GENERAL GOVERNMENT SECURITIES MONEY MARKET FUNDS INC
N-30D, 2000-02-07
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General Government

Securities Money

Market Fund

ANNUAL REPORT November 30, 1999

(reg.tm)







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

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

Year 2000 Issues (Unaudited)

The fund could be adversely affected if the computer systems used by Dreyfus and
the fund's other service providers do not properly process and calculate
date-related information from and after January 1, 2000. Dreyfus has taken steps
designed to avoid year 2000-related problems in its systems and to monitor the
readiness  of other service providers.  In addition, issuers of securities in
which the fund invests may be adversely affected by year 2000-related problems.
This could have an impact on the value of the fund's investments and its share
price.




                                 Contents

                                 THE FUND

                             2   Letter from the President

                             3   Discussion of Fund Performance

                             6   Statement of Investments

                             8   Statement of Assets and Liabilities

                             9   Statement of Operations

                            10   Statement of Changes in Net Assets

                            11   Financial Highlights

                            13   Notes to Financial Statements

                            19   Report of Independent Auditors

                            20   Important Tax Information

                                 FOR MORE INFORMATION

                                 Back Cover



                                                                       The Fund

                                                  General Government Securities

                                                              Money Market Fund

LETTER FROM THE PRESIDENT

Dear Shareholder:

We  are  pleased to present this annual report for General Government Securities
Money  Market  Fund,  covering the 12-month period from December 1, 1998 through
November  30,  1999. Inside, you'll find valuable information about how the fund
was  managed during the reporting period, including a discussion with the fund's
portfolio manager, Bernard W. Kiernan, Jr.

When  the reporting period began, the Federal Reserve Board had just completed a
series  of  short-term  interest-rate  cuts  in an attempt to stimulate economic
growth  after  the spread of a global financial crisis in overseas markets.  Its
strategy  apparently  worked,  because signs of renewed economic strength in the
U.S.  and  abroad  became evident early in 1999, fueling fears that inflationary
pressures might re-emerge.

As a result, after remaining relatively steady during the first quarter of 1999,
yields  on  money  market  securities  rose in response to expectations that the
Federal  Reserve  Board  might  raise  short-term  interest  rates. In fact, the
Federal  Reserve  Board  raised  rates three times during the summer and fall of
1999   in  an  attempt  to  forestall  a  potential  resurgence  of  inflation.

We  appreciate  your  confidence over the past year, and we look forward to your
continued  participation  in  General  Government  Securities Money Market Fund

Sincerely,



/s/Stephen E. Canter
_______________________
Stephen E. Canter
President and Chief Investment Officer
The Dreyfus Corporation
December 15, 1999


2





DISCUSSION OF FUND PERFORMANCE

Bernard W. Kiernan, Jr., Portfolio Manager

How did General Government Securities Money Market Fund perform during the
period?

For  the  12-month  period ended November 30, 1999, the fund produced a yield of
4.33%  for  Class  A  shares  and  4.09%  for Class B shares, which, taking into
account the effect of compounding, created an effective yield of 4.42% for Class
A shares and 4.17% for Class B shares.(1)

What factors influenced the fund's performance?

For  the  U.S.  economy,  economic uncertainty and fear, largely a result of the
Asian  financial  crisis  and  Russian  default,  marked  the  beginning  of the
reporting period. The Federal Reserve Board, in an attempt to cushion the United
States  economy  from  negative  overseas  events,  sharply  lowered  short-term
interest rates.

Global  markets  remained  unsettled  as  1999 began. However, despite continued
concerns regarding uncertainty about Japanese economic reform and devaluation of
the Russian ruble, the general atmosphere of crisis eased, and the focus of U.S.
monetary policy makers shifted back to the domestic economy. As concern over the
impact  of  offshore  events  faded,  the  Fed  began  to  voice  concerns about
inflationary pressures.

