DREYFUS GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND
N-30D, 1999-08-06
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General New York
Municipal Money
Market Fund

SEMIANNUAL REPORT
May 31, 1999

<PAGE>

The views expressed herein are current to the date of this report. These views
and the composition of the fund's portfolio are subject to change at any time
based on market and other conditions.

  * Not FDIC-Insured
  * Not Bank-Guaranteed
  * May Lose Value

Year 2000 Issues (Unaudited)

The fund could be adversely affected if the computer systems used by The Dreyfus
Corporation and the fund's other service providers do not properly process and
calculate date-related information from and after January 1, 2000. The Dreyfus
Corporation is working to avoid Year 2000-related problems in its systems and to
obtain assurances from other service providers that they are taking similar
steps. In addition, issuers of securities in which the fund invests may be
adversely affected by Year 2000-related problems. This could have an impact on
the value of the fund's investments and its share price.

<PAGE>
                                   Contents

                                   THE FUND

- -------------------------------------------

                              2     Letter from the President

                              3     Discussion of Fund Performance

                              6     Statement of Investments

                             10     Statement of Assets and Liabilities

                             11     Statement of Operations

                             12     Statement of Changes in Net Assets

                             13     Financial Highlights

                             15     Notes to Financial Statements

                                    FOR MORE INFORMATION

- --------------------------------------------------------

                                    Back Cover

<PAGE>

           General New York
Municipal Money Market Fund          The Fund

LETTER FROM THE PRESIDENT

Dear Shareholder:

We are pleased to present this semiannual report for General New York Municipal
Money Market Fund, covering the six-month period from December 1, 1998 through
May 31, 1999. Inside, you'll find valuable information about how the fund was
managed during the reporting period, including a discussion with the fund's
portfolio manager, Karen Hand.

Yields on both taxable and tax-exempt money market securities generally declined
early in the reporting period in the wake of the Federal Reserve Board's
decision in the fall of 1998 to ease monetary policy. While the U.S. economy has
continued to grow, the Federal Reserve was concerned about persistent economic
weakness abroad. Their adoption of lower short-term interest rates was intended
to stimulate not just domestic economic growth, but the economies of other
nations as well.

Despite lower nominal interest rates for tax-exempt money market instruments,
very low inflation continued to support attractive real returns, which are
nominal yields less the rate of inflation.

We appreciate your confidence over the past six months, and we look forward to
your continued participation in General New York Municipal Money Market Fund.

Sincerely,

/s/ Stephen E. Canter

Stephen E. Canter
President and Chief Investment Officer
The Dreyfus Corporation
June 14, 1999

2

<PAGE>

DISCUSSION OF FUND PERFORMANCE

Karen Hand, Portfolio Manager

How did General New York Municipal Money Market Fund perform during the period?

For the six-month period ended May 31, 1999, General New York Municipal Money
Market Fund produced an annualized, tax-exempt yield of 2.33% for Class A shares
and 2.01% for Class B shares. After taking into account the effect of
compounding, the fund's Class A shares provided an annualized effective yield of
2.36% while the fund's Class B shares produced an annualized effective yield of
2.03%.(1)

For the six-month period ended May 31, 1999, the fund's Class A shares and Class
B shares provided total returns of 1.17% and 1.00%,(2) respectively, compared to
the Lipper New York Tax-Exempt Money Market Funds category average total return
of 1.24% for the same time period.(3)

What is the fund's investment approach?

Our goal is to seek a high level of federal, state and New York City tax-exempt
income while maintaining a stable $1.00 share price. We also seek to provide a
competitive total return, and we attempt to be especially vigilant in our
efforts to preserve capital.

To achieve these objectives, we employ two primary strategies. First, we attempt
to add value by constructing a diverse portfolio of high-quality, tax-exempt
money market instruments from New York issuers. Second, we actively manage the
portfolio's average maturity in anticipation of interest rate trends and
supply-and-demand changes in New York's short-term municipal marketplace.

For example, if we expect supply to increase temporarily when many
municipalities issue short-term debt at once -- as they tend to do immediately
after passage of the state's annual budget, for example -- we may reduce the
portfolio's average maturity to make cash available

                                                                      The Fund 3

<PAGE>
DISCUSSION OF FUND PERFORMANCE (continued)

for the purchase of higher-yielding securities. That's because yields tend to
rise if many issuers are competing for investor interest. If we expect demand
to surge at a time when we anticipate little issuance and, therefore, lower
yields -- as often happens in January -- we may increase the portfolio's
average maturity prior to that time to maintain current yields for as long as
possible. Overall, we try to maintain an average maturity that reflects our
view of short-term interest rate trends, note issuance and anticipated cash
flows.

