GENERAL MUNICIPAL MONEY MARKET FUNDS INC
497, 1999-05-14
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General Money Market Funds

General Money Market Fund

General Municipal Money Market Fund

Investing in high quality, short-term securities for current income, safety of
principal and liquidity

PROSPECTUS May 1, 1999

CLASS X SHARES

As  with  all  mutual  funds,  the  Securities  and  Exchange Commission has not
approved  or  disapproved  these  securities or passed upon the adequacy of this
prospectus. Any representation to the contrary is a criminal offense.



<PAGE>




<PAGE>

The Funds

Contents

The Funds
- --------------------------------------------------------------------------------

Introduction                                                              1

General Money Market Fund                                                 2

General Municipal
Money Market Fund                                                         4

Management                                                                6

Financial Highlights                                                      7

Your Investment
- --------------------------------------------------------------------------------

Account Policies                                                          8

Distributions and Taxes                                                  11

Services for Fund Investors                                              11

Instructions for Regular Accounts                                        13

Instructions for IRAs                                                    14

For More Information
- --------------------------------------------------------------------------------

MORE   INFORMATION   ON   EACH   FUND  CAN  BE  FOUND  IN  THE  FUND'S  CURRENT
ANNUAL/SEMIANNUAL REPORT.  SEE BACK COVER.

Introduction

Each  fund  is  a money market mutual fund with a separate investment portfolio,
and  operations and results which are unrelated to those of the other fund. This
combined  prospectus  has  been  prepared  for  your convenience so that you can
consider two investment choices in one document.

As  a  money  market  fund,  each  fund  is  subject  to  maturity,  quality and
diversification requirements designed to help it maintain a stable share price.

Generally,  each  fund  is  required to invest at least 95% of its assets in the
securities  of  issuers with the highest credit rating or the unrated equivalent
as  determined  by  Dreyfus,  with the remainder invested in securities with the
second-highest credit rating.

An  investment  in  a  fund  is not insured or guaranteed by the Federal Deposit
Insurance  Corporation  or any other government agency. Although each fund seeks
to  preserve  the value of your investment at $1.00 per share, it is possible to
lose money by investing in a fund.

Concepts to understand

MONEY MARKET FUND: a specific type of fund that seeks to maintain a $1.00 price
per share. Money market funds are subject to strict federal requirements and
must do the following:

(pound) maintain an average dollar-weighted portfolio maturity of 90 days or
less

(pound) buy individual securities that have remaining maturities of 13 months or
less

(pound) buy only high quality, dollar-denominated obligations

CREDIT RATING: a measure of the issuer's expected ability to make all required
interest and principal payments in a timely manner. An issuer with the highest
credit rating has a very strong degree of certainty (or safety) with respect to
making all payments. An issuer with the second-highest credit rating has a
strong capacity to make all payments, but the degree of safety is somewhat
less.

                                                                      The Funds

<PAGE>


                                                      General Money Market Fund
                                                          ------------------
                                                             Ticker Symbol: N/A

GOAL/APPROACH

The  fund  seeks  as  high  a  level of current income as is consistent with the
preservation  of capital. To pursue this goal, the fund invests in a diversified
portfolio of high quality, short-term debt securities, including the following:


(pound) securitieses issued or guaranteed by the U.S. government or its agencies
        or instrumentalities


(pound) certificates of deposit, time deposits, bankers' acceptances and other
        short-term securities issued by domestic or  foreign  banks  or  their
        subsidiaries or branches

(pound) repurchase agreements

(pound) asset-backed securities

(pound) domestic and  dollar-denominated  foreign  commercial paper, and other
        short-term corporate obligations, including those with floating or
        variable rates of interest

(pound) dollar-denominated obligations  issued  or  guaranteed  by one or more
        foreign governments or any of their political subdivisions or agencies

Normally,  the  fund  invests  at  least  25%  of  its net assets in domestic or
dollar-denominated foreign bank obligations.

MAIN RISKS

The  fund's yield will vary as the short-term securities in its portfolio mature
and  the  proceeds  are  reinvested in securities with different interest rates.

