DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1995-07-27
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LETTER TO SHAREHOLDERS
Dear Shareholder:
    We are pleased to provide you with this semi-annual report for the
General New York Municipal Money Market Fund. For the period ended May 31,
1995, the annualized yield provided by your Fund was 3.35%. After taking into
account the effect of compounding, the annualized effective yield was 3.40%.*
 Dividends of approximately $.017 per share paid during the period were
exempt from Federal, New York State and New York City 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 letter, the Federal Reserve Board limited its actions to
just one interest rate hike of 50 basis points which represented a decrease
in magnitude from previous actions. The fact that the increase was smaller
reflected, in part, the belief that some slowing in the economy had occurred.
However, as some economic indicators continued to conflict with that belief,
the argument for at least a moderate hike appeared reasonable at the time.
More recent events suggest the Fed may ease interest rates soon and, in large
part, market levels now reflect those expectations.
    While market fundamentals do affect the short-term municipal market, the
overriding influence continues to be market
technical factors (i.e. supply/demand). Since the rates on those securities
in the portfolio which provide the highest degree of liquidity (1-day and
7-day demand notes) are adjusted on a daily or weekly basis, your Fund's
yield reflects these rapid adjustments and fluctuates accordingly. As of May
31, rates on such securities provided an attractive return, trading at better
than 75% of the taxable overnight repurchase rates. We anticipate that these
yields will drop significantly in the coming weeks as many holdings in
municipal money market funds mature at the end of June. However, if previous
summer technical patterns are repeated, we expect the situation should
reverse in late July and August as issuers return to the market with their
summer financings.
    In the wake of the Orange County, California bankruptcy filing in
December, we continue to devote our resources to locating those credits which
achieve our high internal standards and which provide your Fund with
attractive returns.  We have included a current Statement of Investments and
recent financial statements for your review and look forward to serving your
investment needs in the future.

