UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                   FORM N-CSR

              CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT
                              INVESTMENT COMPANIES

Investment Company Act file number:       811-3456

             GENERAL GOVERNMENT SECURITIES MONEY MARKET FUNDS, INC.
               (Exact name of Registrant as specified in charter)


                           c/o The Dreyfus Corporation
                                 200 Park Avenue
                            New York, New York 10166
               (Address of principal executive offices) (Zip code)

                              Mark N. Jacobs, Esq.
                                 200 Park Avenue
                            New York, New York 10166
                     (Name and address of agent for service)

Registrant's telephone number, including area code:    (212) 922-6000

Date of fiscal year end:     11/30

Date of reporting period:    11/30/03






                                          FORM N-CSR

ITEM 1.         REPORTS TO STOCKHOLDERS.

      General Government
      Securities Money
      Market Fund

      ANNUAL REPORT November 30, 2003


YOU, YOUR ADVISOR AND
DREYFUS
A MELLON FINANCIAL COMPANY(SM)


The  views  expressed in this report reflect those of the portfolio manager only
through the end of the period covered and do not necessarily represent the views
of  Dreyfus  or any other person in the Dreyfus organization. Any such views are
subject  to change at any time based upon market or other conditions and Dreyfus
disclaims any responsibility to update such views. These views may not be relied
on as investment advice and, because investment decisions for a Dreyfus fund are
based  on  numerous  factors,  may  not be relied on as an indication of trading
intent on behalf of any Dreyfus fund.

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


                                 Contents

                                 THE FUND
- --------------------------------------------------

                             2   Letter from the Chairman

                             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

                            21   Board Members Information

                            23   Officers of the Fund

                                 FOR MORE INFORMATION
- ---------------------------------------------------------------------------

                                 Back Cover

                                                                       The Fund

                                                  General Government Securities
                                                              Money Market Fund

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This  annual  report  for General Government Securities Money Market Fund covers
the  12-month  period  from December 1, 2002, through November 30, 2003. 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.

Recent  reports  of  marked  improvement  in  the  growth of U.S. Gross Domestic
Product  suggest to us that the economy has started to turn the corner. Tax cuts
and  low  mortgage  rates  have put cash in consumers' pockets, and corporations
have begun to increase spending and investment. As a result, after several years
of  falling  interest rates, longer-term bond yields have begun to creep upward.
However, the Federal Reserve Board repeatedly has affirmed its commitment to low
short-term  interest rates, and yields of money market instruments have remained
near    historical    lows.

Of  course,  we  have  seen  upturns before, only to be disappointed when growth
proved unsustainable over the longer term. However, based on recent data, we are
cautiously optimistic about the current economic environment. As always, we urge
you  to  speak  regularly  with  your  financial advisor, who may be in the best
position  to  suggest  the  Dreyfus  funds  designed to meet your current needs,
future goals and attitudes toward risk.

Thank you for your continued confidence and support.

Sincerely,

/s/ Stephen E. Canter

Stephen E. Canter
Chairman and Chief Executive Officer
The Dreyfus Corporation
December 15, 2003




DISCUSSION OF FUND PERFORMANCE

Bernard W. Kiernan, Jr., Portfolio Manager

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

During  the 12-month period ended November 30, 2003, the fund produced yields of
0.51%  for  Class A shares and 0.29% for Class B shares. Taking into account the
effects  of compounding, the fund produced effective yields of 0.52% for Class A
shares and 0.29% for Class B shares for the same period.(1)

What is the fund's investment 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 solely in securities issued or guaranteed
by  the  U.S.  government  or  its agencies or instrumentalities, and repurchase
agreements collateralized by these securities.

What other factors influenced the fund's performance?

Although the Federal Reserve Board (the "Fed") reduced short-term interest rates
by  50  basis  points in early November 2002, just weeks before the start of the
reporting  period,  the  economy  remained  persistently  sluggish, growing at a
disappointing  1.4%  annualized  rate  in  the  fourth quarter of 2002 as rising
geopolitical tensions, corporate scandals and a declining stock market continued
to take their toll on economic activity.