While  the  fund has maintained a constant share price since inception, and will
continue  to  try to do so, the following factors could reduce the fund's income
level and/or share price:

(pound) interest rates could rise sharply, causing the fund's share price to
        drop

(pound) any of the fund's holdings could have its credit rating downgraded or
        could default

(pound) the risks  generally  associated with concentrating investments in the
        banking industry, such as interest rate risk, credit risk and regulatory
        developments relating to the banking industry

(pound) the risks generally associated  with  dollar-denominated  foreign
        investments, such as economic and  political  developments,  seizure  or
        nationalization of deposits, imposition of taxes or other restrictions
        on the payment of principal and interest





<PAGE>

PAST PERFORMANCE

The  tables  below  show  some  of the risks of investing in the fund. The first
table shows the changes in the fund's Class A performance from year to year. The
second  table  averages  the  fund' s Class A performance over time. Both tables
assume  reinvestment  of  dividends  and  distributions.  Class A shares are not
offered  in  this  prospectus; however, except to the extent Class A and Class X
have  different  expenses  and  Class X may be subject to a CDSC, Class X should
have similar annual returns to Class A, since each invests in the same portfolio
of securities. Of course, past performance is no guarantee of future results.

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

Year-by-year total return AS OF 12/31 EACH YEAR (%)

CLASS A SHARES

<TABLE>
               8.84     7.71     5.84     3.39     2.58     3.51     5.44     4.83     4.99     4.93
<S>            <C>      <C>      <C>      <C>      <C>      <C>      <C>      <C>      <C>      <C>
                '89      '90      '91      '92      '93      '94      '95      '96      '97      '98

</TABLE>



BEST QUARTER:                    Q2 '89                          +2.28%

WORST QUARTER:                   Q3 '93                          +0.63%

The fund's 7-day yield on 12/31/98 was 4.42%. For the fund's current yield, call
toll-free 1-800-645-6561.
- --------------------------------------------------------------------------------

Average annual total return AS OF 12/31/98

1 Year                            5 Years                        10 Years
- --------------------------------------------------------------------------------

4.93%                              4.74%                           5.19%

What this fund is -- and isn't

This fund is a mutual fund: a pooled investment that is professionally managed
and gives you the opportunity to participate in financial markets. It strives to
reach its stated goal, although as with all mutual funds, it cannot offer
guaranteed results.

An investment in this fund is not a bank deposit. It is not insured or
guaranteed by the FDIC or any other government agency. It is not a complete
investment program. You could lose money in this fund, but you also have the
potential to make money.

EXPENSES

As  an  investor, you pay certain fees and expenses in connection with the fund,
which are described in the table below.
- --------------------------------------------------------------------------------

Fee table

SHAREHOLDER TRANSACTIONS FEES (FEE PAID FROM YOUR ACCOUNT)

Maximum deferred sales charge (CDSC)                                    4.00%

AS A % OF THE PURCHASE OR SALE PRICE, WHICHEVER IS LESS
- --------------------------------------------------------------------------------

ANNUAL FUND OPERATING EXPENSES (EXPENSES PAID FROM FUND ASSETS)

% OF AVERAGE DAILY NET ASSETS

Management fees                                                         0.50%

Rule 12b-1 fee                                                          0.25%

Shareholder services fee                                                0.25%

Other expenses                                                          0.05%
- --------------------------------------------------------------------------------

TOTAL                                                                   1.05%

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

Expense example

                            1 Year       3 Years
- --------------------------------------------------------------------------------

WITH REDEMPTION             $507         $634

WITHOUT REDEMPTION          $107         $334

This  example  shows  what you could pay in expenses over time. It uses the same
hypothetical  conditions  other funds use in their prospectuses: $10,000 initial
investment, 5% total return each year and no changes in expenses. Because actual
return and expenses will be different, the example is for comparison only.

Concepts to understand

MANAGEMENT FEE: the fee paid to the investment adviser for managing the fund's
portfolio and assisting in all aspects of the fund's operations.

RULE 12B-1 FEE: the fee paid to the fund's distributor to finance the sale of
Class X shares. Because this fee is paid out of the fund's assets on an ongoing
basis, over time it will increase the cost of your investment and may cost you
more than paying other types of sales charges.

SHAREHOLDER SERVICES FEE: the fee paid to the fund's distributor for providing
shareholder services.

OTHER EXPENSES: estimated fees to be paid by the fund for miscellaneous items
such as transfer agency, custody, professional and registration fees.

                                                      General Money Market Fund





<PAGE>

                                            General Municipal Money Market Fund
                                                          ------------------
                                                             Ticker Symbol: N/A

GOAL/APPROACH

The  fund  seeks  to maximize current income exempt from federal personal income
tax,  as  is  consistent with the preservation of capital and the maintenance of
liquidity.

To  pursue  this goal, the fund normally invests substantially all net assets in
municipal  obligations,  the interest from which is exempt from federal personal
income tax. When the fund manager believes that acceptable municipal obligations
are unavailable for investment, the fund may invest temporarily in high quality,
taxable  money  market  instruments. Municipal obligations are typically divided
into two types:

(pound) GENERAL OBLIGATION  BONDS,  which  are  secured  by the full faith and
        credit of the issuer and its taxing power

(pound) REVENUE BONDS,  which  are  payable  from  the revenues derived from a
        specific revenue source, such as charges for water and sewer service or
        highway tolls

MAIN RISKS

The  fund's yield will vary as the short-term securities in its portfolio mature
and the proceeds are reinvested in securities with different interest rates.