                          Very truly yours,

                          Richard J. Moynihan
                          Director, Municipal Portfolio Management
                          The Dreyfus Corporation
June 16, 1995
New York, N.Y.
*  Annualized effective yield is based upon dividends declared daily and
reinvested monthly.
**Some income may be subject to the Federal Alternative Minimum Tax (AMT) for
certain shareholders.
<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS                                                                                  MAY 31, 1995 (UNAUDITED)
                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS-100.0%                                                                        AMOUNT              VALUE
                                                                                                --------------      --------------
<S>                                                                                            <C>                 <C>
NEW YORK-96.5%
Babylon Industrial Development Agency, RRR, VRDN
    (Equity Babylon Project) 4.45% (LOC; Union Bank of Switzerland) (a,b)...                   $    6,000,000      $    6,000,000
East Northport Union Free School District, TAN 4.40%, 6/30/95...............                        5,600,000           5,601,504
Erie County, RAN 4.75%, 8/15/95 (LOC; Union Bank of Switzerland) (b)........                       18,000,000          18,026,666
Erie County Water Authority, Water Revenue, VRDN
    3.90%, Series A (Insured; AMBAC and Liquidity Facility; Industrial Bank of Japan) (a)           9,000,000           9,000,000
Town of Islip Industrial Development Agency, IDR, VRDN
    (Brentwood Distribution Project)4.275% (LOC; Bankers Trust) (a,b).......                        1,000,000           1,000,000
Metropolitan Transport Authority, Commuter Facilities Revenue, VRDN
    3.75% (LOC: Bank of Tokyo, Industrial Bank of Japan, Mitsubishi Bank,
    Morgan Bank, Morgan Guaranty Trust Co., National Westminster Bank and Sumitomo Bank) (a,b)     28,500,000          28,500,000
New York City, VRDN:
    4.25%, Series A-5 (LOC; Krediet Bank) (a,b).............................                        9,215,000           9,215,000
    4.25%, Series A-6 (LOC; Landesbank) (a,b)...............................                       10,000,000          10,000,000
    4.25%, Series B (Insured; MBIA) (a).....................................                        9,600,000           9,600,000
    4.25%, Series D (Insured; FGIC) (a).....................................                       18,100,000          18,100,000
    4.25%, Series E-2 (LOC; Industrial Bank of Japan) (a,b).................                        4,200,000           4,200,000
    4.25%, Series E-5 (LOC; Sumitomo Bank) (a,b)............................                       11,100,000          11,100,000
    4.30%, Series A-4 (SBPA; Chemical Bank) (a).............................                        5,300,000           5,300,000
    4.30%, Series A-10 (LOC; Sumitomo Bank) (a,b)...........................                        3,900,000           3,900,000
    4.30%, Series D (Insured; FGIC, Liquidity Facility; GE Capital) (a).....                        4,500,000           4,500,000
    4.40%, Series A-7 (LOC; Morgan Guaranty Trust Co.) (a,b)................                        8,100,000           8,100,000
    4.45%, Series B (Insured; MBIA) (a).....................................                        4,600,000           4,600,000
    4.45%, Series B (Insured; MBIA and SBPA; WestDeutsche Landesbank) (a)...                       20,000,000          20,000,000
    4.75%, Series E (LOC: Industrial Bank of Japan and
      Morgan Guaranty Trust Co.) (a,b)......................................                        6,100,000           6,100,000
New York City Housing Development Corp., Mortgage Revenue, VRDN:
    (Multi-Family York Avenue Development Project) 3.90% (LOC; Chemical Bank) (a,b)                 8,000,000           8,000,000
    (Park Gate Tower) 3.80% (LOC; Citibank) (a,b)...........................                        2,720,000           2,720,000
    (Residential East 17th Street) 4.35%, Series A (LOC; Chemical Bank) (a,b)                       6,800,000           6,800,000
New York City Industrial Development Agency, VRDN:
    Civil Facility Revenue (Children's Oncology Society/ Ronald McDonald
    House) 3.85% (LOC; Barclays Bank) (a,b).................................                        3,200,000           3,200,000
    IDR:
       4%, Series E (LOC; ABN-Amro Bank) (a,b)...............................                         900,000             900,000
       (Field Hotel Association JFK Project) 4% (LOC; Banque Indosuez) (a,b).                       4,000,000           4,000,000
       (Japan Airlines Co. Limited Project) 4.40% (LOC; Morgan Guaranty Trust Co.) (a,b)            8,000,000           8,000,000
       (Nobart-New York Ink Project) 4.40% (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, VRDN 4.25%, Series C (Insured; FGIC) (a).....................                       5,500,000           5,500,000
       New York State Energy, Research and Development Authority:
       Electric Facilities Revenue, VRDN (Lilco Project)
       3.80%, Series B (LOC; Toronto Dominion Bank) (a,b)....................                       8,000,000           8,000,000

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                      MAY 31, 1995 (UNAUDITED)
                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                   AMOUNT           VALUE
                                                                                                --------------      --------------
NEW YORK (CONTINUED)