The  performance  of  the  U.S.  economy  in  the first quarter of 1999 was much
stronger  than  expected. Even though the Gross Domestic Product (GDP) grew at a
rate  of  4.3%, inflation was benign. Despite a tight labor market, there was no
evidence  of  advancing  wage  pressure.  Many  economic  analysts believed that
advances  in  technology  would  make it possible for the economy to grow faster
than  previously  thought  possible  without igniting inflation. Despite concern
that  imbalances  in  the economy might eventually derail the nine-year economic
expansion,  the  U.S.  economy  continued  to  grow  and  the Fed held steady on
short-term interest rates.

                                                             The Fund 3




DISCUSSION OF FUND PERFORMANCE (CONTINUED)

A  surprisingly  large  jump  in  the  Consumer Price Index in May pushed policy
makers  closer  to  a  rate  hike.  Although  the  Fed did not immediately raise
interest  rates,  it did announce a significant shift, adopting a "bias" towards
tightening  -- that is, raising short-term rates. With that shift in bias came a
resulting  change  in  market  psychology,  and  market  participants  began  to
anticipate a move by the Fed toward higher rates.

That  move  came  in  June,  when  at its Open Market Committee meeting, the Fed
raised  short-term  rates by 0.25%. At the same time, however, it announced that
it  was  shifting  its  bias  back  to  neutral  - indicating no intention of an
immediate  rate  increase. The market hoped that this pre-emptive strike to head
off the threat of inflation would signal an end to Fed tightening.

Such  hopes would be short-lived, however, as strong economic growth with rising
wages  and  benefits  renewed  inflationary  concerns. At its August Open Market
Committee meeting, the Fed raised the federal funds rate by an additional 0.25%,
and  signaled  its added resolve by raising the discount rate by 0.25%. Although
second  quarter  GDP  growth  dropped  to  a  seemingly  more  sustainable, less
inflationary  1.9% , the  effects  of  the two short-term rate hikes have yet to
fully affect the performance of the economy.

As  the  fund' s fiscal year ended, the economy continued to send mixed signals.
Third  quarter  GDP  growth  accelerated  to a rapid 4.8%, yet key indicators of
employment  costs, job creation and inflation were at lower levels than would be
expected  given  such  economic  strength.  A  continued  fear  of  inflationary
pressures  led  the  Fed  to  institute a third rate hike in November. The Fed's
primary  concern  continues to be the tightness of the U.S. labor market. At the
end  of  the  fund' s  fiscal  year,  there appeared to be no imminent threat of
inflation.  The  question remains, however, how long the economy can sustain its
current rate of growth without igniting unfavorable inflationary pressures.

4


What is the fund's current strategy?

The  shift  in  market  psychology towards rising rates had a negative impact on
money market performance. The stock market showed increased volatility, and such
volatility often spilled over into the Treasury bond and money markets. Currency
market  volatility  impacted  the performance of dollar-denominated fixed-income
securities.  During the period there was also the occasional "flight to quality"
when  credit  concerns  lead  investors  to  seek  out  bonds  and  money market
instruments of only the highest quality issuers.

In  response,  your fund has adopted a somewhat defensive strategy, reducing the
average  maturity  of  our  investments  and  building a liquidity cushion. This
higher  level  of  cash  should aid in protecting the fund from potential future
volatility,  as  well  as position the fund to benefit if interest rates rise in
the near future.

December 15, 1999

(1)  EFFECTIVE YIELD IS BASED UPON DIVIDENDS DECLARED DAILY AND REINVESTED
MONTHLY. PAST PERFORMANCE IS NO GUARANTEE OF FUTURE RESULTS. YIELDS FLUCTUATE.
AN INVESTMENT IN THE FUND IS NOT INSURED OR GUARANTEED BY THE FDIC OR ANY OTHER
GOVERNMENT AGENCY. ALTHOUGH THE FUND SEEKS TO PRESERVE THE VALUE OF YOUR
INVESTMENT AT $1.00 PER SHARE, IT IS POSSIBLE TO LOSE MONEY BY INVESTING IN THE
FUND. YIELD FIGURES PROVIDED FOR CLASS B SHARES REFLECT THE ABSORPTION OF FUND
EXPENSES BY THE DREYFUS CORPORATION PURSUANT TO AN UNDERTAKING IN EFFECT THAT
MAY BE EXTENDED, TERMINATED OR MODIFIED AT ANY TIME. HAD THESE EXPENSES NOT BEEN
ABSORBED, THE FUND'S CLASS B YIELDS WOULD HAVE BEEN LOWER. WITHOUT THE EXPENSE
ABSORPTION, THE FUND'S CLASS B SHARES WOULD HAVE PRODUCED A YIELD OF 4.06% AND
AN EFFECTIVE YIELD OF 4.14%.