What other factors influenced the fund's performance?

Although the fund, by definition, contains primarily securities from New York
issuers, the entire U.S. fixed-income marketplace was influenced just prior to
the reporting period by economic events overseas. When the Asian currency and
credit crisis threatened Latin America last summer and fall, the Federal Reserve
Board and other central banks reduced key short-term interest rates. This move
was intended to help boost economic activity by making borrowing less expensive
for corporations. An additional consequence was lower yields on money market
securities.

Despite economic weakness in some overseas markets, the U.S. and New York
economies remained strong. Because municipalities have enjoyed higher tax
revenues during this period of economic prosperity, many have had less need to
borrow. As a result, fewer tax-exempt money market securities were issued in New
York than in the same six-month period one year ago. Yet, demand from investors
seeking to minimize their income tax liabilities remained high. This imbalance
helped push short-term tax-exempt yields down further during the final months of
1998. Tax-exempt yields have remained relatively stable so far in 1999.

4

<PAGE>
What is the fund's current strategy?

We have continued to focus on high-quality money market instruments from a wide
array of tax-exempt issuers. Some of the most frequently used instruments
include Variable Rate Demand Notes (VRDNs), which are issued by investment banks
through the securitization of longer-term municipal bonds. With a put feature of
either one or seven days attached to each VRDN, we believe that VRDNs afford a
high degree of liquidity as well as high quality to the Portfolio. Accordingly,
as of May 31, 1999, approximately 48% of the portfolio was composed of VRDNs.
The remaining 52% was comprised of municipal notes as well as non-rated
short-term debt from New York counties and school districts that have been
deemed equivalent to the highest credit agency ratings by Dreyfus credit
analysts.

June 14, 1999
[FN]
1 Annualized effective yield is based upon dividends declared daily and
  reinvested monthly. Past performance is no guarantee of future results. Yields
  fluctuate. An investment in the fund is not insured or guaranteed by the
  FDIC or any other government agency. Although the fund seeks to preserve the
  value of your investment at $1.00 per share, it is possible to lose money by
  investing in the fund.
2 Total return includes reinvestment of dividends. The fund's Class B shares'
  return figure provided reflects the absorption of fund expenses by The
  Dreyfus Corporation pursuant to an undertaking in effect that may be extended,
  terminated or modified at any time. Had these expenses not been absorbed, the
  fund's Class B shares' return would have been lower. Income may be subject to
  state and local taxes for non-New York residents, and some income may be
  subject to the Federal Alternative Minimum Tax (AMT) for certain investors.
3 Source: Lipper Analytical Services, Inc.
</FN>
                                                                      The Fund 5

<PAGE>

STATEMENT OF INVESTMENTS
May 31, 1999 (Unaudited)