New York State Energy, Research and Development Authority (continued):
    PCR:
      Bonds:
          (Lilco Project) 4.70%, Series A, 3/1/96 (LOC; Deutsche Bank) (b)..                    $  10,000,000       $  10,000,000
          (New York State Electric and Gas Corp.):
            4.60%, Series D, 12/1/95 (LOC; Union Bank of Switzerland) (b)...                       11,450,000          11,450,000
            4.65%, 3/15/96 (LOC; JP Morgan) (b).............................                       12,000,000          12,000,000
            4.15%, Series B, 10/15/95 (LOC; Union Bank of Switzerland) (b)..                        9,000,000           9,000,000
      VRDN:
          (Central Hudson Gas and Electric Project)
            4.05%, Series A (LOC; Bankers Trust) (a,b)......................                        3,800,000           3,800,000
          (Niagara Mohawk Project Corp.):
            4.30%, Series B (LOC; Toronto Dominion Bank) (a,b)..............                       23,900,000          23,900,000
            4.30%, Series C (LOC; Canadian Imperial Bank of Commerce) (a,b).                       22,100,000          22,100,000
            4.90%, Series A (LOC; Morgan Guaranty Trust Co.) (a,b)..........                       36,000,000          36,000,000
            4.90%, Series B (LOC; Morgan Guaranty Trust Co.) (a,b)..........                       12,000,000          12,000,000
New York State Environment Facilities Corp., RRR, VRDN
    (Equity Huntington Project) 4.35% (LOC; Union Bank of Switzerland) (a,b)                        8,600,000           8,600,000
New York State Local Government Assistance Corp., VRDN
    3.75%, Series B (LOC: Credit Suisse and Swiss Bank Corp.) (a,b).........                       24,600,000          24,600,000
New York State Medical Care Facilities Finance Agency, Revenue, VRDN
    (Pooled Equipment Loan Program):
      3.90%, Series I (LOC; Chemical Bank) (a,b)............................                       45,500,000          45,500,000
      3.90%, Series II (LOC; Chemical Bank) (a,b)...........................                        9,900,000           9,900,000
Niagara County, BAN 5.50%, 1/25/96..........................................                        8,900,000           8,924,838
North Hempstead Solid Waste Management Authority,
    Solid Waste Management Revenue, Refunding, VRDN
    3.80%, Series A (LOC; National Westminster Bank) (a,b)..................                       11,050,000          11,050,000
Onondaga County Industrial Development Agency, IDR, VRDN
    (Edgecomb Metals Co. Project)
    3.90% (LOC; Banque Nationale de Paris) (a,b)............................                        2,000,000           2,000,000
Port Authority of New York and New Jersey, VRDN:
    Special Obigation Revenue 3.95%, Series 3 (LOC; Deutsche Bank) (a,b)....                       12,000,000          12,000,000
    Versatile Structure Obligations 4.30%, Series I
      (Liquidity Facility: Bank of Tokyo, Sanwa Bank and Sumitomo Bank) (a).                        7,000,000           7,000,000
Rochester, BAN:
    4.75%, Series I, 11/2/95................................................                       37,122,000          37,200,113
    4.75%, 3/12/96..........................................................                       11,000,000          11,063,022
Suffolk County, TAN:
    4.50%, Series II, 9/14/95...............................................                       18,000,000          18,020,859
    5.25%, 8/15/95 (LOC; WestDeutsche Landesbank) (b).......................                       10,000,000          10,009,007
Triborough Bridge and Tunnel Authority, Special Obligation, VRDN
    4.95% (Insured; FGIC) (a)...............................................                       19,900,000          19,900,000

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF INVESTMENTS (CONTINUED)                                                                      MAY 31, 1995 (UNAUDITED)
                                                                                                     PRINCIPAL
TAX EXEMPT INVESTMENTS (CONTINUED)                                                                   AMOUNT              VALUE
                                                                                                --------------      --------------
NEW YORK (CONTINUED)

Westchester County, TAN 5%, 12/14/95........................................                    $  15,000,000       $  15,038,972
William Floyd Union Free School District, TAN 4.75%, 6/30/95................                       12,000,000          12,004,182
Yonkers Industrial Development Authority, Civic Revenue, Consumers Union
Facilities,
    VRDN 3.75% (Insured; AMBAC and Liquidity Facility; Credit Local de France) (a)                  3,400,000           3,400,000
U.S. RELATED-3.5%
Commonwealth of Puerto Rico Government Development Bank, Refunding, VRDN
    3.70% (LOC; Credit Suisse) (a,b)........................................                       23,000,000          23,000,000
                                                                                                                     -------------
TOTAL INVESTMENTS
    (cost $652,324,163).....................................................                                         $652,324,163
                                                                                                                     =============
</TABLE>
<TABLE>
<CAPTION>
SUMMARY OF ABBREVIATIONS
<S>           <C>                                                <S>         <C>
AMBAC         American Municipal Bond Assurance Corporation      PCR         Pollution Control Revenue
BAN           Bond Anticipation Notes                            RAN         Revenue Anticipation Notes
FGIC          Financial Guaranty Insurance Company               RRR         Resources Recovery Revenue
IDR           Industrial Development Revenue                     SBPA        Standby Bond Purchase Agreement
LOC           Letter of Credit                                   TAN         Tax Anticipation Notes
MBIA          Municipal Bond Investors Assurance                 VRDN        Variable Rate Demand Notes
              Insurance Corporation
</TABLE>
<TABLE>
<CAPTION>
SUMMARY OF COMBINED RATINGS (UNAUDITED)
FITCH (C)              OR          MOODY'S             OR         STANDARD & POOR'S          PERCENTAGE OF VALUE
- --------                           --------                       ------------------        --------------------
<S>                                <C>                            <C>                               <C>
F1+/F1                             VMIG1/MIG1                     SP1+/SP1                          94.1%
AAA/AA (d)                         Aaa/Aa (d)                     AAA/AA (d)                         0.5
Not Rated (e)                      Not Rated (e)                  Not Rated (e)                      5.4
                                                                                                   -------
                                                                                                   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 May 31, 1995, 66.5% 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 and Morgan
    Guaranty Trust Co. provided letters of credit to 10.7% and 10.7%,
    respectively, of the Fund's net assets.
    (c)  Fitch currently provides creditworthiness information for a limited
    number of investments.
    (d)  Notes which are not F, MIG or SP rated are represented by bond
    ratings of the issuers.
    (e)  Securities which, while not rated by Fitch, Moody's or Standard &
    Poor's have been determined by the Fund's Board of Trustees to be of
    comparable quality to those rated securities in which the Fund may
    invest.