While the fund has maintained a constant share price since inception, and will
continue to try to do so, the following factors could reduce the fund's income
level and/or share price:

(pound) interest rates could rise sharply, causing the fund's share price to
        drop

(pound) any of the fund's holdings could have its credit rating downgraded or
        could default

Although  the  fund's objective is to generate income exempt from federal income
tax,  interest  from  some  of  its  holdings  may  be  subject  to  the federal
alternative  minimum  tax.  In  addition,  the  fund  occasionally may invest in
taxable money market instruments.



<PAGE>

PAST PERFORMANCE

The  tables  below  show  some  of the risks of investing in the fund. The first
table shows the changes in the fund's Class A performance from year to year. The
second  table  averages  the  fund' s Class A performance over time. Both tables
assume  reinvestment  of  dividends  and  distributions.  Class A shares are not
offered  in  this  prospectus; however, except to the extent Class A and Class X
have  different  expenses  and  Class X may be subject to a CDSC, Class X should
have similar annual returns to Class A, since each invests in the same portfolio
of  securities.  Of  course, past performance is no guarantee of future results.

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

Year-by-year total return AS OF 12/31 EACH YEAR (%)
<TABLE>
CLASS A SHARES

                5.91     5.53     4.19     2.62     2.05    2.40     3.42     2.93     3.15     2.98
                <C>      <C>      <C>      <C>      <C>     <C>      <C>      <C>      <C>      <C>
                 '89      '90      '91      '92      '93     '94      '95      '96      '97      '98

</TABLE>

BEST QUARTER:                    Q2 '89                          +1.56%

WORST QUARTER:                   Q1 '94                          +0.46%

The fund's 7-day yield on 12/31/98 was 3.25%. For the fund's current yield, call
toll-free 1-800-645-6561.
- --------------------------------------------------------------------------------

Average annual total return AS OF 12/31/98

1 Year                            5 Years                        10 Years
- --------------------------------------------------------------------------------

2.98%                              2.97%                           3.51%

What this fund is -- and isn't

This fund is a mutual fund: a pooled investment that is professionally managed
and gives you the opportunity to participate in financial markets. It strives to
reach its stated goal, although as with all mutual funds, it cannot offer
guaranteed results.

An investment in this fund is not a bank deposit. It is not insured or
guaranteed by the FDIC or any other government agency. It is not a complete
investment program. You could lose money in this fund, but you also have the
potential to make money.

EXPENSES

As an investor, you pay certain fees and expenses in connection with the fund,
which are described in the table below.
- --------------------------------------------------------------------------------

Fee table

SHAREHOLDER TRANSACTIONS FEES (FEE PAID FROM YOUR ACCOUNT)

Maximum deferred sales charge (CDSC)                                    4.00%

AS A % OF THE PURCHASE OR SALE PRICE, WHICHEVER IS LESS
- --------------------------------------------------------------------------------

ANNUAL FUND OPERATING EXPENSES (EXPENSES PAID FROM FUND ASSETS)

% OF AVERAGE DAILY NET ASSETS

Management fees                                                         0.50%

Rule 12b-1 fee                                                          0.25%

Shareholder services fee                                                0.25%

Other expenses                                                          0.05%

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

TOTAL                                                                   1.05%
- --------------------------------------------------------------------------------

Expense example

                            1 Year       3 Years
- --------------------------------------------------------------------------------

WITH REDEMPTION             $507         $634

WITHOUT REDEMPTION          $107         $334

This  example  shows  what you could pay in expenses over time. It uses the same
hypothetical  conditions  other funds use in their prospectuses: $10,000 initial
investment, 5% total return each year and no changes in expenses. Because actual
return and expenses will be different, the example is for comparison only.

Concepts to understand

MANAGEMENT FEE: the fee paid to the investment adviser for managing the fund's
portfolio and assisting in all aspects of the fund's operations.

RULE 12B-1 FEE: the fee paid to the fund's distributor to finance the sale of
Class X shares. Because this fee is paid out of the fund's assets on an ongoing
basis, over time it will increase the cost of your investment and may cost you
more than paying other types of sales charges.

SHAREHOLDER SERVICES FEE: the fee paid to the fund's distributor for providing
shareholder services.

OTHER EXPENSES: estimated fees to be paid by the fund for miscellaneous items
such as transfer agency, custody, professional and registration fees.

