GENERAL MONEY MARKET FUND INC
497, 1999-10-01
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General Money Market Funds


General Money Market Fund

General Government Securities Money Market Fund

General Municipal Money Market Fund

General California Municipal Money Market Fund

General Minnesota Municipal Money Market Fund

General New York Municipal Money Market Fund


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

PROSPECTUS April 1, 1999
As revised, September 30, 1999


CLASS B SHARES


This prospectus is to be used only by clients of select broker-dealers.


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 Government Securities
Money Market Fund                                                         4

General Municipal
Money Market Fund                                                         6

General California Municipal
Money Market Fund                                                         8

General Minnesota Municipal
Money Market Fund                                                        10

General New York Municipal
Money Market Fund                                                        12

Management                                                               14

Financial Highlights                                                     15

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

Account Policies                                                         18

Distributions and Taxes                                                  20


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.
The operations and results of a fund are unrelated to those of each other fund.
This combined prospectus has been prepared for your convenience so that you can
consider six 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:

*  maintain an average dollar-weighted portfolio maturity of 90 days or
less

*  buy individual securities that have remaining maturities of 13 months or
less


*  invest only in 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: GMBXX


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:

*   securities issued or guaranteed by the U.S. government or its agencies

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

*   repurchase agreements

*   asset-backed securities

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

*   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:

*   interest rates could rise sharply, causing the fund's share price to drop

*   any of the fund's holdings could have its credit rating downgraded or could
    default

*   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

*   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 2>

PAST PERFORMANCE


The tables below show some of the risks of investing in Class B. The first table
shows changes in the fund's performance from year to year. The second table
averages the fund's performance over time. Both tables assume reinvestment of
dividends and distributions. Of course, past performance is no guarantee of
future results.

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


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

                                                         4.68     4.84     4.73
  89     90      91      92      93       94      95       96       97       98

BEST QUARTER:                    Q4 '97                          +1.22%

WORST QUARTER:                   Q4 '98                          +1.09%

The fund's 7-day yield on 12/31/98 was 4.25%. For the fund's current yield, call
toll-free 1-800-645-6561.
- --------------------------------------------------------------------------------

Average annual total return AS OF 12/31/98


                                                              Inception
         1 Year                                               (3/31/95)
- --------------------------------------------------------------------------------

         4.73%                                                  4.84%



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 for Class B in the table below. Annual fund operating
expenses are paid out of fund assets, so their effect is included in the share
price.

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

Fee table

ANNUAL FUND OPERATING EXPENSES

% OF AVERAGE DAILY NET ASSETS

Management fees                                                         0.50%


Rule 12b-1 fee                                                          0.20%


Shareholder services fee                                                0.25%

Other expenses                                                          0.11%
- --------------------------------------------------------------------------------

TOTAL                                                                   1.06%
- --------------------------------------------------------------------------------

Expense example

1 Year             3 Years               5 Years                   10 Years
- ------------------------------------------------------------------------------

$108               $337                  $585                      $1,294

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. The figures
shown would be the same whether you sold your shares at the end of a period or
kept them. Because actual return and expenses will be different, the example is
for comparison only.

Concepts to understand


MANAGEMENT FEE: the fee paid to Dreyfus for managing the fund's portfolio and
assisting in all aspects of the fund's operations. For the fiscal year ended
November 30, 1998, Dreyfus assumed certain fund expenses pursuant to an
undertaking, reducing total expenses from 1.06% to 1.00%. This undertaking was
voluntary.

RULE 12B-1 FEE: a fee of up to 0.20% to reimburse the fund's distributor for
distributing Class B 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: a fee paid to the fund's distributor for shareholder
account service and maintenance.

OTHER EXPENSES: a fee of 0.05% paid by the fund for sub-accounting services
provided by third parties and fees paid by the fund for miscellaneous items such
as transfer agency, custody, professional and registration fees.


General Money Market Fund




<PAGE 3>


General Government Securities Money Market Fund
- ----------------------
Ticker Symbol: GSBXX


GOAL/APPROACH

The fund seeks as high a level of current income as is consistent with the
preservation of capital and the maintenance of liquidity.

To pursue this goal, the fund invests in securities issued or guaranteed by the
U.S. government or its agencies or instrumentalities, and repurchase agreements
in respect of these securities.