See independent accountants' review report and notes to financial statements.
<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF ASSETS AND LIABILITIES                                                                       MAY 31, 1995 (UNAUDITED)
<S>                                                                                                  <C>             <C>
ASSETS:
    Investments in securities, at value-Note 1(a)...........................                                         $652,324,163
    Interest receivable.....................................................                                            5,820,521
    Prepaid expenses........................................................                                               46,759
                                                                                                                     -------------
                                                                                                                       658,191,443
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                         $245,796
    Accrued expenses and other liabilities..................................                          179,483             425,279
                                                                                                --------------       -------------
NET ASSETS  ................................................................                                         $657,766,164
                                                                                                                     =============
REPRESENTED BY:
    Paid-in capital.........................................................                                         $657,833,657
    Accumulated net realized (loss) on investments..........................                                             (67,493)
                                                                                                                     -------------
NET ASSETS at value applicable to 657,833,657 outstanding shares of
    Beneficial Interest, equivalent to $1.00 per share (unlimited number
    of $.001 par value shares authorized)...................................                                         $657,766,164
                                                                                                                     =============

STATEMENT OF OPERATIONS                                                                  SIX MONTHS ENDED MAY 31, 1995 (UNAUDITED)
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                          $12,875,913
    EXPENSES:
      Management fee-Note 2(a)..............................................                       $1,663,062
      Shareholder servicing costs-Note 2(c).................................                          350,616
      Professional fees.....................................................                           28,291
      Custodian fees........................................................                           23,319
      Trustees' fees and expenses-Note 2(d).................................                           12,256
      Prospectus and shareholders' reports-Note 2(b)........................                            9,194
      Registration fees.....................................................                            2,538
      Miscellaneous.........................................................                            8,475
                                                                                                   -----------
                                                                                                    2,097,751
      Less-reduction in management fee due to
          undertakings-Note 2(a)............................................                          357,590
                                                                                                    ----------
            TOTAL EXPENSES..................................................                                            1,740,161
                                                                                                                      ------------
INVESTMENT INCOME-NET.......................................................                                           11,135,752
NET REALIZED (LOSS) ON INVESTMENTS-Note 1(b)................................                                              (18,598)
                                                                                                                      ------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                          $11,117,154
                                                                                                                      ============