                                            General Municipal Money Market Fund








<PAGE>

MANAGEMENT

The  investment  adviser  for  each  fund  is  The Dreyfus Corporation, 200 Park
Avenue,  New  York,  New  York 10166. Founded in 1947, Dreyfus manages more than
$120  billion in over 160 mutual fund portfolios. For the past fiscal year, each
fund  paid Dreyfus an investment advisory fee at the annual rate of 0.50% of the
fund' s average daily net assets. Dreyfus is the primary mutual fund business of
Mellon Bank Corporation, a broad-based financial services company with a bank at
its  core.  With  more  than  $389  billion  of assets under management and $1.9
trillion  of  assets  under  administration  and custody, Mellon provides a full
range  of  banking,  investment  and trust products and services to individuals,
businesses   and   institutions.   Mellon   is   headquartered  in  Pittsburgh,
Pennsylvania.

The  Dreyfus  asset management philosophy is based on the belief that discipline
and  consistency  are  important  to  investment success. For each fund, Dreyfus
seeks  to  establish  clear  guidelines  for  portfolio  management  and  to  be
systematic  in  making decisions. This approach is designed to provide each fund
with a distinct, stable identity.

Dreyfus  has a personal securities trading policy (the "Policy") which restricts
the personal securities transactions of its employees. Its primary purpose is to
ensure  that  personal  trading  by  Dreyfus employees does not disadvantage any
Dreyfus-managed  fund. Dreyfus portfolio managers and other investment personnel
who  comply  with  the  Policy's  preclearance and disclosure procedures may be
permitted  to  purchase, sell or hold certain types of securities which also may
be or are held in the fund(s) they advise.

Concepts to understand

YEAR 2000 ISSUES: these funds could be adversely affected if the computer
systems used by Dreyfus and the funds' other service providers do not properly
process and calculate date-related information from and after January 1, 2000.

Dreyfus 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 these funds invest may be
adversely affected by year 2000-related problems. This could have an impact on
the value of a fund's investments and its share price.




<PAGE>

FINANCIAL HIGHLIGHTS

The  following tables describe the performance of each fund's Class A shares for
the  fiscal  periods indicated. "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
independently  audited by Ernst & Young LLP, whose report, along with the fund's
financial statements, is included in the annual report. No financial information
is  provided for Class X shares which had not been offered as of the date of the
financial  statements.  The Rule 12b-1 distribution fee and shareholder services
fee  paid  by  Class X will cause such shares to have a higher expense ratio, to
pay  lower  dividends,  and to have a lower total investment return than Class A
shares.
<TABLE>

                                                     YEAR ENDED      TEN MONTHS ENDED
                                                    NOVEMBER 30,       NOVEMBER 30,                 YEAR ENDED JANUARY 31,

 GENERAL MONEY MARKET FUND                              1998              1997(1)           1997       1996      1995       1994
- ---------------------------------------------------------------------------------------------------------------------------------
<S>                                                     <C>               <C>               <C>        <C>         <C>      <C>
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         .049               .041             .047      .053       .037     .025

 Distributions:          Dividends from investment
                         income -- net                  (.049)             (.041)           (.047)    (.053)     (.037)    (.025)

 Net asset value, end of period                           1.00               1.00             1.00      1.00      1.00      1.00

 Total return (%)                                         4.98             4.99(2)            4.81      5.42       3.75     2.56
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

 Ratio of expenses to average net assets (%)               .77              .88(2)            .84       .86        .94       .94

 Ratio of net investment income
 to average net assets (%)                                4.88             4.89(2)           4.71      5.28       3.68      2.53

 Decrease reflected in above expense ratios
 due to actions by Dreyfus (%)                              --                 --               --       .01        .04      .02
- ------------------------------------------------------------------------------------------------------------------------------------

 Net assets, end of period ($ x 1,000)                 835,706            903,313          764,119   654,581    572,116    616,072

(1)  THE FUND CHANGED ITS FISCAL YEAR END FROM JANUARY 31 TO NOVEMBER 30.

