trust) (b)..........          8,000,000         8,000,000
        2.85%, Series B, 10/15/94 (LOC; Union Bank of Switzerland) (b).......          7,200,000         7,200,000
    VRDN:
      (Central Hudson Gas and Electric Project):
        2.35%, Series B (LOC; Bankers Trust) (a,b)...........................          8,700,000         8,700,000
        2.40%, Series A (LOC; Bankers Trust) (a,b)...........................          3,800,000         3,800,000
      Electric Facilities Revenue (Lilco Project) 2.85%, Series B
        (LOC; Toronto Dominion Bank) (a,b)...................................          8,000,000         8,000,000
      (Niagara Mohawk Project):
        2.20%, Series A (LOC; Morgan Guaranty Trust) (a,b)...................         41,000,000        41,000,000
        2.20%, Series B (LOC; JP Morgan) (a,b)...............................         16,000,000        16,000,000
        2.30%, Series C (LOC; Canadian Imperial Bank of Commerce) (a,b)......          5,000,000         5,000,000
        2.45%, Series A (LOC; Toronto Dominion Bank) (a,b)...................         21,200,000        21,200,000
New York State Housing Finance Agency, Revenue, VRDN
  (Liberty View Apartment Housing Project) 2.20% (LOC; Chemical Bank) (a,b)..         10,850,000        10,850,000
New York State Job Development Authority, VRDN:
  2.47%, Series A1 Thru A9 (LOC; Sumitomo Bank) (a,b)........................            720,000           720,000
  2.47%, Series C1 Thru C34 (LOC; Sumitomo Bank) (a,b).......................            550,000           550,000
  2.47%, Series D1 Thru D16 (LOC; Sumitomo Bank) (a,b).......................            220,000           220,000
  2.50%, Series E1 Thru E55 (LOC; Sumitomo Bank) (a,b).......................          1,475,000         1,475,000
New York State Local Government Assistance Corp., VRDN 2%, Series 93A
  (LOC: Credit Suisse, Swiss Bank Corp. and Union Bank of Switzerland) (a,b).         12,000,000        12,000,000
New York State Medical Care Facilities Finance Agency, Revenue, VRDN
  (Pooled Equipment Loan Program) 2.15% (LOC; Chemical Bank) (a,b)...........         26,900,000        26,900,000
North Hempstead Solid Waste Management Authority, Solid Waste
  Management Revenue VRDN 2% (LOC; National Westminster Bank) (a,b)..........          8,500,000         8,500,000
Onondaga County Industrial Development Agency, IDR, VRDN (Edgecomb Metals)
  2.55% (LOC; Banque Nationale De Paris) (a,b)...............................          2,000,000         2,000,000
Port Authority of New York and New Jersey, Special Obigation Revenue, VRDN
  2.20%, Series 3 (LOC; Deutsche Bank) (a,b).................................         24,000,000        24,000,000
Rochester County, BAN 2.23%, 3/14/94.........................................         25,000,000        25,000,000
Rockland County, RAN 2.75%, 4/8/94...........................................          5,000,000         5,005,106
Rockland County Industrial Development Agency, IDR, VRDN (Wilton Foods)
  2.40% (LOC; Bank of Tokyo) (a,b)...........................................          3,000,000         3,000,000
Suffolk County, TAN 3%, 9/15/94 (LOC; Chemical Bank) (b).....................         20,000,000        20,023,008
Syracuse, BAN 3%, 6/17/94....................................................          7,163,000         7,182,526
U.S. RELATED-5.7%
Commonwealth of Puerto Rico Government Development Bank, Refunding, VRDN
  2.25% (LOC: Credit Suisse and Sumitomo Bank) (a,b).........................         23,000,000        23,000,000
Commonwealth of Puerto Rico Highway and Transportation Authority,
  Highway Revenue VRDN 2% (LOC: Landesbank Hessen, Swiss Bank Corp. and
  United Bank of Switzerland) (a,b)..........................................          3,000,000         3,000,000
Puerto Rico Industrial Medical and Environmental Pollution Control
  Facilities Financing Authority, Revenue Bonds
  (Abbott Laboratories Project) 2.70%, Series A, 3/1/94......................          8,250,000         8,250,000
                                                                                                      ------------
TOTAL INVESTMENTS
  (cost $605,085,392)........................................................                         $605,085,392
                                                                                                      ============
</TABLE>
<TABLE>
<CAPTION>