During  the opening months of 2003, hopes of a more sustainable economic rebound
faded when the impending war in Iraq caused businesses and consumers to postpone
spending.  However,  after it became clear in late March that major combat would
be  over quickly, investors became more optimistic, and money market yields rose
at the
                                                                The Fund


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

longer  end  of the curve. Nonetheless, the rate of economic expansion failed to
improve  during  the  first quarter, with U.S. GDP growing at an annualized 1.4%
rate for the second consecutive quarter.

The  manufacturing sector began to show signs of more sustainable improvement in
May,  and  consumer confidence rebounded. These encouraging signs were supported
by  gains  in  the  stock  market,  low inflation, moderating oil prices, rising
productivity  and legislation enacting new tax cuts. However, the Fed maintained
its  relatively  cautious  stance at its May meeting, saying economic risks were
"weighted toward weakness for the foreseeable future."

Economic  indicators continued to improve in June, and the economy expanded at a
greater   than  expected  3.3%  annualized  rate  during  the  second  quarter.
Unfortunately,  the unemployment rate climbed to 6.4%, its highest level in nine
years,  and  most investors expected the Fed to reduce interest rates further at
its  meeting  in late June. The Fed did not disappoint them, driving the federal
funds rate down another 25 basis points to 1%, a 45-year low.

In  July,  new  signs  of  economic  strength created a sudden shift in investor
sentiment  amid  concerns  that rising inflation and a ballooning federal budget
deficit  might lead to higher interest rates. As a result, prices of longer-term
bonds plunged, producing one of the most severe six-week declines in the history
of  the  bond market. Although heightened volatility roiled the longer-term bond
markets,  money  market yields remained relatively steady, anchored at the short
end of the curve by the 1% federal funds rate.

The  economy continued to improve in the fall as it became clearer that business
investment  and  consumer  spending  were rebounding, even as inflation remained
well under control. Jobless claims dropped in September to their lowest level in
eight  months,  and sales at department stores rose as consumers spent their tax
refunds.  It  was  later  estimated  that  the  economy  grew  at  a robust 8.2%
annualized rate during the third quarter of 2003.


Economic  indicators  in  October  and  November  provided  more  evidence of an
improving  economy,  including  an encouraging increase in the number of jobs in
the  U.S.  economy  and  a decrease in the unemployment rate to 6.0%. Orders for
durable   goods  rose  more  strongly  in  November,  suggesting  that  business
investment  was  finally  contributing  in a meaningful way to the recovery, and
consumer  confidence  advanced  to  its  highest level in more than a year. As a
result,  yields of most U.S. Treasury and agency securities began to rise at the
longer  end  of  the fund's maturity range. However, as was widely expected, the
Fed  held  the  overnight federal funds rate steady at its December meeting just
after  the  end of the reporting period and reiterated its commitment to keeping
borrowing rates low for "a considerable period."

What is the fund's current strategy?

We  generally have maintained the fund's weighted average maturity in a range we
consider longer than average. This strategy is designed to capture higher yields
at  the  longer  end of the fund's maturity range. Of course, we are prepared to
adjust our strategies as economic and market conditions evolve.

December 15, 2003

(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 THE U.S.
GOVERNMENT. 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. YIELDS
PROVIDED FOR THE FUND'S 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 CLASS B YIELDS WOULD HAVE BEEN LOWER.