(2)  ANNUALIZED.
</TABLE>
<TABLE>

                                                                                              YEAR ENDED NOVEMBER 30,

 GENERAL MUNICIPAL MONEY MARKET FUND                                             1998       1997       1996      1995       1994
- ---------------------------------------------------------------------------------------------------------------------------------
<S>                                                                              <C>        <C>        <C>       <C>        <C>
PER-SHARE DATA ($)

 Net asset value, beginning of period                                              1.00       1.00      1.00       1.00     1.00

Investment operations:

    Investment income -- net                                                      .030        .031      .029       .034     .023

Distributions:

    Dividends from investment income -- net                                      (.030)     (.031)    (.029)     (.034)    (.023)

 Net asset value, end of period                                                    1.00       1.00      1.00       1.00     1.00

 Total return (%)                                                                 3.02       3.14       2.97       3.41     2.27
- ---------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

 Ratio of expenses to average net assets (%)                                       .60        .62       .66        .66       .64

 Ratio of net investment income to average net assets (%)                         2.98        3.09      2.93       3.35     2.22
- ---------------------------------------------------------------------------------------------------------------------------------

 Net assets, end of period ($ x 1,000)                                          280,398    273,058   256,862    294,379  294,711
</TABLE>
                                                           Financial Highlights



<PAGE>

                                                                Your Investment

ACCOUNT POLICIES

GENERAL  FUNDS  ARE  DESIGNED  PRIMARILY  FOR PEOPLE who are investing through a
third  party  such  as a bank, broker-dealer or financial adviser. Third parties
with  whom  you  open  a  fund account may impose policies, limitations and fees
which are different than those described here.

YOU  MAY  BUY  CLASS  X  SHARES  ONLY  IF you establish an Auto-Exchange Account
pursuant  to  which  the  Class X shares purchased will be exchanged for Class B
shares  of  up  to  five  Dreyfus Premier funds within two years of your initial
purchase  of  Class  X  shares. Subsequent purchases of Class X shares of a fund
must  be  exchanged for Class B shares within two years of your initial
purchase.

CLASS  X SHARES AND CLASS B SHARES of the Dreyfus Premier funds are subject to a
contingent deferred sales charge (CDSC), which is assessed only if you sell your
shares  within  six  years of purchase. Under certain circumstances, you may not
have  to  pay a CDSC when you sell shares. Consult your financial representative
or  the  SAI  to see if a CDSC waiver may apply to you. The following table sets
forth the rates of the CDSC for Class X shares and Class B shares of the Dreyfus
Premier funds for which Class X may be automatically exchanged.
- --------------------------------------------------------------------------------
Sales charges

CDSC -- CHARGED WHEN YOU SELL SHARES

                                    Contingent deferred sales charge
Time since you bought               as a % of your initial investment or
the shares you are selling          your redemption (whichever is less)

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

Up to 2 years                       4.00%

2 -- 4 years                        3.00%

4 -- 5 years                        2.00%

5 -- 6 years                        1.00%

More than 6 years                   Shares will automatically
                                    convert to Class A of the
                                    selected Dreyfus Premier fund

CLASS  X  SHARES  ALSO  CARRY  an  annual Rule 12b-1 fee of 0.25% of the Class's
average  daily  net  assets. The Class B shares of the Dreyfus Premier funds you
receive  in exchange for your fund Class X shares will convert to Class A shares
of  the  Dreyfus  Premier  funds  approximately  six  years  after  the date you
purchased the exchanged Class X shares. Upon conversion to Class A shares, Class
B  shares  of  the  Dreyfus Premier funds will not be subject to a CDSC. Class A
shares of the Dreyfus Premier funds are not subject to a Rule 12b-1 fee. Class A
shares  of  the  Dreyfus  Premier  funds  are  subject  to an annual shareholder
services  fee  of  0.25%  paid  to  the  distributor  for  providing shareholder
services.

You  should  invest  in  Class  X  shares  of a fund only as part of a long-term
investment  in the Dreyfus Family of Funds. If you are seeking only to invest in
a money market fund and do not expect to exchange fund shares for Class B shares
of  a  Dreyfus  Premier  fund,  you  should  consider more suitable investments,
including another class of the fund's shares or other money market funds offered
by   Dreyfus.   Consult   your   financial  representative  for  more  details.





<PAGE>

Buying shares

YOUR  PRICE  FOR  FUND  SHARES  is  the  fund's net asset value (NAV), which is
generally  calculated  twice  a  day,  at 5 p.m. and 8 p.m. Eastern time for the
taxable  money  market fund and three times a day, at 12 noon, 2 p.m. and 8 p.m.
Eastern  time  for the municipal money market fund, every day the New York Stock
Exchange  or the fund's transfer agent is open. Your order will be priced at the
next NAV calculated after your order is accepted by the fund's transfer agent or
other  authorized  entity. Each fund's investments are valued based on amortized
cost.