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.

A security backed by the U.S. Treasury or the full faith and credit of the
United States is guaranteed only as to the timely payment of interest and
principal when held to maturity. The current market prices for such securities
are not guaranteed and will fluctuate. The fund is subject to the risk that
interest rates could rise sharply, causing the fund's share price to drop.




<PAGE 4>

PAST PERFORMANCE


The tables below show some of the risks of investing in Class B. The first table
shows changes in the fund's performance from year to year. The second table
averages the fund's performance over time. Both tables assume reinvestment of
dividends and distributions. Of course, past performance is no guarantee of
future results.

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

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

                                                         4.60     4.69     4.61
  89     90      91      92      93       94      95       96       97       98


BEST QUARTER:                    Q4 '97                          +1.18%

WORST QUARTER:                   Q4 '98                          +1.06%

The fund's 7-day yield on 12/31/98 was 4.08%. For the fund's current yield, call
toll-free 1-800-645-6561.
- --------------------------------------------------------------------------------

Average annual total return AS OF 12/31/98


                                                              Inception
         1 Year                                               (3/31/95)
- --------------------------------------------------------------------------------

         4.61%                                                  4.72%



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 for Class B in the table below. Annual fund operating
expenses are paid out of fund assets, so their effect is included in the share
price.

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

Fee table

ANNUAL FUND OPERATING EXPENSES

% OF AVERAGE DAILY NET ASSETS

Management fees                                                         0.50%


Rule 12b-1 fee                                                          0.20%


Shareholder services fee                                                0.25%

Other expenses                                                          0.07%
- --------------------------------------------------------------------------------

TOTAL                                                                   1.02%
- --------------------------------------------------------------------------------

Expense example

1 Year                3 Years               5 Years           10 Years
- -----------------------------------------------------------------------------

$104                  $325                  $563              $1,248

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. The figures
shown would be the same whether you sold your shares at the end of a period or
kept them. Because actual return and expenses will be different, the example is
for comparison only.

Concepts to understand


MANAGEMENT FEE: the fee paid Dreyfus for managing the fund's portfolio and
assisting in all aspects of the fund's operations. For the fiscal year ended
November 30, 1998, Dreyfus assumed certain fund expenses pursuant to an
undertaking, reducing total expenses from 1.02% to 0.97%. This undertaking was
voluntary.

RULE 12B-1 FEE: a fee of up to 0.20% to reimburse the fund's distributor for
distributing Class B 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: a fee paid to the fund's distributor for shareholder
account service and maintenance.

OTHER EXPENSES: a fee of 0.05% paid by the fund for sub-accounting services
provided by third parties and fees paid by the fund for miscellaneous items such
as transfer agency, custody, professional and registration fees.


General Government Securities Money Market Fund



<PAGE 5>


General Municipal Money Market Fund
- -----------------------
Ticker Symbol: GBMXX


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. The fund also may invest in high quality, short-term structured
notes which are derivative instruments whose value is tied to underlying
municipal obligations. Structured notes typically are purchased in privately
negotiated transactions from financial institutions. When the portfolio 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 of two types:


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

*   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:

*   interest rates could rise sharply, causing the fund's share price to drop

*   any of the fund's holdings could have its credit rating downgraded or could
    default


Derivative securities, such as structured notes, can be highly volatile and the
possibility of default by the financial institution or counterparty may be
greater for these securities than for other types of money market instruments.

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 6>

PAST PERFORMANCE


The tables below show some of the risks of investing in Class B. The first table
shows changes in the fund's performance from year to year. The second table
averages the fund's performance over time. Both tables assume reinvestment of
dividends and distributions. Of course, past performance is no guarantee of
future results.

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

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

                                                         2.66     2.86     2.60
  89     90      91      92      93       94      95       96       97       98

BEST QUARTER:                    Q2 '97                          +0.76%

WORST QUARTER:                   Q4 '98                          +0.61%

The fund's 7-day yield on 12/31/98 was 2.83%. For the fund's current yield, call
toll-free 1-800-645-6561.
- --------------------------------------------------------------------------------

Average annual total return AS OF 12/31/98


                                                              Inception
         1 Year                                               (3/31/95)
- --------------------------------------------------------------------------------

         2.60%                                                 2.77%



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 for Class B in the table below. Annual fund operating
expenses are paid out of fund assets, so their effect is included in the share
price.