                                                             The Fund

STATEMENT OF INVESTMENTS

STATEMENT OF INVESTMENTS

November 30, 2003


                                                                                                              

                                                                          Annualized
                                                                            Yield on
                                                                             Date of              Principal
U.S. GOVERNMENT AGENCIES--99.9%                                          Purchase (%)            Amount ($)            Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

Federal Farm Credit Bank, Consolidated

  Systemwide Floating Rate Notes

   6/2/2004                                                                      1.03  (a)       45,000,000        45,002,266

   11/23/2005                                                                    1.06  (a)      110,000,000       110,011,885

Federal Home Loan Banks,

  Discount Notes

   12/5/2003                                                                     1.01           100,000,000        99,988,778

   12/30/2003                                                                    1.25            25,000,000        24,975,108

   1/21/2004                                                                     1.05           100,000,000        99,851,250

   2/11/2004                                                                     1.09            11,110,000        11,085,802

   2/13/2004                                                                     1.09            25,000,000        24,944,038

   3/10/2004                                                                     1.09            50,000,000        49,850,000

   6/4/2004                                                                      1.17            18,462,000        18,351,446

Federal Home Loan Banks,
   Floating Rate Notes

   7/30/2004                                                                     1.01  (a)      150,000,000       150,000,000

   12/2/2004                                                                     1.02  (a)      100,000,000       100,010,696

Federal Home Loan Banks, Notes

   12/1/2003                                                                      .99            46,771,000        46,771,000

   4/16/2004                                                                     1.01            25,000,000        25,356,247

   8/13/2004                                                                     1.13             5,000,000         5,036,543

Federal Home Loan Mortgage Corporation,

  Discount Notes

   12/19/2003                                                                    1.27            25,000,000        24,984,250

Federal Home Loan Mortgage Corporation,
   Notes

   7/15/2004                                                                     1.17            35,699,000        36,468,932

   11/16/2004                                                                    1.42            70,000,000        70,000,000

Federal National Mortgage Association,

  Discount Notes

   8/20/2004                                                                     1.27            17,794,000        17,630,206

Federal National Mortgage Association,

  Floating Rate Notes

   10/7/2004                                                                     1.03  (a)      100,000,000        99,974,440

   10/28/2004                                                                    1.02  (a)      150,000,000       149,972,637

   1/10/2005                                                                     1.03  (a)      100,000,000        99,944,393

   3/10/2005                                                                     1.02  (a)       50,000,000        50,000,000


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

Federal National Mortgage Association,

  Notes

   3/15/2004                                                                     1.24              12,352,000        12,474,052

   7/27/2004                                                                     1.15              25,000,000        25,000,000

   10/18/2004                                                                    1.28             100,000,000       100,000,000

TOTAL U.S. GOVERNMENT AGENCIES

   (cost $1,497,683,969)                                                                                           1,497,683,969
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $1,497,683,969)                                                           99.9%            1,497,683,969

CASH AND RECEIVABLES (NET)                                                                          .1%                1,213,518

NET ASSETS                                                                                       100.0%            1,498,897,487

(A) VARIABLE INTEREST RATE--SUBJECT TO PERIODIC CHANGE.

SEE NOTES TO FINANCIAL STATEMENTS.


                                                             The Fund

STATEMENT OF ASSETS AND LIABILITIES

November 30, 2003

                                                             Cost         Value
- --------------------------------------------------------------------------------

ASSETS ($):

Investments in securities--See Statement of
Investments                                        1,497,683,969  1,497,683,969

Interest receivable                                                   2,514,198

Prepaid expenses and other assets                                        85,494

                                                                  1,500,283,661
- --------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                         1,136,008

Cash overdraft due to Custodian                                         143,870

Payable for shares of Common Stock redeemed                              44,218

Accrued expenses                                                         62,078

                                                                      1,386,174
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                    1,498,897,487
- --------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                   1,498,985,351

Accumulated net realized gain (loss) on investments                    (87,864)
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                    1,498,897,487

NET ASSET VALUE PER SHARE

                                                          Class A       Class B
- --------------------------------------------------------------------------------

Net Assets ($)                                        565,856,754    933,040,733

Shares Outstanding                                    565,952,428    933,032,925
- --------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                                1.00          1.00

SEE NOTES TO FINANCIAL STATEMENTS.