IF  YOUR PAYMENTS ARE RECEIVED in or converted into Federal Funds by 12 noon for
the  taxable money market fund or by 4 p.m. for the municipal money market fund,
you  will  receive the dividend declared that day. If your payments are received
in  or  converted  into Federal Funds after 12 noon for the taxable money market
fund  or  after  4  p.m.  for the municipal money market fund, you will begin to
accrue  dividends  on  the  following  business  day. Qualified institutions may
telephone  orders  to  buy  shares.  If  such an order is made by 5 p.m. for the
taxable  money market fund or by 2 p.m. for the municipal money market fund, and
Federal Funds are received by 6 p.m. or 4 p.m., respectively, the shares will be
purchased  at the next NAV determined after the telephone order is accepted, and
will  receive  the  dividend declared that day. If such an order is made after 5
p.m.  for  the taxable money market fund or after 2 p.m. for the municipal money
market  fund,  but by 8 p.m., and Federal Funds are received by 11 a.m. the next
business  day,  the shares will be purchased at the NAV determined at 8 p.m. and
will  begin  to accrue dividends on the next business day. All times are Eastern
time.


Because  the  municipal  money  market  fund  seeks tax-exempt income, it is not
recommended for purchase in IRAs or other qualified plans.
- --------------------------------------------------------------------------------

Minimum investments

                                   Initial            Additional
- --------------------------------------------------------------------------------

REGULAR ACCOUNTS                   $2,500             $100

TRADITIONAL IRAS                   $750               NO MINIMUM

SPOUSAL IRAS                       $750               NO MINIMUM

ROTH IRAS                          $750               NO MINIMUM

EDUCATION IRAS                     $500               NO MINIMUM
                                                      AFTER THE FIRST YEAR

All investments must be in U.S. dollars. Third-party checks cannot be accepted.
You may be charged a fee for any check that does not clear.

                                                                Your Investment



<PAGE>

ACCOUNTS POLICIES (CONTINUED)

Selling shares

YOU  MAY SELL (REDEEM) SHARES AT ANY TIME through your financial representative,
or  you  can contact the fund directly. Your shares will be sold at the next NAV
calculated  after  your  order is accepted by the fund's transfer agent or other
authorized  entity. Any certificates representing fund shares being sold must be
returned with your redemption request. Your order will be processed promptly and
you will generally receive the proceeds within a week.

TO  KEEP  YOUR  CDSC AS LOW AS POSSIBLE, each time you request to sell shares we
will  first sell shares that are subject to the lowest charge. The CDSC is based
on  the  lesser of the original purchase cost or the current market value of the
shares being sold.

BEFORE  SELLING  RECENTLY PURCHASED SHARES, please note that if the fund has not
yet  collected  payment for the shares you are selling, it may delay sending the
proceeds  for  up  to  eight  business  days  or until it has collected payment.

Written sell orders

Some circumstances require written sell orders along with signature guarantees.
These include:

(pound) amounts of $1,000 or more on accounts whose address  has been changed
        within the last 30 days

(pound) requests to send the proceeds to a different payee or address

Written sell orders of $100,000 or more must also be signature guaranteed.

A SIGNATURE GUARANTEE helps protect against fraud. You can obtain one from most
banks or securities dealers, but not from a notary public. For joint accounts,
each signature must be guaranteed. Please call us to ensure that your signature
guarantee will be processed correctly.


Limitations on selling shares by phone

Proceeds
sent by                 Minimum                 Maximum
- --------------------------------------------------------------------------------

CHECK                   NO MINIMUM              $150,000 PER DAY

WIRE                    $1,000                  $250,000 FOR JOINT ACCOUNTS
                                                EVERY 30 DAYS

General policies

IF YOUR ACCOUNT FALLS BELOW $500, the fund may ask you to increase your balance.
If  it  is  still  below $500 after 45 days, the fund may close your account and
send you the proceeds.

UNLESS  YOU  DECLINE  TELEPHONE  PRIVILEGES  on  your  application,  you  may be
responsible  for  any  fraudulent  telephone  order  as  long  as  Dreyfus takes
reasonable measures to verify the order.

EACH FUND RESERVES THE RIGHT TO:

(pound) refuse any purchase or exchange request that could adversely affect the
        fund  or its operations, including those from any individual or group
        who, in the fund's view, is likely to engage in excessive trading
        (usually defined as more than four exchanges out of the fund within a
        calendar year)

(pound) refuse any  purchase or exchange request in excess of 1% of the fund's
        total assets

(pound) change or  discontinue  its exchange privilege, or temporarily suspend
        this privilege during unusual market conditions

(pound) change its minimum investment amounts

(pound) delay sending  out redemption proceeds for up to seven days (generally
        applies only in cases of very large redemptions, excessive trading or
        during unusual market conditions)

Each  fund  also reserves the right to make a "redemption in kind" -- payment in
portfolio  securities  rather  than  cash  -- if the amount you are redeeming is
large  enough to affect fund operations (for example, if it represents more than
1% of the fund's assets).