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

Fee table

ANNUAL FUND OPERATING EXPENSES

% OF AVERAGE DAILY NET ASSETS

Management fees                                                          0.50%


Rule 12b-1 fee                                                           0.20%


Shareholder services fee                                                 0.25%

Other expenses                                                           0.10%
- --------------------------------------------------------------------------------

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

Expense example

1 Year              3 Years                  5 Years                 10 Years
- ------------------------------------------------------------------------------

$107                $334                     $579                    $1,283

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. The figures
shown would be the same whether you sold your shares at the end of a period or
kept them. Because actual return and expenses will be different, the example is
for comparison only.

Concepts to understand


MANAGEMENT FEE: the fee paid to Dreyfus for managing the fund's portfolio and
assisting in all aspects of the fund's operations. For the fiscal year ended
November 30, 1998, Dreyfus assumed certain fund expenses pursuant to an
undertaking, reducing total expenses from 1.05% to 0.96%. This undertaking was
voluntary.

RULE 12B-1 FEE: a fee of up to 0.20% to reimburse the fund's distributor for
distributing Class B 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: a fee paid to the fund's distributor for shareholder
account service and maintenance.

OTHER EXPENSES: a fee of 0.05% paid by the fund for sub-accounting services
provided by third parties and fees paid by the fund for miscellaneous items such
as transfer agency, custody, professional and registration fees.


General Municipal Money Market Fund




<PAGE 7>


General California Municipal Money Market Fund
- ----------------------
Ticker Symbol: GENXX


GOAL/APPROACH

The fund seeks to maximize current income exempt from federal and California
state personal income taxes, 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 and
California state personal income taxes. The fund also may invest in high
quality, short-term structured notes which are derivative instruments whose
value is tied to underlying municipal obligations. Structured notes typically
are purchased in privately negotiated transactions from financial institutions.
When the portfolio manager believes that acceptable California municipal
obligations are unavailable for investment, the fund may invest in securities
that may be subject to California state income tax, but are free from federal
income tax. Municipal obligations are typically of two types:


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

*   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:

*   interest rates could rise sharply, causing the fund's share price to drop

*   any of the fund's holdings could have its credit rating downgraded or could
    default

*   California's economy and revenues underlying municipal obligations may
    decline

*   the fund's portfolio securities may be more sensitive to risks that are
    specific to investing primarily in a single state


Derivative securities, such as structured notes, can be highly volatile and the
possibility of default by the financial institution or counterparty may be
greater for these securities than for other types of money market instruments.

Although the fund's objective is to generate income exempt from federal and
California state income taxes, interest from some of its holdings may be subject
to the federal alternative minimum tax. In addition, the fund occasionally may
invest in taxable bonds and/or municipal bonds that are exempt only from federal
personal income taxes.


The fund is non-diversified, which means that a relatively high percentage of
the fund's assets may be invested in a limited number of issuers. Therefore, its
performance may be more vulnerable to changes in the market value of a single
issuer or a group of issuers.




<PAGE 8>

PAST PERFORMANCE


The tables below show some of the risks of investing in Class B. The first table
shows changes in the fund's performance from year to year. The second table
averages the fund's performance over time. Both tables assume reinvestment of
dividends and distributions. Of course, past performance is no guarantee of
future results.

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

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

                                                         2.48     2.62     2.34
  89     90      91      92      93       94      95       96       97       98

BEST QUARTER:                    Q2 '97                          +0.71%

WORST QUARTER:                   Q3 '98                          +0.53%

The fund's 7-day yield on 12/31/98 was 2.59%. For the fund's current yield, call
toll-free 1-800-645-6561.
- --------------------------------------------------------------------------------

Average annual total return AS OF 12/31/98


                                                              Inception
         1 Year                                               (8/1/95)
- --------------------------------------------------------------------------------

         2.34%                                                 2.52%



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 for Class B in the table below. Annual fund operating
expenses are paid out of fund assets, so their effect is included in the share
price.