                                                             The Fund 5
<TABLE>
<CAPTION>



STATEMENT OF INVESTMENTS

November 30, 1999

                                                                          Annualized
                                                                            Yield on
                                                                             Date of              Principal
U.S. GOVERNMENT AGENCIES--103.0%                                         Purchase (%)            Amount ($)            Value ($)

Federal Farm Credit Bank, Consolidated Systemwide

  Floating Rate Notes

<S>                                                                              <C>             <C>                   <C>
      1/28/2000                                                                  5.57  (a)       50,000,000            50,000,000

      2/9/2000                                                                   5.55  (a)       25,000,000            24,999,089

      3/17/2000                                                                  5.55  (a)       50,000,000            49,997,248

Federal Home Loan Banks, Discount Notes

   12/1/1999                                                                     5.57            37,979,000            37,979,000

   2/4/2000                                                                      5.59            67,278,000            66,615,966

   2/4/2000                                                                      5.03            16,365,000            16,354,890

   2/22/2000                                                                     4.89            50,000,000            49,994,520

   3/2/2000                                                                      5.04            28,727,000            28,374,615

   3/15/2000                                                                     4.94            10,000,000             9,862,625

   5/26/2000                                                                     5.24            40,000,000            39,992,560

   7/13/2000                                                                     5.44            40,000,000            39,981,803

   7/28/2000                                                                     5.70            25,000,000            24,101,667

   12/1/2000                                                                     5.86            47,400,000            47,347,386

Federal Home Loan Banks, Floating Rate Notes

   2/4/2000                                                                      5.59  (a)       50,000,000            50,000,000

   4/7/2000                                                                      5.60  (a)       25,000,000            24,995,716

   4/14/2000                                                                     5.59  (a)       50,000,000            49,991,701

   6/21/2000                                                                     5.60  (a)      100,000,000            99,978,242

   8/11/2000                                                                     5.67  (a)      100,000,000           100,000,000

   10/5/2000                                                                     5.62  (a)       50,000,000            50,000,000

Federal Home Loan Banks, Notes

   1/14/2000                                                                     4.77            65,000,000            65,001,992

Federal Home Loan Mortgage Corporation,

  Discount Notes

      3/2/2000                                                                   4.97             3,640,000             3,595,907

      6/13/2000                                                                  5.42            25,000,000            24,303,958

Federal National Mortgage Association,

  Discount Notes

      12/2/1999                                                                  5.32            25,000,000            24,996,347

      2/4/2000                                                                   4.89            25,000,000            24,789,653

      3/10/2000                                                                  5.14            26,845,000            26,840,086

      4/20/2000                                                                  4.96            25,000,000            24,994,414

      5/22/2000                                                                  5.10            25,000,000            24,994,284

      8/17/2000                                                                  5.77            20,000,000            19,211,333

Federal National Mortgage Association,

  Floating Rate Notes

      12/1/1999                                                                  5.58  (a)       50,000,000            50,000,000

      8/9/2000                                                                   5.67  (a)      100,000,000            99,965,574



6

                                                                           Annualized
                                                                            Yield on
                                                                             Date of              Principal
U.S. GOVERNMENT AGENCIES (CONTINUED)                                     Purchase (%)            Amount ($)            Value ($)

Student Loan Marketing Association,

  Floating Rate Notes

      2/25/2000                                                                  5.60  (a)       50,000,000           49,994,227

Student Loan Marketing Association, Notes

   11/1/2000                                                                     5.80             8,654,000            8,662,367

TOTAL INVESTMENTS

   (cost $1,307,917,170)                                                                         103.0%            1,307,917,170