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------------
                                                                      Principal
Tax Exempt Investments--98.8%                                        Amount ($)          Value ($)
- --------------------------------------------------------------------------------------------------
<S>                                                                  <C>                <C>
New York--96.4%
Erie County, RAN 4%, 10/13/99 (LOC; The Bank of New York)            10,000,000         10,035,635
Erie County Water Authority, Water Revenue, VRDN
  3%, Series A (Insured; AMBAC and Liquidity Facility;
  National Bank of Australia)(a)                                      9,000,000          9,000,000
Hicksville Union Free School District, TAN 4%, 6/23/99                8,000,000          8,001,859
Town of Islip Industrial Development Agency, IDR, VRDN
  (Brentwood Distribution Project) 3.25% (LOC; Fleet Bank)(a)         1,000,000          1,000,000
 Long Island Power Authority, Electric Systems Revenue, CP:
  2.80%, Series 4, 8/12/99 (LOC: Bayerische Landesbank
    and Westdeutsche Landesbank)                                     10,000,000         10,000,000
  3.05%, Sub-Series 1, 8/17/99 (LOC: Bayerische
    Landesbank and Westdeutsche Landesbank)                          10,000,000         10,000,000
Metropolitan Transportation Authority, Transit Facilities
  Revenue, Series 1, Sub-Series B, CP:
    3%, 7/9/99 (LOC; ABN-Amro Bank)                                  10,000,000         10,000,000
    2.65%, 7/14/99 (LOC; ABN-Amro Bank)                              14,000,000         14,000,000
    3.05%, 7/20/99 (LOC; ABN-Amro Bank)                              12,000,000         12,000,000
New York City, VRDN:
  3.20%, Sub-Series A-6 (LOC; Landesbank Hessen)(a)                   8,000,000          8,000,000
  3.30%, Series B, Sub-Series B-4
    (Insured; MBIA and Liquidity Facility; Credit Agricole
      de Indosuez)(a)                                                15,000,000         15,000,000
  3.40%, Sub-Series E-4 (LOC; State Street Bank and
    Trust Co.)(a)                                                     4,300,000          4,300,000
New York City Health and Hospital Corporation, Health
  Systems Revenue, VRDN
  3.05%, Series A (LOC; Morgan Guaranty Trust Co.)(a)                 9,700,000          9,700,000
New York City Housing Development Corporation, VRDN:
  MFMR (York Avenue Development Project) 4%
    (LOC; Midland Bank)(a)                                            8,000,000          8,000,000
  Multi-Family Rental Housing Revenue (Monterey)
    3%, Series A (LOC; FNMA)(a)                                      10,000,000         10,000,000
New York City Transitional Finance Authority, Future
  Tax Secured
  2.90%, Sub-Series 1, 11/1/99 (Liquidity Facility;
  Morgan Guaranty Trust Co.)                                         15,000,000         15,000,000
New York City Trust, Cultural Resource Revenue,
  Refunding, VRDN
  (American Museum of Natural History)
  3%, Series A (Insured; MBIA and Liquidity Facility;
  Credit Suisse)(a)                                                   3,000,000          3,000,000

</TABLE>

6

<PAGE>

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------------
                                                                      Principal
Tax Exempt Investments (continued)                                   Amount ($)          Value ($)
- --------------------------------------------------------------------------------------------------
<S>                                                                  <C>                <C>
New York (continued)
New York State, CP 2.65, 7/16/99 (Liquidity Facility;
  Westdeutsche Landesbank)                                           20,000,000        20,000,000
New York State Dorm Authority, Revenues, VRDN
  (Oxford University Press Inc.)
  3.30% (LOC; Landesbank Hessen)(a)                                   8,700,000         8,700,000
New York State Energy, Research and Development
  Authority, PCR:
  (New York State Electric and Gas) 3%, Series D, 12/1/99
    (LOC; Union Bank of Switzerland)                                 10,000,000        10,000,000
  VRDN (Central Hudson Gas and Electric Project)
    3.20%, Series A (LOC; Union Bank of Switzerland)a                 7,800,000         7,800,000
New York State Environmental Quality 3%, Series G,
  12/8/99 (LOC; Westdeutsche Landesbank)                              8,000,000         8,000,000
New York State Housing Finance Agency, Revenue, VRDN:
  Contract Obligation 3.05%, Series A (LOC; Commerzbank)(a)          14,400,000        14,400,000
  (Normandie Court I Project) 3% (LOC; Landesbank Hessen)(a)          7,900,000         7,900,000
New York State Local Government Assistance Corporation,
  VRDN:
    3%, Series A (LOC: Bayerische Landesbank and
      Westdeutsche Landesbank)(a)                                    27,600,000        27,600,000
    3%, Series B (LOC; Krediet Bank)(a)                              30,000,000        30,000,000
    3%, Series F (LOC; Toronto-Dominion Bank)(a)                     10,000,000        10,000,000
New York State Medical Care Facilities Finance Agency,
  Revenue, VRDN
  (Pooled Equipment Loan Program):
    3%, Series I (LOC; Chase Manhattan Bank)(a)                       2,000,000         2,000,000
    3%, Series II (LOC; Chase Manhattan Bank)(a)                      5,470,000         5,470,000
New York State Power Authority, CP:
  3%, Series 1, 7/8/99 (Liquidity Facility: Bank of
    Nova Scotia, Commerzbank, Credit Locale
    de France, Landesbank Hessen, Morgan Guaranty
    Trust Co. and Toronto-Dominion Bank)                              8,450,000         8,450,000
  3.10%, 9/9/99 (Liquidity Facility: Bank of Nova Scotia,
    Commerzbank, Credit Locale de France, Landesbank
    Hessen, Morgan Guaranty Trust Co. and
    Toronto-Dominion Bank)                                           10,000,000        10,000,000
Onondaga County Industrial Development Agency, IDR,
  VRDN (Edgecomb Metals Co. Project)
  3.25% (LOC; Banque Nationale de Paris)(a)                           2,000,000         2,000,000
Oyster Bay, BAN:
  4%, 10/1/99                                                         7,000,000         7,014,710
  3.25%, Series A, 11/30/99                                          10,000,000        10,012,114