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

</TABLE>
<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
STATEMENT OF CHANGES IN NET ASSETS
                                                                                       YEAR ENDED                SIX MONTHS ENDED
                                                                                      NOVEMBER 30,                 MAY 31, 1995
                                                                                         1994                      (UNAUDITED)
                                                                                   -----------------           -------------------
<S>                                                                               <C>                             <C>
OPERATIONS:
    Investment income-net.............................................            $      15,380,550               $    11,135,752
    Net realized (loss) on investments................................                      (39,573)                     (18,598)
                                                                                   -----------------           -------------------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS............                   15,340,977                    11,117,154
                                                                                   -----------------           -------------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net.............................................                  (15,380,550)                 (11,135,752)
                                                                                   -----------------           -------------------
BENEFICIAL INTEREST TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold.....................................                1,264,417,458                   582,010,829
    Dividends reinvested..............................................                   14,609,328                    10,551,461
    Cost of shares redeemed...........................................               (1,201,510,009)                 (624,695,611)
                                                                                   -----------------           -------------------
      INCREASE (DECREASE) IN NET ASSETS FROM
          BENEFICIAL INTEREST TRANSACTIONS............................                   77,516,777                   (32,133,321)
                                                                                   -----------------           -------------------
            TOTAL INCREASE (DECREASE) IN NET ASSETS...................                   77,477,204                   (32,151,919)
NET ASSETS:
    Beginning of period...............................................                  612,440,879                   689,918,083
                                                                                   -----------------           -------------------
    End of period.....................................................             $    689,918,083               $   657,766,164
                                                                                   =================           ===================





See independent accountants' review report and notes to financial statements.
</TABLE>
<TABLE>
<CAPTION>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Beneficial Interest outstanding, total investment return, ratios to average
net assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.


                                                                                                                 SIX MONTHS ENDED
                                                          YEAR ENDED NOVEMBER 30,                                  MAY 31, 1995
                                                  --------------------------------------------------
PER SHARE DATA:                                     1990       1991         1992       1993         1994           (UNAUDITED)
                                                  ---------  ---------   ---------   --------     --------       -----------------
    <S>                                           <C>        <C>         <C>         <C>          <C>                <C>
    Net asset value, beginning of period          $  .9991   $  .9999    $  .9999    $1.0000      $1.0000            $  .9999
                                                  ---------  ---------   ---------   --------     --------       -----------------
    INVESTMENT OPERATIONS:
    Investment income-net...............             .0561      .0436       .0275      .0198        .0232               .0167
    Net realized and unrealized gain (loss)
      on investments....................             .0008        --        .0001       --         (.0001)               --
                                                  ---------  ---------   ---------   --------     --------       -----------------

      TOTAL FROM INVESTMENT OPERATIONS..             .0569     .0436        .0276      .0198        .0231              .0167
                                                  ---------  ---------   ---------   --------     --------       -----------------
    DISTRIBUTIONS;
    Dividends from investment income-net            (.0561)   (.0436)      (.0275)    (.0198)      (.0232)            (.0167)
                                                  ---------  ---------   ---------   --------     --------       -----------------
    Net asset value, end of period......          $  .9999   $ .9999      $1.0000    $1.0000      $ .9999          $  .9999
                                                  ---------  ---------   ---------   --------     --------       -----------------
TOTAL INVESTMENT RETURN.................            5.76%     4.45%        2.78%      2.00%        2.34%             3.37%*
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets          --        .09%         .25%       .32%         .34%              .52%*
    Ratio of net investment income to
      average net assets................            5.58%     4.44%        2.99%      1.98%        2.33%             3.35%*
    Decrease reflected in above expense ratios
      due to undertakings by the manager             .66%      .55%         .38%       .35%         .32%               .11%*
    Net Assets, end of period (000's Omitted)    $500,947 $586,933     $630,899   $612,441    $689,918            $657,766
*  Annualized.