LIABILITIES, LESS CASH AND RECEIVABLES                                                           (3.0%)             (38,220,872)

NET ASSETS                                                                                       100.0%            1,269,696,298

(A) THE INTEREST RATE, WHICH WILL CHANGE PERIODICALLY, IS BASED ON THE BANK'S PRIME RATE.
</TABLE>

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund 7



STATEMENT OF ASSETS AND LIABILITIES

November 30, 1999

                                                             Cost         Value

ASSETS ($):

Investments in securities--See Statement of
Investments                                        1,307,917,170  1,307,917,170

Cash                                                                    603,176

Interest receivable                                                   9,429,673

Prepaid expenses and other assets                                        37,654

                                                                  1,317,987,673

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                           480,484

Due to Distributor                                                      374,562

Payable for investment securities purchased                          47,347,386

Accrued expenses                                                         88,943

                                                                     48,291,375

NET ASSETS ($)                                                    1,269,696,298

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                   1,269,880,532

Accumulated net realized gain (loss) on investments                   (184,234)

NET ASSETS ($)                                                    1,269,696,298

NET ASSET VALUE PER SHARE

                                                          Class A      Class B

Net Assets ($)                                        610,511,208   659,185,090

Shares Outstanding                                    610,653,178   659,227,356

NET ASSET VALUE PER SHARE ($)                                1.00          1.00

SEE NOTES TO FINANCIAL STATEMENTS.

8


STATEMENT OF OPERATIONS

Year Ended November 30, 1999


INVESTMENT INCOME ($):

INTEREST INCOME                                                     62,724,330

EXPENSES:

Management fee-Note 2(a)                                             6,149,979

Distribution fees--Note 2(b)                                         2,459,992

Shareholder servicing costs-Note 2(c)                                2,206,675

Registration fees                                                      145,472

Custodian fees                                                         100,278

Professional fees                                                       44,603

Directors' fees and expenses-Note 2(d)                                  34,016

Prospectus and shareholders' reports                                    32,053

Miscellaneous                                                           12,420

TOTAL EXPENSES                                                      11,185,488

Less--reduction in shareholder servicing costs due to
  undertaking--Note 2(c)                                             (226,715)

NET EXPENSES                                                        10,958,773

INVESTMENT INCOME--NET                                              51,765,557

NET REALIZED GAIN (LOSS) ON INVESTMENTS--NOTE 1(B) ($):               (17,123)

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                51,748,434

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund 9



STATEMENT OF CHANGES IN NET ASSETS

                                                     Year Ended November 30,

                                                     1999                1998

OPERATIONS ($):

Investment income--net                         51,765,557          47,782,386

Net realized gain (loss) on investments          (17,123)                 822

NET INCREASE (DECREASE) IN NET ASSETS
   RESULTING FROM OPERATIONS                  51,748,434            47,783,208

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A shares                               (24,572,923)         (25,243,444)

Class B shares                               (27,192,634)         (22,538,942)

TOTAL DIVIDENDS                              (51,765,557)         (47,782,386)

CAPITAL STOCK TRANSACTIONS ($):

Net proceeds from shares sold:

Class A shares                              4,892,448,521        4,880,850,136

Class B shares                              1,874,341,394        1,928,335,745

Dividends reinvested:

Class A shares                                 24,329,688           24,694,104

Class B shares                                 26,105,216           21,778,602

Cost of shares redeemed:

Class A shares                            (4,846,137,806)      (4,875,955,150)

Class B shares                            (1,887,236,183)      (1,668,976,351)

INCREASE (DECREASE) IN NET ASSETS FROM
   CAPITAL STOCK TRANSACTIONS                 83,850,830          310,727,086

TOTAL INCREASE (DECREASE) IN NET ASSETS       83,833,707          310,727,908

NET ASSETS ($):

Beginning of Period                         1,185,862,591         875,134,683

END OF PERIOD                               1,269,696,298       1,185,862,591

SEE NOTES TO FINANCIAL STATEMENTS.