</TABLE>

                                                                      The Fund 7

<PAGE>

STATEMENT OF INVESTMENTS (Unaudited) (continued)

<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------------
                                                                      Principal
Tax Exempt Investments (continued)                                   Amount ($)          Value ($)
- --------------------------------------------------------------------------------------------------
<S>                                                                  <C>                <C>
New York (continued)
Port Authority of New York and New Jersey,
Special Obligation Revenue, VRDN
  (Versatile Structure):
    3.25%, Series 2 (LOC; Morgan Guaranty Trust Co.)(a)               6,900,000          6,900,000
    3.30%, Series 6 (Liquidity Facility; Bank of Nova Scotia)(a)      3,000,000          3,000,000
    3.35%, Series 3 (Liquidity Facility; Morgan Guaranty
      Trust Co.)(a)                                                   3,200,000          3,200,000
Rochester, BAN 3.50%, Series 1, 3/8/2000                             12,000,000         12,030,635
Sachem Central School District, TAN (Holbrook) 4%, 6/25/99            7,500,000          7,501,572
Three Village Central School District, TAN (Brookhaven and
  Smithtown) 4%, 6/30/99                                              8,500,000          8,502,606
Westchester County, TAN 2.83%, 12/30/99                              18,000,000         18,000,991
Yonkers Industrial Development Agency, Civic Facilities
  Revenue, Consumers Union Facilities
  VRDN 3.15% (Insured; AMBAC and Liquidity Facility;
  Credit Local de France)(a)                                          3,300,000          3,300,000

U.S. Related--2.4%
Commonwealth of Puerto Rico, TRAN 3.50%,
  Series A, 7/30/99                                                  10,000,000         10,010,368
- --------------------------------------------------------------------------------------------------
Total Investments (cost $418,830,490)                                     98.8%        418,830,490

Cash and Receivables (Net)                                                 1.2%          5,145,045

Net Assets                                                               100.0%        423,975,535

</TABLE>

8

<PAGE>

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

AMBAC  American Municipal Bond               MFMR  Multi-Family Mortgage Revenue
         Assurance Corporation               PCR   Pollution Control Revenue
BAN    Bond Anticipation Notes               RAN   Revenue Anticipation Notes
CP     Commercial Paper                      TAN   Tax Anticipation Notes
FNMA   Federal National Mortgage Association TRAN  Tax and Revenue Anticipation
IDR    Industrial Development Revenue                Notes
LOC    Letter of Credit                      VRDN  Variable Rate Demand Notes
MBIA   Municipal Bond Investors
         Assurance Insurance Corporation

- --------------------------------------------------------------------------------

Summary of Combined Ratings

Fitch            or       Moody's     or  Standard & Poor's        Value (%)
- --------------------------------------------------------------------------------
F1+/F1                    VMIG1/MIG1, P1  SP1+/SP1, A1+/A1             90.7
AAA/AA(b)                 Aaa/Aa(b)       AAA/AA(b)                      .5
Not Rated(c)              Not Rated(c)    Not Rated(c)                  8.8
                                                                      100.0
[FN]
a Securities payable on demand. Variable interest rate-subject to periodic
  change.
b Notes which are not F, MIG or SP rated are represented by bond ratings of
  the issuers.
c Securities which, while not rated by Fitch, Moody's and Standard & Poor's
  have been determined by the Manager to be of comparable quality to those
  rated securities in which the fund may invest.
See notes to financial statements.
</FN>
                                                                      The Fund 9

<PAGE>

STATEMENT OF ASSETS AND LIABILITIES
May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------

                                                            Cost          Value
- --------------------------------------------------------------------------------
Assets ($):
Investments in securities--See Statement of
  Investments                                        418,830,490    418,830,490
Cash                                                                  1,873,627
Interest receivable                                                   3,453,447
Prepaid expenses                                                         50,123
                                                                    424,207,687
- --------------------------------------------------------------------------------
Liabilities ($):
Due to The Dreyfus Corporation and affiliates                           189,627
Due to Distributor                                                        8,303
Accrued expenses                                                         34,222
                                                                        232,152
- --------------------------------------------------------------------------------
Net Assets ($)                                                      423,975,535
- --------------------------------------------------------------------------------
Composition of Net Assets ($):
Paid-in capital                                                     424,041,774
Accumulated net realized gain (loss) on investments                     (66,239)
- --------------------------------------------------------------------------------
Net Assets ($)                                                      423,975,535
- --------------------------------------------------------------------------------