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

Fee table


ANNUAL FUND OPERATING EXPENSES

% OF AVERAGE DAILY NET ASSETS

Management fees                                                          0.50%


Rule 12b-1 fee                                                           0.20%


Shareholder services fee                                                 0.25%

Other expenses                                                           0.12%
- --------------------------------------------------------------------------------

TOTAL                                                                    1.07%
- --------------------------------------------------------------------------------

Expense example

1 Year           3 Years               5 Years                  10 Years
- -------------------------------------------------------------------------------

$109             $340                  $590                     $1,306

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. The figures
shown would be the same whether you sold your shares at the end of a period or
kept them. Because actual return and expenses will be different, the example is
for comparison only.

Concepts to understand


MANAGEMENT FEE: the fee paid to Dreyfus for managing the fund's portfolio and
assisting in all aspects of the fund's operations. For the fiscal year ended
November 30, 1998, Dreyfus assumed certain fund expenses pursuant to an
undertaking, reducing total expenses from 1.07% to 1.00%. This undertaking was
voluntary.

RULE 12B-1 FEE: a fee of up to 0.20% to reimburse the fund's distributor for
distributing Class B 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: a fee paid to the fund's distributor for shareholder
account service and maintenance.

OTHER EXPENSES: a fee of 0.05% paid by the fund for sub-accounting services
provided by third parties and fees paid by the fund for miscellaneous items such
as transfer agency, custody, professional and registration fees.


General California Municipal Money Market Fund




<PAGE 9>


General Minnesota Municipal Money Market Fund
- -----------------------
Ticker Symbol: GMNXX


GOAL/APPROACH

The fund seeks to maximize current income exempt from federal and Minnesota
state personal income taxes, 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 and
Minnesota state personal income taxes. When the portfolio manager believes that
acceptable Minnesota municipal obligations are unavailable for investment, the
fund may invest in securities that may be subject to Minnesota state income tax,
but are free from federal income tax. Municipal obligations are typically of two
types:


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

*   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:

*   interest rates could rise sharply, causing the fund's share price to drop

*   any of the fund's holdings could have its credit rating downgraded or could
    default

*   Minnesota's economy and revenues underlying municipal obligations may
    decline

*   the fund's portfolio securities may be more sensitive to risks that are
    specific to investing primarily in a single state


Although the fund's objective is to generate income exempt from federal and
Minnesota state income taxes, interest from some of its holdings may be subject
to the federal alternative minimum tax. In addition, the fund occasionally may
invest in taxable bonds and/or municipal bonds that are exempt only from federal
personal income taxes.


The fund is non-diversified, which means that a relatively high percentage of
the fund's assets may be invested in a limited number of issuers. Therefore, its
performance may be more vulnerable to changes in the market value of a single
issuer or a group of issuers.



<PAGE 10>

PAST PERFORMANCE

Since the fund has less than one calendar year of performance, past performance
information is not included. For performance information as of the end of the
fund's first fiscal period, please refer to the Statement of Additional
Information (SAI).

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 for Class B in the table below. Annual fund operating
expenses are paid out of fund assets, so their effect is included in the share
price.

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

Fee table

ANNUAL FUND OPERATING EXPENSES

% OF AVERAGE DAILY NET ASSETS

Management fees                                                          0.50%

Rule 12b-1 fee                                                           0.20%

Shareholder services fee                                                 0.25%

Other expenses                                                           0.72%
- --------------------------------------------------------------------------------

TOTAL                                                                    1.67%
- --------------------------------------------------------------------------------

Expense example

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

$170                  $526

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. The figures
shown would be the same whether you sold your shares at the end of a period or
kept them. Because actual return and expenses will be different, the example is
for comparison only.


Concepts to understand


MANAGEMENT FEE: the fee paid to Dreyfus for managing the fund's portfolio and
assisting in all aspects of the fund's operations. For the fiscal period ended
November 30, 1998, Dreyfus waived its fee and assumed certain other fund
expenses pursuant to an undertaking, reducing total expenses from 1.67% to
0.80%. This undertaking was voluntary.

RULE 12B-1 FEE: a fee of up to 0.20% to reimburse the fund's distributor for
distributing Class B 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: a fee paid to the fund's distributor for shareholder
account service and maintenance.

OTHER EXPENSES: a fee of 0.05% paid by the fund for sub-accounting services
provided by third parties and estimated fees to be paid by the fund for
miscellaneous items such as transfer agency, custody, professional and
registration fees.