See independent accountants' review report and notes to financial statements.
</TABLE>
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a non-diversified open-end management investment company. Premier Mutual
Fund Services, Inc. (the "Distributor") acts as the exclusive distributor of
the Fund's shares, which are sold to the public without a sales charge. The
Distributor, located at One Exchange Place, Boston, Massachusetts 02109, is a
wholly-owned subsidiary of FDI Distribution Services, Inc., a provider of
mutual fund administation services, which in turn is a wholly-owned
subsidiary of FDI Holdings, Inc., the parent company of which is Boston
Institutional Group, Inc. The Dreyfus Corporation ("Manager") serves as the
Fund's investment adviser. The Manager is a direct subsidiary of Mellon Bank,
N.A.
    It is the Fund's policy to maintain a continuous net asset value per
share of $1.00; the Fund has adopted certain investment, portfolio valuation
and dividend and distribution policies to enable it to do so. There is no
assurance, however, that the Fund will be able to maintain a stable net asset
value of $1.00.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Trustees to represent the fair
value of the Fund's investments.
    (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities
transactions are recorded on a trade date basis. Interest income, adjusted
for amortization of premiums and original issue discounts on investments, is
earned from settlement date and recognized on the accrual basis. Realized
gain and loss from securities transactions are recorded on the identified
cost basis.
    The Fund follows an investment policy of investing primarily in municipal
obligations of one state. Economic changes affecting the state and certain of
its public bodies and municipalities may affect the ability of issuers within
the state to pay interest on, or repay principal of, municipal obligations
held by the Fund.
    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends daily from investment income-net. Such dividends are paid monthly.
Dividends from net realized capital gain, if any,  are normally declared and
paid annually, but the Fund may make distributions on a more frequent basis
to comply with the distribution requirements of the Internal Revenue Code. To
the extent that net realized capital gain can be offset by capital loss
carryovers, it is the policy of the Fund not to distribute such gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, which can distribute tax exempt
dividends, by complying with the applicable provisions of the Internal
Revenue Code, and to make distributions of income and net realized capital
gain sufficient to relieve it from substantially all Federal income and
excise taxes.
    The Fund has an unused capital loss carryover of approximately $49,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to November 30, 1994. If not
applied, $9,000 of the carryover expires in fiscal 1998 and $40,000 expires
in fiscal 2002.
    At May 31, 1995, the cost of investments for Federal income tax purposes
was substantially the same as the cost for financial reporting purposes (see
the Statement of Investments).

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 ("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. The Manager had undertaken from December 1,
1994 to April 16, 1995 to reduce the management fee paid by the Fund, to the
extent that the Fund's aggregate expenses (excluding certain expenses as
described above) exceeded an annual rate of .50 of 1% of the average daily
value of the Fund's net assets, and thereafter had undertaken from April 17,
1995 through May 31, 1995, to reduce the management fee paid by the Fund to
the extent that the Fund's aggregate expenses (excluding certain expenses as
described above) exceeded specified annual percentages of the Fund's average
daily net assets. The reduction in management fee, pursuant to the
undertakings, amounted to $357,590 for the six months ended May 31, 1995.
    (B) Pursuant to the Fund's Shareholder Services Plan, the Fund reimburses
Dreyfus Service Corporation 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 six months
ended May 31, 1995, the Fund was charged an aggregate of $187,157 pursuant to
the Shareholder Services Plan.
    (C) Each trustee who is not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $250
per meeting. The Chairman of the Board receives an additional 25% of such
compensation.

GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF TRUSTEES
GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
    We have reviewed the accompanying statement of assets and liabilities of
General New York Municipal Money Market Fund, including the statement of
investments, as of May 31, 1995, and the related statements of operations and
changes in net assets and financial highlights for the six month period ended
May 31, 1995. These financial statements and financial highlights are the
responsibility of the Fund's management.
    We conducted our review in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures
to financial data, and making inquiries of persons responsible for financial
and accounting matters. It is substantially less in scope than an audit
conducted in accordance with generally accepted auditing standards, which
will be performed for the full year with the objective of expressing an
opinion regarding the financial statements and financial highlights taken as
a whole. Accordingly, we do not express such an opinion.
    Based on our review, we are not aware of any material modifications that
should be made to the interim financial statements and financial highlights
referred to above for them to be in conformity with generally accepted
accounting principles.
    We have previously audited, in accordance with generally accepted
auditing standards, the statement of changes in net assets for the year ended
November 30, 1994 and financial highlights for each of the five years in the
period ended November 30, 1994 and in our report dated January 5, 1995,
we expressed an unqualified opinion on such statement of changes in net
assets and financial highlights.

(Ernst & Young LLP  Signature Logo)

New York, New York
June 30, 1995



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
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.                            574SA955
General New York
Municipal
Money Market Fund
Semi-Annual Report
May 31, 1995




(Dreyfus Logo)



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