10

<TABLE>
<CAPTION>

FINANCIAL HIGHLIGHTS

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

                                                                             Ten Months Ended
                                                      Year Ended November 30,     November 30,    Year Ended January 31,

CLASS A SHARES                                            1999       1998              1997(a)    1997     1996      1995

PER SHARE DATA ($):

<S>                                                       <C>        <C>                 <C>      <C>       <C>      <C>
Net asset value, beginning of period                      1.00       1.00                1.00     1.00      1.00     1.00

Investment Operations:

Investment income--net                                     .043        .048               .040     .047       .052    .038

Distributions:

Dividends from investment income--net                     (.043)      (.048)             (.040)   (.047)     (.052)  (.038)

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

TOTAL RETURN (%)                                          4.42        4.88               4.84(b)  4.75       5.35    3.90

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                    .76         .77                .82(b)   .82        .84     .83

Ratio of net investment income
   to average net assets                                  4.35        4.77               4.78(b)  4.65       5.22    3.82

Net Assets, end of period ($ x 1,000)                  610,511     539,878              510,289 519,861   530,054  513,345

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

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.

                                                                                                                The Fund 11




FINANCIAL HIGHLIGHTS (Continued)

                                                                             Ten Months Ended
                                                   Year Ended November 30,        November 30,            Year Ended January 31,

CLASS B SHARES                                       1999          1998                1997(a)             1997         1996(b)

PER SHARE DATA ($):

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

Investment Operations:

Investment income--net                               .041           .046                 .038               .045            .042

Distributions:

Dividends from
   investment income--net                           (.041)         (.046)               (.038)             (.045)          (.042)

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

TOTAL RETURN (%)                                    4.17           4.66                 4.69(c)            4.58           5.04(c)

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to
   average net assets                                1.00          0.97                 1.00(c)            1.00           1.00(c)

Ratio of net investment income
   to average net assets                             4.09          4.55                 4.60(c)            4.48           5.01(c)

Decrease reflected in above
   expense ratios due to
   undertakings by the Manager                        .03           .05                  .05(c)             .08            .10(c)

Net Assets,
   end of period ($ x 1,000)                      659,185       645,984                 364,845          90,175               58

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

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

(C) ANNUALIZED.
</TABLE>

SEE NOTES TO FINANCIAL STATEMENTS.

12



NOTES TO FINANCIAL STATEMENTS

NOTE 1--Significant Accounting Policies:

General  Government  Securities  Money  Market  Fund  (the "fund") is a separate
diversified  series  of  General  Government Securities Money Market Funds, Inc.
(the "Company") which is registered under the Investment Company Act of 1940, as
amended  (the  "Act"), as an open-end management investment company and operates
as  a  series  company,  currently  offering two series, including the fund. The
fund' s  investment  objective  is  to provide investors with as high a level of
current  income  as  is  consistent  with  the  preservation  of capital and the
maintenance  of liquidity. The Dreyfus Corporation (the "Manager") serves as the
fund' s  investment  adviser. The Manager is a direct subsidiary of Mellon Bank,
N.A. , which is a wholly-owned subsidiary of Mellon Financial Corporation.

Effective October 25, 1999, the fund's name was changed from "General Government
Securities  Money  Market  Fund,  Inc."  to "General Government Securities Money
Market Fund".

Premier Mutual Fund Services, Inc. (the "Distributor") is the distributor of the
fund' s  shares,  which are sold to the public without a sales load. The fund is
authorized  to issue 16 billion shares of $.001 par value Common Stock. The fund
currently  offers  two classes of shares: Class A (15 billion shares authorized)
and Class B (1 billion shares authorized). Class A shares and Class B shares are
identical  except  for  the  services  offered to and the expenses borne by each
class  and  certain  voting rights. Class A shares are subject to a Service Plan
adopted  pursuant  to  Rule 12b-1 under the Act, Class B shares are subject to a
Distribution Plan adopted pursuant to Rule 12b-1 under the Act and, in addition,
Class  B  shares  are  charged  directly for sub-accounting services provided by
Service  Agents  (a  securities  dealer, financial institution or other industry
professional)  at  an  annual rate of .05% of the value of the average daily net
assets of Class B shares.