SUMMARY OF ABBREVIATIONS

<S>     <S>                                               <S>     <S>
AMBAC   American Municipal Bond Assurance Corporation     PCR     Pollution Control Revenue
BAN     Bond Anticipation Notes                           RAN     Revenue Anticipation Notes
CP      Commercial Paper                                  RRR     Resource Recovery Revenue
FGIC    Financial Guaranty Insurance Corporation          SBPA    Standby Bond Purchase Agreement
GO      General Obligation                                TAN     Tax Anticipation Notes
IDR     Industrial Development Revenue                    TRAN    Tax and Revenue Anticipation Notes
LOC     Letter of Credit                                  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>                       <S>                                <S>                               <C>
F1+/F1                    VMIG1/MIG1, P1 (d)                 SP1+/SP1, A1+/A1 (d)               88.6%
AAA/AA (e)                Aaa/Aa (e)                         AAA/AA (e)                          4.6
Not Rated (f)             Not Rated (f)                      Not Rated (f)                       6.8
                                                                                               ------
                                                                                               100.0%
                                                                                               ======

</TABLE>
NOTES TO STATEMENT OF INVESTMENTS:
(a)  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.
(b)  Secured by letters of credit. At November 30, 1993, 68.1% 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 10.9% of the Fund's net assets.
(c)  Fitch currently provides creditworthiness information for a limited
     amount 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 Directors to be of comparable quality to those rated securities
     in which the Fund may invest.
(g)  At November 30, 1993, the Fund had $156,802,485 (25.6% of net
     assets) invested in securities whose payment of
     principal and interest is dependent upon revenues generated from
     City of New York Municipal G.O. projects.


GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
<TABLE>
<CAPTION>
STATEMENT OF ASSETS AND LIABILITIES                                                              NOVEMBER 30, 1993

ASSETS:
  <S>                                                                             <C>                 <C>
  Investments in securities, at value-Note 1(a).........................                              $605,085,392
  Cash..................................................................                                 4,335,569
  Interest receivable...................................................                                 3,179,949
  Prepaid expenses......................................................                                    82,311
                                                                                                      ------------
                                                                                                       612,683,221

LIABILITIES:
  Due to The Dreyfus Corporation........................................          $     73,587
  Accrued expenses......................................................               168,755             242,342
                                                                                  ------------        ------------
NET ASSETS                                                                                            $612,440,879
                                                                                                      ============

REPRESENTED BY:
  Paid-in capital.......................................................                              $612,450,201
  Accumulated net realized (loss) on investments........................                                    (9,322)
                                                                                                      ------------

NET ASSETS at value applicable to 612,450,201 shares outstanding
  (unlimited number of $.001 par value shares of Beneficial
  Interest authorized)..................................................                              $612,440,879
                                                                                                      ============

NET ASSET VALUE, offering and redemption price per share
  ($612,440,879 divide 612,450,201 shares).............................                                     $1.00
                                                                                                            =====

STATEMENT OF OPERATIONS                                                               YEAR ENDED NOVEMBER 30, 1993
INVESTMENT INCOME:

  INTEREST INCOME.......................................................                              $ 13,559,117

  EXPENSES:
    Management fee-Note 2(a)............................................             2,951,496
    Shareholder servicing costs-Note 2(c)...............................               842,176
    Custodian fees......................................................                57,040
    Professional fees...................................................                45,493
    Prospectus and shareholders' reports-Note 2(b)......................                32,848
    Trustees' fees and expenses-Note 2(d)...............................                18,941
    Registration fees...................................................                 4,007
    Miscellaneous.......................................................                 1,629
                                                                                    ----------
                                                                                     3,953,630
    Less-reduction in management fee due to
      undertaking-Note 2(a).............................................             2,066,047
                                                                                    ----------
        TOTAL EXPENSES..................................................                                 1,887,583
                                                                                                      ------------

        INVESTMENT INCOME-NET...........................................                                11,671,534

REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
  Net realized gain on investments-Note 1(b)............................            $   33,905
  Net unrealized (depreciation) on investments..........................               (23,949)
                                                                                    ----------

        NET REALIZED AND UNREALIZED GAIN ON INVESTMENTS.................                                     9,956
                                                                                                      ------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS....................                              $ 11,681,490
                                                                                                      ============
See notes to financial statements.