- --------------------------------------------------------------------------------
Net Asset Value Per Share

                                                         Class A        Class B
- --------------------------------------------------------------------------------
Net Assets ($)                                       380,829,129     43,146,406
Shares Outstanding                                   380,895,487     43,146,287
- --------------------------------------------------------------------------------
Net Asset Value Per Share ($)                               1.00           1.00

See notes to financial statements.

10

<PAGE>

STATEMENT OF OPERATIONS
Six Months Ended May 31, 1999 (Unaudited)

- --------------------------------------------------------------------------------

Investment Income ($)
- --------------------------------------------------------------------------------
Interest Income                                                   6,558,357
Expenses:
Management fee--Note 2(a)                                         1,089,690
Shareholder servicing costs--Note 2(c)                              270,570
Distribution fees (Class B)--Note 2(b)                              123,309
Professional fees                                                    23,470
Custodian fees                                                       22,134
Registration fees                                                    21,940
Prospectus and shareholders' reports                                 14,759
Trustees' fees and expenses--Note 2(d)                               12,697
Miscellaneous                                                         5,344
Total Expenses                                                    1,583,913
Less--reduction in shareholder servicing costs due to
  undertaking--Note 2(c)                                            (22,545)
Net Expenses                                                      1,561,368
Investment Income--Net, representing net increase in net assets
  resulting from operations                                       4,996,989

See notes to financial statements.

                                                                     The Fund 11

<PAGE>

STATEMENT OF CHANGES IN NET ASSETS

- --------------------------------------------------------------------------------
                                           Six Months Ended
                                               May 31, 1999          Year Ended
                                                (Unaudited)   November 30, 1998
- --------------------------------------------------------------------------------
Operations ($):
Investment income--net                            4,996,989          12,831,699
Net realized gain (loss) on investments                  --                 147
Net Increase (Decrease) in Net Assets
  Resulting from Operations                       4,996,989          12,831,846
- --------------------------------------------------------------------------------
Dividends to Shareholders from ($):
Investment income--net:
Class A shares                                   (4,504,420)        (11,691,987)
Class B shares                                     (492,569)         (1,139,712)
Total Dividends                                  (4,996,989)        (12,831,699)
- --------------------------------------------------------------------------------
Beneficial Interest Transactions
  ($1.00 per share):
Net proceeds from shares sold:
Class A shares                                  464,642,168       1,060,136,234
Class B shares                                   52,894,390         107,077,205
Dividends reinvested:
Class A shares                                    4,340,272          11,286,121
Class B shares                                      492,270           1,135,035
Cost of shares redeemed:
Class A shares                                 (493,207,326)     (1,107,118,496)
Class B shares                                  (57,237,342)       (103,384,014)
Increase (Decrease) in Net Assets from
  Beneficial Interest Transactions              (28,075,568)        (30,867,915)
Total Increase (Decrease) in Net Assets         (28,075,568)        (30,867,768)
- --------------------------------------------------------------------------------
Net Assets ($):
Beginning of Period                             452,051,103         482,918,871
End of Period                                   423,975,535         452,051,103

See notes to financial statements.

12

<PAGE>

FINANCIAL HIGHLIGHTS

The following tables describe the performance for each share class for the
fiscal periods indicated. Certain information reflects financial results for a
single fund share. Total return shows how much your investment in the fund
would have increased (or decreased) during each period, assuming you had
reinvested all dividends and distributions. These figures have been derived
from the fund's financial statements.

- --------------------------------------------------------------------------------
                     Six Months Ended
                         May 31, 1999            Year Ended November 30,
                                         --------------------------------------
Class A Shares             (Unaudited)   1998    1997     1996     1995    1994
- --------------------------------------------------------------------------------
Per Share Data ($):
Net asset value,
  beginning of period            1.00    1.00    1.00     1.00     1.00    1.00
Investment Operations:
Investment income--net           .012    .027    .029     .028     .032    .023
Distributions:
Dividends from investment
  income--net                   (.012)  (.027)  (.029)   (.028)   (.032)  (.023)
Net asset value, end of period   1.00    1.00    1.00     1.00     1.00    1.00
- --------------------------------------------------------------------------------
Total Return (%)*                2.35*   2.77    2.98     2.84     3.28    2.34
- --------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average
  net assets                      .68*    .68     .66      .68      .58     .34
Ratio of net investment income
  to average net assets          2.33*   2.74    2.94     2.80     3.23    2.33
Decrease reflected in above
  expense ratios due to
  undertakings by the Manager      --      --      --       --      .05     .32
- --------------------------------------------------------------------------------
Net Assets, end of period
  ($ x 1,000)                 380,829 405,054 440,750  507,537  636,013 689,918

* Annualized.
See notes to financial statements.