The  Company  accounts  separately for the assets, liabilities and operations of
each  series.  Expenses directly attributable to each series are charged to that
series'  operations;  expenses  which are applicable to all series are allocated
among them on pro rata basis.

                                                             The Fund 13



NOTES TO FINANCIAL STATEMENTS (CONTINUED)

It  is  the  fund's policy to maintain a continuous net asset value per share of
$1.00; the fund has adopted certain investment, portfolio valuation and dividend
and distribution policies to enable it to do so. There is no assurance, however,
that  the  fund  will  be able to maintain a stable net asset value per share of
$1.00.

The  fund's  financial  statements  are  prepared  in accordance with generally
accepted accounting principles which may require the use of management estimates
and assumptions. Actual results could differ from those estimates.

(a) Portfolio valuation: Investments in securities are valued at amortized cost,
which has been determined by the fund's Board of Directors to represent the fair
value of the fund's investments.

(b)  Securities  transactions and investment income: Securities transactions are
recorded  on  a  trade  date  basis.  Realized  gain  and  loss  from securities
transactions  are  recorded  on  the  identified  cost basis. Interest income is
recognized  on the accrual basis. Cost of investments represents amortized cost.
Under the terms of the custody agreement, the fund received net earnings credits
of  $6,975 based on available cash balances left on deposit. Income earned under
this arrangement is included in interest income.

The  fund  may  enter  into  repurchase  agreements with financial institutions,
deemed  to  be  creditworthy  by  the  fund' s  Manager, subject to the seller's
agreement  to repurchase and the fund's agreement to resell such securities at a
mutually   agreed   upon  price.  Securities  purchased  subject  to  repurchase
agreements are deposited with the fund's custodian and, pursuant to the terms of
the  repurchase  agreement,  must have an aggregate market value greater than or
equal  to  the repurchase price plus accrued interest at all times. If the value
of  the underlying securities falls below the value of the repurchase price plus
accrued  interest,  the  fund  will  require  the  seller  to deposit additional
collateral by the next business day. If the request for additional collateral is
not met, or the seller defaults on its repurchase obligation, the fund maintains
the  right  to  sell the underlying securities at market value and may claim any
resulting loss against the seller.


14

(c) Dividends to shareholders: It is the policy of the fund to declare dividends
from  investment  income-net  on  each  business  day.  Such  dividends are paid
monthly. Dividends from net realized capital gain are normally declared and paid
annually, but the fund may make distributions on a more frequent basis to comply
with  the  distribution  requirements  of  the Internal Revenue Code of 1986, as
amended (the "Code"). To the extent that net realized capital gain can be offset
by  capital loss carryovers, it is the policy of the fund not to distribute such
gain.

(d) Federal income taxes: It is the policy of the fund to continue to qualify as
a  regulated  investment company, if such qualification is in the best interests
of  its  shareholders,  by complying with the applicable provisions of the Code,
and  to  make  distributions  of  taxable  income  sufficient to relieve it from
substantially all Federal income and excise taxes.

The  fund  has  an  unused  capital  loss  carryover  of  approximately $189,000
available  for  Federal  income  tax  purposes  to be applied against future net
securities  profits,  if  any,  realized subsequent to November 30, 1999. If not
applied,  $19,000  of  the  carryover expires in fiscal 2003, $63,000 expires in
fiscal 2004, $90,000 expires in fiscal 2005 and $17,000 expires in fiscal 2007.

At  November  30,  1999, the cost of investments for Federal income tax purposes
was substantially the same as the cost for financial reporting purposes (see the
Statement of Investments).

NOTE 2--Management Fee and Other Transactions with Affiliates:

(a)  Pursuant  to  a  management  agreement  ("Agreement") with the Manager, the
management  fee  is computed at the annual rate of .50 of 1% of the value of the
fund' s  average daily net assets and is payable monthly. The Agreement provides
that if in any full fiscal year the aggregate expenses of the fund, exclusive of
taxes,  brokerage,  interest  on  borrowings  and extraordinary expenses, exceed
1 1/2% of the  value of the fund's average net assets, the fund may deduct
from payments to be made to the Manager, or the Manager will bear such excess


                                                                    The Fund 15



NOTES TO FINANCIAL STATEMENTS (CONTINUED)

expense.  During  the  period  ended  November  30,  1999,  there was no expense
reimbursement pursuant to the Agreement.