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

                                                                                                 November 30,
                                                                                         -----------------------------
                                                                                              1992             1993
                                                                                         ------------      -----------
OPERATIONS:
  <S>                                                                                     <C>              <C>
  Investment income--net.......................................................           $ 16,247,789     $ 1,671,534
  Net realized gain on investments............................................                  7,498           33,905
  Net unrealized appreciation (depreciation) on investments for the year......                 23,949          (23,949)
                                                                                         ------------    -------------
    Net Increase In Net Assets Resulting From Operations......................             16,279,236       11,681,490
                                                                                         ------------    -------------
DIVIDENDS TO SHAREHOLDERS FROM;
  Investment income--net.......................................................            (16,247,789)    (11,671,534)
                                                                                         ------------    -------------
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
  Net proceeds from shares sold...............................................            979,147,788    1,221,685,330
  Dividends reinvested........................................................             15,427,173       11,110,335
  Cost of shares redeemed.....................................................           (950,640,453)  (1,251,263,666)
                                                                                         ------------    -------------
    Increase (Decrease) In Net Assets From Beneficial Interest Transactions...             43,934,508      (18,468,001)
                                                                                         ------------    -------------
      Total Increase (Decrease) In Net Assets.................................             43,965,955      (18,458,045)

  Beginning of year...........................................................            586,932,969      630,898,924
                                                                                         ------------    -------------
  End of year.................................................................           $630,898,924     $612,440,879
                                                                                         ============    =============
See notes to financial statements.

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


                                                                              YEAR ENDED NOVEMBER 30,
                                                               --------------------------------------------------
PER SHARE DATA:                                                  1989       1990       1991       1992       1993
                                                               ------     ------     ------     ------     ------
  <S>                                                          <C>        <C>        <C>       <C>        <C>
  Net asset value, beginning of year.....................      $.9989     $.9991     $.9999    $ .9999    $1.0000
                                                               ------     ------     ------     ------     ------
  INVESTMENT OPERATIONS:
  Investment income-net..................................       .0523      .0561      .0436     .0275       .0198
  Net realized and unrealized gain on investments........       .0002      .0008        --      .0001         --
                                                               ------     ------     ------     ------     ------
    TOTAL FROM INVESTMENT OPERATIONS.....................       .0525      .0569      .0436     .0276       .0198
                                                               ------     ------     ------     ------     ------
  DISTRIBUTIONS;
  Dividends from investment income-net...................      (.0523)    (.0561)    (.0436)   (.0275)     (.0198)
                                                               ------     ------     ------     ------     ------

  Net asset value, end of year...........................      $.9991     $.9999     $.9999   $1.0000     $1.0000
                                                               ======     ======     ======   =======     =======
TOTAL INVESTMENT RETURN..................................       5.36%       5.76%      4.45%     2.78%       2.00%

RATIOS/SUPPLEMENTAL DATA:

  Ratio of expenses to average net assets................        .75%        --         .09%      .25%        .32%
  Ratio of net investment income to average net assets...       5.97%       5.58%      4.44%     2.99%       1.98%

  Decrease reflected in above expense ratios due to
    undertakings by the Manager..........................        .15%        .66%       .55%      .38%        .35%

    Net Assets, end of year (000's Omitted)..............    $49,335    $500,947   $586,933  $630,899    $612,441

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. Dreyfus
Service Corporation ("Distributor") acts as the distributor of the
Fund's shares, which are sold to the public without a sales load. The
Distributor is a wholly-owned subsidiary of The Dreyfus Corporation
("Manager").