General Minnesota Municipal Money Market Fund






<PAGE 11>


General New York Municipal Money Market Fund
- ----------------------
Ticker Symbol: GNYXX


GOAL/APPROACH

The fund seeks to maximize current income exempt from federal, New York state
and New York city personal income taxes, 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, New York
state and New York city personal income taxes. The fund also may invest in high
quality, short-term structured notes which are derivative instruments whose
value is tied to underlying municipal obligations. Structured notes typically
are purchased in privately negotiated transactions from financial institutions.
When the portfolio manager believes that acceptable New York municipal
obligations are unavailable for investment, the fund may invest in securities
that may be subject to New York state and New York city income taxes, but are
free from federal income tax. Municipal obligations are typically of two types:


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

*   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:

*   interest rates could rise sharply, causing the fund's share price to drop

*   any of the fund's holdings could have its credit rating downgraded or could
    default

*   New York's economy and revenues underlying municipal obligations may
    decline

*   the fund's portfolio securities may be more sensitive to risks that are
    specific to investing primarily in a single state


Derivative securities, such as structured notes, can be highly volatile and the
possibility of default by the financial institution or counterparty may be
greater for these securities than for other types of money market instruments.

Although the fund's objective is to generate income exempt from federal, New
York state and New York city income taxes, interest from some of its holdings
may be subject to the federal alternative minimum tax. In addition, the fund
occasionally may invest in taxable bonds and/or municipal bonds that are exempt
only from federal personal income tax.


The fund is non-diversified, which means that a relatively high percentage of
the fund's assets may be invested in a limited number of issuers. Therefore, its
performance may be more vulnerable to changes in the market value of a single
issuer or a group of issuers.





<PAGE 12>

PAST PERFORMANCE


The tables below show some of the risks of investing in Class B. The first table
shows changes in the fund's performance from year to year. The second table
averages the fund's performance over time. Both tables assume reinvestment of
dividends and distributions. Of course, past performance is no guarantee of
future results.

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


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

                                                         2.51     2.70     2.42
  89     90      91      92      93       94      95       96       97       98

BEST QUARTER:                    Q2 '97                          +0.70%

WORST QUARTER:                   Q4 '98                          +0.55%

The fund's 7-day yield on 12/31/98 was 2.61%. For the fund's current yield, call
toll-free 1-800-645-6561.
- --------------------------------------------------------------------------------

Average annual total return AS OF 12/31/98


                                                              Inception
         1 Year                                               (9/8/95)
- --------------------------------------------------------------------------------

         2.42%                                                 2.57%



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 for Class B in the table below. Annual fund operating
expenses are paid out of fund assets, so their effect is included in the share
price.

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

Fee table


ANNUAL FUND OPERATING EXPENSES

% OF AVERAGE DAILY NET ASSETS

Management fees                                                          0.50%

Rule 12b-1 fee                                                           0.20%

Shareholder services fee                                                 0.25%

Other expenses                                                           0.11%
- --------------------------------------------------------------------------------

TOTAL                                                                    1.06%
- --------------------------------------------------------------------------------

Expense example

1 Year           3 Years                5 Years                10 Years
- ------------------------------------------------------------------------------

$108            $337                    $585                   $1,294

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. The figures
shown would be the same whether you sold your shares at the end of a period or
kept them. Because actual return and expenses will be different, the example is
for comparison only.

Concepts to understand


MANAGEMENT FEE: the fee paid to Dreyfus for managing the fund's portfolio and
assisting in all aspects of the fund's operations. For the fiscal year ended
November 30, 1998, Dreyfus assumed certain fund expenses pursuant to an
undertaking, reducing total expenses from 1.06% to 0.98%. This undertaking was
voluntary.

RULE 12B-1 FEE: a fee of up to 0.20% to reimburse the fund's distributor for
distributing Class B 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: a fee paid to the fund's distributor for shareholder
account service and maintenance.

OTHER EXPENSES: a fee of 0.05% paid by the fund for sub-accounting services
provided by third parties and fees paid by the fund for miscellaneous items such
as transfer agency, custody, professional and registration fees.