(b)  Under the Service Plan with respect to Class A shares (the "Plan"), adopted
pursuant  to Rule 12b-1 under the Act, Class A shares directly bear the costs of
preparing,  printing  and distributing prospectuses and statements of additional
information  and  implementing  and  of operating the Plan. In addition, Class A
shares  reimburse  (a)  the Distributor for payments made for distributing their
shares  and  servicing  shareholder  accounts ("Servicing") and (b) the Manager,
Dreyfus Service Corporation, a wholly-owned subsidiary of the Manager, and their
affiliates  (collectively "Dreyfus") for  payments  made  for Servicing, at an
aggregate  annual  rate  of  up  to .20 of 1% of the value of the fund's average
daily  net  assets  of Class A. Both the Distributor and Dreyfus may pay Service
Agents  a  fee  in respect of Class A Shares owned by shareholders with whom the
Service  Agent has a Servicing relationship or for whom the Service Agent is the
dealer  or  holder of record. The schedule of such fees and the basis upon which
such fees will be paid shall be determined from time to time by the fund's Board
of  Directors.  If a holder of Class A shares ceases to be a client of a Service
Agent, but continues to hold Class A shares, Dreyfus will be permitted to act as
a  Service Agent in respect of such fund shareholders and receive payments under
the  Service  Plan  for  Servicing.  The  fees payable for Servicing are payable
without regard to actual expenses incurred. During the period ended November 30,
1999, Class A shares were charged $1,131,021 pursuant to the Plan.

Under  the  Distribution  Plan  with  respect  to  Class  B  shares  (" Class  B
Distribution  Plan" ), adopted  pursuant  to  Rule  12b-1 under the Act, Class B
shares   directly  bear  the  costs  of  preparing,  printing  and  distributing
prospectuses  and  statements  of additional information and of implementing and
operating  the  Class B Distribution Plan. In addition, Class B shares reimburse
the  Distributor  for  payments  made  to third parties for distributing Class B
shares  at  an  aggregate  annual  rate  of  up to .20 of 1% of the value of the
average  daily net assets of Class B. During the period ended November 30, 1999,
Class  B  shares  were  charged  $1,328,971 pursuant to the Class B Distribution
Plan.

16


(c) Under the fund's Shareholder Services Plan with respect to Class A ("Class A
Shareholder   Services   Plan"), Class  A  shares  reimburse  Dreyfus  Service
Corporation  an amount not to exceed an annual rate of .25 of 1% of the value of
the fund's average daily net assets of Class A for certain allocated expenses of
providing   personal  services  and/or  maintaining  shareholder  accounts.  The
services   provided  may  include  personal  services  relating  to  shareholder
accounts,  such  as  answering  shareholder  inquiries  regarding  the  fund and
providing reports and other information, and services related to the maintenance
of  shareholder  accounts.  During  the  period ended November 30, 1999, Class A
shares were charged $122,119 pursuant to the Class A Shareholder Services Plan.

Under  the  fund's  Shareholder Services Plan with respect to Class B ("Class B
Shareholder  Services  Plan"), Class  B  shares  pay  the  Distributor  for the
provision  of  certain  services  to  the  holders of Class B shares a fee at an
annual  rate  of .25 of 1% of the value of the average daily net assets of Class
B.  The  services provided may include personal services relating to shareholder
accounts,  such  as answering shareholder inquiries regarding Class B shares and
providing reports and other information, and services related to the maintenance
of  shareholder accounts. The Distributor may make payments to Service Agents in
respect  of these services. The Distributor determines the amounts to be paid to
Service Agents.