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.
(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, when appropriate, 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 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 provisions available to certain
investment companies, as defined in applicable sections of the Internal
Revenue Code, and to make distributions of income and net realized
capital gain sufficient to relieve it from all, or substantially all,
Federal income taxes.

The Fund has an unused capital loss carryover of approximately $9,000
available for Federal income tax pur-poses to be applied against future
net securities profits, if any, realized subsequent to November 30,
1993. If not applied, the carryover expires in fiscal 1998.
At November 30, 1993, 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 11/2% of the average
value of the Fund's net assets for any full fiscal year. However, the
Manager has undertaken from December 1, 1992 to waive receipt of the
management fee payable to it by the Fund in excess of an annual rate of
.15 of 1% of the Fund's average daily net assets. The reduction in
management fee, pursuant to the undertaking, amounted to $2,066,047 for
the year ended November 30, 1993.

The Manager may modify the expense limitation percentages from time to
time, provided that the resulting expense reimbursement would not be
less than the amount required pursuant to the Agreement.

(B) The Fund has adopted a Service Plan, (the "Plan") pursuant to which
the Fund will bear the costs of preparing, printing and distributing
certain of the Fund's prospectuses and statements of additional
information and costs associated with implementing and operating the
Plan, not to exceed the greater of $100,000 or .005 of 1% of the Fund's
average daily net assets for any full fiscal year. During the year ended
November 30, 1993, the Fund was charged $14,751 pursuant to the Plan.

(C) Pursuant to the Fund's Shareholder Services Plan, the Fund
reimburses the distributor an amount not to exceed an annual rate of .25
of 1% of the value of the Fund's average daily net assets 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. During the year ended November 30, 1993, the Fund was charged
an aggregate of $433,771 pursuant to the Shareholder Services Plan.

(D) Certain officers and trustees of the Fund are "affiliated persons,"
as defined in the Act, of the Manager and/or the Distributor. Each
trustee who is not an "affiliated person" receives an annual fee of
$2,500 and an attendance fee of $250 per meeting.

(E) On December 5, 1993, the Manager entered into an Agreement and Plan
of Merger providing for the merger of the Manager with a subsidiary of
Mellon Bank Corporation ("Mellon").

Upon closing of the merger, it is planned that the Manager will retain
its New York headquarters and will be a separate subsidiary within the
Mellon organization. It is expected that the Manager's management team
and mutual fund managers will remain in place, and the Dreyfus mutual
funds will be operated in the same manner as they are currently.

Following the merger, the Manager will be either a direct or indirect
subsidiary of Mellon, whose principal banking subsidiary is Mellon Bank,
N.A. Closing of this merger is subject to a number of contingencies,
including the receipt of certain regulatory approvals and the approvals
of the stockholders of the Manager and of Mellon. The merger is expected
to occur in mid-1994, but could occur significantly later.

Because the merger will constitute an "assignment" of the Fund's
Management Agreement with the Manager under the Investment Company Act
of 1940, and thus a termination of such Agreement, the Manager will seek
prior approval from the Fund's Board and shareholders.


GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
REPORT OF ERNST & YOUNG, 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, 1993, 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, 1993 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, 1993, the results of its operations for the year then
ended, the changes in its net assets for each of the two years in the
period then ended, and the financial highlights for each of the
indicated years, in conformity with generally accepted accounting
principles.

Ernst & Young Signature

New York, New York
January 3, 1994


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, 1993 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).


General New York
Municipal
Money Market Fund
Annual Report
November 30, 1993

GENERAL NEW YORK
MUNICIPAL MONEY MARKET FUND
144 Glenn Curtiss Boulevard
Uniondale, NY 11556

MANAGER
The Dreyfus Corporation
200 Park Avenue
New York, NY 10166

DISTRIBUTOR
Dreyfus Service Corporation
200 Park Avenue
New York, NY 10166

CUSTODIAN
The Bank of New York
110 Washington Street
New York, NY 10286

TRANSFER AGENT &
DIVIDEND DISBURSING AGENT
The Shareholder Services Group, Inc.
P.O. Box 9671
Providence, RI 02940

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

Printed in U.S.A.     574AR9311



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