General New York Municipal Money Market Fund





<PAGE 13>

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 a management 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 $426 billion of assets under management and $2.0 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. Its mutual fund companies place Mellon as the leading bank
manager of mutual funds. 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 perclearance 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 14>

FINANCIAL HIGHLIGHTS

The following tables describe the performance of each fund's Class B 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.
<TABLE>
<CAPTION>
<S>                                                     <C>          <C>              <C>            <C>

                                                       YEAR ENDED   TEN MONTHS ENDED
                                                       NOVEMBER 30,    NOVEMBER 30,   YEAR ENDED JANUARY 31,
 GENERAL MONEY MARKET FUND                                 1998          1997(1)       1997          1996(2)
- ------------------------------------------------------------------------------------------------------------

PER-SHARE DATA ($)

 Net asset value, beginning of period                      1.00          1.00         1.00           1.00

 Investment operations:  Investment income -- net          .047          .039         .046           .043

 Distributions:          Dividends from investment
                         income -- net                     (.047)       (.039)       (.046)         (.043)

 Net asset value, end of period                             1.00         1.00        1.00            1.00

 Total return (%)                                           4.78         4.83(3)     4.65            5.18(3)
- ------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

 Ratio of expenses to average net assets (%)                1.00        1.00(3)      1.00           1.00(3)

 Ratio of net investment income to
 average net assets (%)                                     4.66        4.78(3)      4.56           5.00(3)

 Decrease reflected in above expense ratios
 due to actions by Dreyfus (%)                               .06         .05(3)       .07            .07(3)
- ------------------------------------------------------------------------------------------------------------

 Net assets, end of period ($ x 1,000)                 2,427,332     1,231,132    369,205         50,446

(1)  THE FUND CHANGED ITS FISCAL YEAR END FROM JANUARY 31 TO NOVEMBER 30.
(2)  FROM MARCH 31, 1995 (COMMENCEMENT OF INITIAL OFFERING) TO JANUARY 31, 1996
(3)  ANNUALIZED.

                                                       YEAR ENDED   TEN MONTHS ENDED
                                                       NOVEMBER 30,    NOVEMBER 30,   YEAR ENDED JANUARY 31,
 GENERAL GOVERNMENT SECURITIES MONEY MARKET FUND          1998          1997(1)       1997          1996(2)
- ------------------------------------------------------------------------------------------------------------


PER-SHARE DATA ($)

 Net asset value, beginning of period                      1.00          1.00          1.00            1.00

 Investment operations:  Investment income -- net          .046          .038          .045            .042

 Distributions:          Dividends from
                         investment income -- net         (.046)        (.038)        (.045)          (.042)

 Net asset value, end of period                            1.00          1.00         1.00             1.00

 Total return (%)                                          4.66         4.69(3)       4.58           5.04(3)
- ------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

 Ratio of expenses to average net assets (%)               .97         1.00(3)        1.00           1.00(3)

 Ratio of net investment income to
 average net assets (%)                                   4.55         4.60(3)        4.48           5.01(3)

 Decrease reflected in above expense ratios
 due to actions by Dreyfus (%)                             .05          .05(3)         .08            .10(3)
- ------------------------------------------------------------------------------------------------------------

 Net assets, end of period ($ x 1,000)                 645,984        364,845       90,175             58

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

(2)  FROM MARCH 31, 1995 (COMMENCEMENT OF INITIAL OFFERING) TO JANUARY 31, 1996

(3) ANNUALIZED.

Financial Highlights



<PAGE 15>

FINANCIAL HIGHLIGHTS (CONTINUED)

                                                                   YEAR ENDED NOVEMBER 30,
 GENERAL MUNICIPAL MONEY MARKET FUND                    1998          1997          1996          1995(1)
- ------------------------------------------------------------------------------------------------------------

PER-SHARE DATA ($)

 Net asset value, beginning of period                    1.00         1.00          1.00            1.00

 Investment operations:  Investment income -- net        .026         .028          .027            .020

 Distributions:          Dividends from
                         investment income -- net       (.026)       (.028)        (.027)          (.020)

 Net asset value, end of period                          1.00         1.00          1.00            1.00

 Total return (%)                                        2.64         2.86          2.70            3.01(2)
- ------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

 Ratio of expenses to average net assets (%)              .96         .95            .85            1.10(2)

 Ratio of net investment income to
 average net assets (%)                                  2.59        2.87           2.65            2.83(2)

 Decrease reflected in above expense ratios
 due to actions by Dreyfus (%)                            .09         .16            .29             .09(2)
- ------------------------------------------------------------------------------------------------------------

 Net assets, end of period ($ x 1,000)               377,636      263,008         17,491           3,024

(1)  FROM MARCH 31, 1995 (COMMENCEMENT OF INITIAL OFFERING) TO NOVEMBER 30, 1995.
(2)  ANNUALIZED.