                                                                     The Fund 13

<PAGE>
FINANCIAL HIGHLIGHTS (continued)

- --------------------------------------------------------------------------------
                         Six Months Ended
                             May 31, 1999         Year Ended November 30,
                                              -------------------------------
Class B Shares                 (Unaudited)    1998    1997     1996     1995a
- --------------------------------------------------------------------------------
Per Share Data ($):
Net asset value, beginning of
  period                             1.00     1.00    1.00     1.00     1.00
Investment Operations:
Investment income--net               .010     .024    .027     .025     .006
Distributions:
Dividends from investment
  income--net                       (.010)   (.024)  (.027)   (.025)   (.006)
Net asset value, end of period       1.00     1.00    1.00     1.00     1.00
- --------------------------------------------------------------------------------
Total Return (%)                     2.01(b)  2.47    2.68     2.55     2.82(b)
- --------------------------------------------------------------------------------
Ratios/Supplemental Data (%):
Ratio of expenses to average
  net assets                          .98(b)   .98     .95      .95     1.04(b)
Ratio of net investment income
  to average net assets              2.00(b)  2.44    2.64     2.47     3.64(b)
Decrease reflected in above expense
  ratios due to undertakings by the
  Manager                             .09(b)   .08     .08      .16       --
- --------------------------------------------------------------------------------
Net Assets, end of period
  ($ x 1,000)                      43,146   46,997  42,169   36,199       --

[FN]
a From September 8, 1995 (commencement of initial offering) to November 30,
  1995.
b Annualized.
See notes to financial statements.
</FN>
14

<PAGE>
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, as amended (the "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 (the "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.

                                                                     The Fund 15

<PAGE>
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

(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 custody agreement, the fund
received net earnings credits of $15,405 during the period ended May 31, 1999
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 of 1986, as amended (the
"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 Code, and to make distributions
of income and net realized capital gain sufficient to relieve it from
substantially all Federal income and excise taxes.

16

<PAGE>
The fund has an unused capital loss carryover of approximately $58,000 available
for Federal income tax purposes to be applied against future net securities
profits, if any, realized subsequent to November 30, 1998. If not applied,
$40,000 of the carryover expires in fiscal 2002 and $18,000 expires in fiscal
2003.

At May 31, 1999, 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, 1999, 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, 1999, Class B shares were charged $49,324
pursuant to the Distribution Plan.

                                                                     The Fund 17


<PAGE>
NOTES TO FINANCIAL STATEMENTS (Unaudited) (continued)

(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 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, 1999, Class A shares were charged $180,198 pursuant to the
Class A 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 Agents in respect of their services. The
Distributor determines the amounts to be paid to Service Agents.

The Manager had undertaken through May 31, 1999, that if the aggregate expenses
of Class B shares, exclusive of taxes, brokerage, interest on borrowings and
extraordinary expenses, exceeded .98 of 1% of the value of the average daily net
assets of Class B, the Manager will reimburse the expenses of the fund under the
Class B Shareholder Services Plan to the extent of any excess expense and up to
the full fee payable under such plan. During the period ended May 31, 1999,
Class B shares were charged $73,985, of which $22,545 was reimbursed by the
Manager.

18

<PAGE>
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, 1999, the fund was charged $55,985 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.

                                                                     The Fund 19
<PAGE>
NOTES

<PAGE>
For More Information

                     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

                     Distributor

                     Premier Mutual Fund Services, Inc.
                     60 State Street
                     Boston, MA 02109

To obtain information:

By telephone
Call 1-800-645-6561

By mail  Write to:
The Dreyfus Family of Funds
144 Glenn Curtiss Boulevard
Uniondale, NY 11556-0144

By E-mail  Send your request
to [email protected]

On the Internet  Information
can be viewed online or
downloaded from:
http://www.dreyfus.com

(c) 1999 Dreyfus Service Corporation  574/700SA995



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