The  Manager had undertaken from December 1, 1998 through November 30, 1999 that
if  the  aggregate  expenses  of Class B shares of the fund, exclusive of taxes,
brokerage, interest on borrowings and extraordinary expenses, exceeded 1% of the
value of the average daily net assets of Class B, the Manager will reimburse the
expenses  of  the fund under the Class B Shareholder Services Plan to the extent
of  any  excess  expense  and  up  to  the  full  fee  payable under the Class B
Shareholder  Services  Plan.  During the period ended November 30, 1999, Class B
shares  were  charged  $1,993,456  pursuant  to the Class B Shareholder Services
Plan, of which $226,715 was reimbursed by the Manager.

                                                             The Fund 17



NOTES TO FINANCIAL STATEMENTS (CONTINUED)

The  fund  compensates  Dreyfus Transfer, Inc., a wholly-owned subsidiary of the
Manager,  under  a  transfer  agency  agreement,  for  providing  personnel  and
facilities  to  perform transfer agency services for the fund. During the period
ended  November 30, 1999, the fund was charged $60,221, pursuant to the transfer
agency agreement.

(d)  Each  director  who  is  not  an  "affiliated person" as defined in the Act
receives  from the Company an annual fee of $2,500 and an attendance fee of $500
per  meeting.  The  Chairman  of  the  Board  receives an additional 25% of such
compensation.


18


REPORT OF INDEPENDENT AUDITORS

Shareholders and Board of Directors

General Government Securities Money Market Fund

We  have audited the accompanying statement of assets and liabilities, including
the statement of investments, of General Government Securities Money Market Fund
(one  of  the  Series  constituting  General  Government Securities Money Market
Funds,  Inc.)  as  of November 30, 1999, and the related statement of operations
for  the year then ended, the statement of changes in net assets for each of the
two  years  in  the  period  then ended and financial highlights for each of the
years indicated therein. These financial statements and financial highlights are
the responsibility of the fund's management. Our responsibility is to express an
opinion  on  these  financial  statements  and financial highlights based on our
audits.

We   conducted  our  audits  in  accordance  with  generally  accepted  auditing
standards.  Those standards require that we plan and perform the audit to obtain
reasonable  assurance  about  whether  the  financial  statements  and financial
highlights  are free of material misstatement. An audit includes examining, on a
test  basis,  evidence  supporting  the amounts and disclosures in the financial
statements  and  financial  highlights.  Our procedures included confirmation of
securities  owned  as  of November 30, 1999 by correspondence with the custodian
and brokers. An audit also includes assessing the accounting principles used and
significant  estimates  made  by  management,  as well as evaluating the overall
financial   statement  presentation.  We  believe  that  our  audits  provide  a
reasonable basis for our opinion.

In  our  opinion,  the financial statements and financial highlights referred to
above  present  fairly,  in  all  material  respects,  the financial position of
General  Government  Securities  Money Market Fund at November 30, 1999, and the
results of its operations for the year then ended, the changes in net assets for
each  of the two years in the period then ended and the financial highlights for
each  of  the  indicated years, in conformity with generally accepted accounting
principles.

                                             [ERNST & YOUNG LLP SINGATURE LOGO]

New York, New York
January 6, 2000

                                                             The Fund 19




IMPORTANT TAX INFORMATION (Unaudited)

For  State  individual income tax purposes, the fund hereby designates 66.65% of
the  ordinary  income  dividends  paid during its fiscal year ended November 30,
1999  as  attributable  to interest income from direct obligations of the United
States.  Such dividends are currently exempt from taxation for individual income
tax  purposes in most states, including New York, California and the District of
Columbia.

20


                                                           For More Information

                        General Government Securities Money Market Fund
                        200 Park Avenue
                        New York, NY 10166

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

                        Custodian
                        The Bank of New York
                        100 Church Street
                        New York, NY 10286

                        Transfer Agent &
                        Dividend Disbursing Agent
                        Dreyfus Transfer, Inc.
                        P.O. Box 9671
                        Providence, RI 02940

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

To obtain information:

BY TELEPHONE Call
1-800-645-6561

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

BY E-MAIL  Send your request
to [email protected]

ON THE INTERNET  Information
can be viewed online or
downloaded from:
http://www.dreyfus.com

(c) 2000 Dreyfus Service Corporation                                  975AR9911







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