<PAGE>

DISTRIBUTIONS AND TAXES

EACH FUND USUALLY PAYS ITS SHAREHOLDERS dividends from its net investment income
once a month, and distributes any net realized securities gains once a year. You
may  choose to receive your dividends and distributions in cash or automatically
reinvest  them  in  shares  of one of your Dreyfus Premier funds through Dreyfus
Dividend   Sweep.  There  are  no  fees  or  sales  charges  on  reinvestments.

DIVIDENDS AND DISTRIBUTIONS PAID by the taxable money market fund are taxable to
U.S.  shareholders  as  ordinary  income (unless your investment is in an IRA or
other tax-advantaged account).

The   municipal   money  market  fund  anticipates  that,  under  normal  market
conditions,  virtually  all  of its income dividends will be exempt from federal
personal  income  taxes.  However,  any dividends and distributions from taxable
investments are taxable as ordinary income.

The  tax  status of any distribution is the same regardless of how long you have
been  in  the  fund  and whether you reinvest your distributions or take them in
cash.

Because everyone's tax situation is unique, always consult your tax professional
about federal, state and local tax  consequences.

Concepts to understand

DIVIDENDS AND DISTRIBUTIONS: income or interest paid by the fund's portfolio
investments and passed on to fund shareholders. These are calculated on a
per-share basis: each share earns the same rate of return, so the more fund
shares you own, the higher your distribution.

SECURITIES GAINS: distributions derived from the profits the fund earns when it
sells securities for a higher price than it paid for them.

SERVICES FOR FUND INVESTORS

THE THIRD PARTY THROUGH WHOM YOU PURCHASE fund shares may impose different
restrictions on the services and privileges offered by the fund, or may not make
them available at all.  Consult your financial representative for more
information on the availability of these services and privileges.

Exchange privilege

YOU  CAN  EXCHANGE  CLASS X SHARES worth $500 or more from one fund into Class B
shares  of  a Dreyfus Premier fund (no minimum for retirement accounts). Class B
shares  of  a  Dreyfus Premier fund may not be exchanged for Class X shares of a
fund. You can request your exchange by contacting your financial representative.
Be  sure  to  read  the  current  prospectus  for  any  fund  into which you are
exchanging.  Any  new account established through an exchange will have the same
privileges  as  your  original account (as long as they are available). There is
currently no fee for exchanges.

Dreyfus Auto-Exchange privilege

TO  INVEST  IN  CLASS X SHARES OF A FUND, you will be required to participate in
the  Dreyfus  Auto-Exchange  privilege.  As  a  participant,  you  will  have to
establish  the  time and amount of your automatic exchanges such that all of the
Class  X  shares  purchased  will  have  been  exchanged for Class B shares of a
Dreyfus  Premier  fund within two years of your initial purchase. You can change
the  time  or  amount  of  your automatic exchanges by contacting your financial
representative.

                                                                Your Investment




<PAGE>

SERVICES FOR FUND INVESTORS (CONTINUED)

CDSC under Exchange and Auto-Exchange privileges

SHARES  WILL  BE  EXCHANGED  PURSUANT TO the Exchange privilege or Auto-Exchange
privilege  at  the  then-current NAV. No CDSC will be imposed at the time of the
exchange;  however,  shares  acquired through an exchange will be subject to the
higher  CDSC  applicable  to  the  exchanged or acquired shares. For purposes of
computing  any  applicable  CDSC,  the length of time you have owned your shares
will  be measured from the date of original purchase and will not be affected by
the exchange.

Reinvestment privilege

UPON  WRITTEN  REQUEST  YOU  CAN reinvest up to the number of Class X shares you
sold  within  45  days of selling them at the current share price. If you paid a
CDSC,  it will be credited back to your account. This privilege may be used only
once.

Dreyfus Dividend Sweep

YOU  CAN  AUTOMATICALLY  REINVEST YOUR DIVIDENDS and distributions from the fund
into  one  or more of the Dreyfus Premier funds you have selected (not available
for IRAs). You can set up this service with your application, or by calling your
financial representative or 1-800-645-6561.

24-hour automated account access

YOU  CAN  EASILY  MANAGE  YOUR  DREYFUS  ACCOUNTS,  check your account balances,
transfer  money  between your Dreyfus funds, get price and yield information and
much more -- when it's convenient for you.

Account statements

EVERY  FUND INVESTOR AUTOMATICALLY RECEIVES regular account statements. You will
also  be  sent  a  yearly  statement  detailing  the  tax characteristics of any
dividends and distributions you have received.


<PAGE>


INSTRUCTIONS FOR REGULAR ACCOUNTS

   TO OPEN AN ACCOUNT

            In Writing

   Complete the application.