                                                       YEAR ENDED   FOUR MONTHS ENDED
                                                       NOVEMBER 30,    NOVEMBER 30,   YEAR ENDED JANUARY 31,
GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND             1998          1997(1)       1997          1996(2)
- ------------------------------------------------------------------------------------------------------------

PER-SHARE DATA ($)

 Net asset value, beginning of period                      1.00           1.00         1.00           1.00

 Investment operations:  Investment income -- net          .024           .009         .026           .025

 Distributions:          Dividends from
                         investment income -- net         (.024)         (.009)       (.026)         (.025)

 Net asset value, end of period                            1.00           1.00         1.00            1.00

 Total return (%)                                          2.39           2.57(3)      2.61            2.56
- ------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

 Ratio of expenses to average net assets (%)               1.00           1.00(3)      1.00            1.00

 Ratio of net investment income to
 average net assets (%)                                    2.34           2.62(3)      2.52            2.45

 Decrease reflected in above expense ratios
 due to actions by Dreyfus (%)                              .07            .13(3)       .07             .08
- ------------------------------------------------------------------------------------------------------------

 Net assets, end of period ($ x 1,000)                    8,760          2,669          928           5,475

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

(2)  FROM AUGUST 1, 1995 (COMMENCEMENT OF INITIAL OFFERING) TO JULY 31, 1996.

(3) ANNUALIZED.
</TABLE>


<PAGE 16>


                                                   PERIOD ENDED NOVEMBER 30,
GENERAL MINNESOTA MUNICIPAL MONEY MARKET FUND               1998(1)
- --------------------------------------------------------------------------------

PER-SHARE DATA ($)

Net asset value, beginning of period                          1.00

Investment operations:  Investment income -- net              .013

Distributions: Dividends from investment income -- net      (.013)

Net asset value, end of period                                1.00

Total return (%)                                              2.67(2)
- -------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

Ratio of expenses to average net assets (%)                    .80(2)

Ratio of net investment income to average net assets (%)      2.63(2)

Decrease reflected in above expense ratios
due to actions by Dreyfus (%)                                  .87(2)
- -------------------------------------------------------------------------------

Net assets, end of period ($ x 1,000)                       28,160

(1)  FROM JUNE 1, 1998 (COMMENCEMENT OF OPERATIONS) TO NOVEMBER 30, 1998.

(2) ANNUALIZED.
<TABLE>
<CAPTION>
<S>                                                                 <C>       <C>       <C>        <C>

                                                                          YEAR ENDED NOVEMBER 30,

 GENERAL NEW YORK MUNICIPAL MONEY MARKET FUND                       1998       1997      1996      1995(1)
- ------------------------------------------------------------------------------------------------------------

PER-SHARE DATA ($)

 Net asset value, beginning of period                               1.00       1.00      1.00       1.00

 Investment operations:  Investment income -- net                   .024       .027      .025       .006

 Distributions:          Dividends from
                         investment income -- net                  (.024)    (.027)     (.025)     (.006)

 Net asset value, end of period                                     1.00      1.00       1.00       1.00

 Total return (%)                                                   2.47      2.68       2.55       2.82(2)
- ------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA

 Ratio of expenses to average net assets (%)                         .98       .95        .95       1.04(2)

 Ratio of net investment income to average net assets (%)           2.44      2.64       2.47       3.64(2)

 Decrease reflected in above expense ratios
 due to actions by Dreyfus (%)                                       .08       .08        .16         --
- ------------------------------------------------------------------------------------------------------------

 Net assets, end of period ($ x 1,000)                             46,997   42,169      36,199        --

(1)  FROM SEPTEMBER 8, 1995 (COMMENCEMENT OF INITIAL OFFERING) TO NOVEMBER 30, 1995.

(2) ANNUALIZED.
</TABLE>

Financial Highlights

<PAGE 17>


Your Investment

ACCOUNT POLICIES

Buying shares

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. To purchase fund shares, contact
your financial representative.


APPLICABLE TO GENERAL MONEY MARKET FUND AND GENERAL GOVERNMENT SECURITIES MONEY
MARKET FUND ONLY:

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., 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, you
will receive the dividend declared that day. If your payments are received in or
converted into Federal Funds after 12 noon, 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. and Federal Funds are received by
6 p.m., the shares will be purchased at the NAV determined at 5 p.m. and will
receive the dividend declared that day. If such an order is made after 5 p.m.
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.

APPLICABLE TO GENERAL CALIFORNIA MUNICIPAL MONEY MARKET FUND, GENERAL MINNESOTA
MUNICIPAL MONEY MARKET FUND, GENERAL MUNICIPAL MONEY MARKET FUND AND GENERAL NEW
YORK MUNICIPAL MONEY MARKET FUND ONLY:

YOUR PRICE FOR FUND SHARES is the fund's net asset value (NAV), which is
generally calculated twice a day, at 12 noon and 8 p.m., for the Minnesota
Municipal Money Market Fund and three times a day, at 12 noon, 2 p.m. and 8
p.m., for each other 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 Minnesota Municipal Money Market Fund or by 4 p.m. for each other 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
Minnesota Municipal Money Market Fund or after 4 p.m. for each other 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 12 noon for the Minnesota Municipal Money Market Fund or by


Concepts to understand

NET ASSET VALUE (NAV): a mutual fund's share price on a given day. A fund's NAV
is calculated by dividing the value of its net assets by the number of existing
shares.

AMORTIZED COST: a method of valuing a money market fund's portfolio securities,
which does not take into account unrealized gains or losses. As a result,
portfolio securities are valued at their acquisition cost, adjusted over time
based on the discounts or premiums reflected in their purchase price. This
method of valuation is designed to permit a fund to maintain a stable NAV.





<PAGE 18>


2 p.m. for each other municipal money market fund, and Federal Funds are
received by 4 p.m., 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 12 noon for the Minnesota Municipal
Money Market Fund or after 2 p.m. for any of the other municipal money market
funds, 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 FUNDS seek tax-exempt income, they are not
recommended for purchase in IRAs or other qualified retirement plans.


Selling shares


YOU MAY SELL (REDEEM) SHARES AT ANY TIME through your financial representative.
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.


BEFORE SELLING OR WRITING A CHECK for 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.



Retirement plans

A variety of retirement plans are offered for the taxable money market funds,
including traditional, Roth and Education IRAs.

In addition, SEP-IRAs, Keogh accounts, 401(k) and 403(b) accounts are also
available. Please call your financial representative for information.


General policies


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 that the order is from a representative of your
financial institution.


EACH FUND RESERVES THE RIGHT TO:

*   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)

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

*   change or discontinue its exchange privilege, or temporarily suspend this
    privilege during unusual market conditions

*   change its minimum investment amounts

*   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).



Your Investment

<PAGE 19>


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.
Your dividends and distributions will be reinvested in the fund unless you
instruct the fund otherwise. There are no fees or sales charges on
reinvestments.

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

EACH MUNICIPAL MONEY MARKET FUND anticipates that, under normal market
conditions, virtually all of its income dividends will be exempt from federal
and, as to California Municipal Money Market Fund, California, as to Minnesota
Municipal Money Market Fund, Minnesota, and as to New York Municipal Money
Market Fund, New York state and New York city, 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: income or interest paid by the investments in a fund's portfolio, net
of expenses, passed on to fund shareholders.

DISTRIBUTIONS: income, net of expenses 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.





<PAGE 20>

NOTES

<PAGE>


For More Information

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

General Government Securities Money Market Fund
- -----------------------------------
SEC file number:  811-3456

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

General California Municipal Money Market Fund
- ----------------------------------
SEC file number:  811-4871

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

General New York Municipal Money Market Fund
- -----------------------------------
SEC file number:  811-4870

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

Annual/Semiannual Report

Describes the 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 1-800-554-4611


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
GENP0999B-GAM




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