   Mail your application and a check to:
   Name of Fund
   P.O. Box 6587
   Providence, RI 02940-6587
   Attn: Institutional Processing

TO ADD TO AN ACCOUNT

Fill out an investment slip, and write your account number on your check.

Mail the slip and the check to:
Name of Fund
P.O. Box 6587
Providence, RI 02940-6587
Attn: Institutional Processing

TO SELL SHARES

Write a letter of instruction that includes:

* your name(s) and signature(s)

* your account number

* the fund name

* the dollar amount you want to sell

* how and where to send the proceeds

Obtain a signature guarantee or other documentation, if required (see page 10).

Mail your request to:
The Dreyfus Family of Funds
P.O. Box 6587
Providence, RI 02940-6587
Attn: Institutional Processing



           By Telephone

   WIRE  Have your bank send your
investment to The Bank of New York, with these instructions:

   * ABA# 021000018

   * fund name and DDA#
   

   * General Money Market Fund
     DDA# 8900051957
    

   * General Municipal Money Market Fund
     DDA# 8900052376

   * the share class

   * your Social Security or tax ID number

   * name(s) of investor(s)

   * dealer number if applicable

Call us to obtain an account number. Return your application with the account
number on the application.



WIRE  Have your bank send your investment to The Bank of New York, with these
instructions:

* ABA# 021000018

* fund name and DDA#
   

* General Money Market Fund DDA# 8900051957
    

* General Municipal Money Market Fund DDA# 8900052376

* the share class

* your account number

* name(s) of investor(s)

* dealer number if applicable

ELECTRONIC CHECK  Same as wire, but insert "1111" before your account number.


WIRE  Call us or your financial representative to request your transaction. Be
sure the fund has your bank account information on file. Proceeds will be wired
to your bank.

CHECK  Call us or your financial representative to request your transaction. A
check will be sent to the address of record.


                                                                Your Investment




<PAGE>

INSTRUCTIONS FOR IRAS


   TO OPEN AN ACCOUNT

            In Writing

Complete an IRA application, making sure to specify the fund name and to
indicate the year the contribution is for.

Mail your application and a check to:
The Dreyfus Trust Company, Custodian
P.O. Box 6427
Providence, RI 02940-6427
Attn: Institutional Processing


TO ADD TO AN ACCOUNT

Fill out an investment slip, and write your account number on your check.
Indicate the year the contribution is for.

Mail in the slip and the check to:
The Dreyfus Trust Company, Custodian
P.O. Box 6427
Providence, RI 02940-6427
Attn: Institutional Processing



TO SELL SHARES

Write a letter of instruction that includes:

* your name and signature

* your account number and fund name

* the dollar amount you want to sell

* how and where to send the proceeds

* whether the distribution is qualified or premature

* whether the 10% TEFRA should be withheld

Obtain a signature guarantee or other documentation, if required (see page 10).

Mail in your request to:
The Dreyfus Trust Company
P.O. Box 6427
Providence, RI 02940-6427
Attn: Institutional Processing

           By Telephone
           ____________


WIRE  Have your bank send your investment to The Bank of New York, with these
instructions:

* ABA# 021000018

* fund name and DDA#
   

* General Money Market Fund DDA# 8900051957
    

* the share class

* your account number

* name of investor

* the contribution year

* dealer number if applicable

ELECTRONIC CHECK  Same as wire, but insert "1111" before your account number.
     ___________


The General Municipal Money Market Fund is not recommended for IRAs.



<PAGE>

NOTES

<PAGE>


NOTES

<PAGE>


NOTES

<PAGE>


                                                           For More Information

General Money Market Fund
- --------------------------------------
SEC file number:  811-3207

General Municipal Money Market Fund
- -------------------------------------
SEC file number:  811-3481

More  information  on  each  fund  is available free upon request, including the
following:

Annual/Semiannual Report

Describes a fund's performance, and lists portfolio holdings.

Statement of Additional Information (SAI)

Provides more details about each fund and its policies. A current SAI is on file
with  the  Securities  and  Exchange  Commission  (SEC)  and  is incorporated by
reference (is legally considered part of this prospectus).

To obtain information:

BY TELEPHONE Call your financial representative or 1-800-645-6561

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

ON THE INTERNET  Text-only versions of fund documents can be viewed online or
downloaded from: http://www.sec.gov

You can also obtain copies by visiting the SEC's Public Reference Room in
Washington, DC (phone 1-800-SEC-0330) or by sending your request and a
duplicating fee to the SEC's Public Reference Section, Washington, DC
20549-6009.

(c) 1999 Dreyfus Service Corporation
996/997P0599

<PAGE>





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