STATEMENT OF OPERATIONS

Year Ended November 30, 2003

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

INVESTMENT INCOME ($):

INTEREST INCOME                                                     21,895,079

EXPENSES:

Management fee--Note 2(a)                                            8,531,164

Shareholder servicing costs--Note 2(c)                               3,579,370

Distribution fees, service fees and prospectus--Note 2(b)            3,427,139

Registration fees                                                      125,042

Custodian fees                                                         114,614

Professional fees                                                       47,298

Directors' fees and expenses--Note 2(d)                                 43,403

Shareholders' reports                                                   10,952

Miscellaneous                                                           23,669

TOTAL EXPENSES                                                      15,902,651

Less--reduction in shareholder servicing costs
  due to undertaking--Note 2(c)                                      (320,598)

NET EXPENSES                                                        15,582,053

INVESTMENT INCOME--NET                                               6,313,026
- --------------------------------------------------------------------------------

NET REALIZED GAIN (LOSS) ON INVESTMENTS--NOTE 1(B) ($)                (13,107)

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                 6,299,919

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

STATEMENT OF CHANGES IN NET ASSETS

                                                     Year Ended November 30,
                                           -------------------------------------
                                                     2003                 2002
- --------------------------------------------------------------------------------

OPERATIONS ($):

Investment income--net                          6,313,026           20,947,155

Net realized gain (loss) on investments          (13,107)               28,539

NET INCREASE (DECREASE) IN NET ASSETS
   RESULTING FROM OPERATIONS                   6,299,919            20,975,694
- --------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A shares                                (3,236,754)         (10,213,063)

Class B shares                                (3,076,272)         (10,734,092)

TOTAL DIVIDENDS                               (6,313,026)         (20,947,155)
- --------------------------------------------------------------------------------

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

Net proceeds from shares sold:

Class A shares                              4,700,029,832       4,554,368,708

Class B shares                              2,477,298,303       2,332,493,736

Dividends reinvested:

Class A shares                                  3,173,385          10,053,123

Class B shares                                  2,641,589           8,765,998

Cost of shares redeemed:

Class A shares                            (4,799,318,073)      (4,707,413,531)

Class B shares                            (2,561,173,141)      (2,153,713,780)

INCREASE (DECREASE) IN NET ASSETS FROM
   CAPITAL STOCK TRANSACTIONS               (177,348,105)          44,554,254

TOTAL INCREASE (DECREASE) IN NET ASSETS     (177,361,212)          44,582,793
- --------------------------------------------------------------------------------

NET ASSETS ($):

Beginning of Period                         1,676,258,699        1,631,675,906

END OF PERIOD                               1,498,897,487        1,676,258,699

SEE NOTES TO FINANCIAL STATEMENTS.


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.


                                                                                                           


                                                                                     Year Ended November 30,
                                                                 -------------------------------------------------------------------
CLASS A SHARES                                                   2003           2002          2001           2000          1999
- ------------------------------------------------------------------------------------------------------------------------------------

PER SHARE DATA ($):

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

Investment Operations:

Investment income--net                                            .005           .014          .040            .054          .043

Distributions:

Dividends from investment income--net                            (.005)         (.014)        (.040)          (.054)        (.043)

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

TOTAL RETURN (%)                                                  .52           1.38          4.05            5.54          4.42
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                           .77            .77           .77             .76           .76

Ratio of net investment income
   to average net assets                                          .52           1.38          3.85            5.40          4.35
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ x 1,000)                         565,857        661,976       804,956         574,630       610,511

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

FINANCIAL HIGHLIGHTS (CONTINUED)

                                                                                      Year Ended November 30,
                                                                --------------------------------------------------------------------
CLASS B SHARES                                                  2003            2002          2001           2000            1999
- ------------------------------------------------------------------------------------------------------------------------------------

PER SHARE DATA ($):

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

Investment Operations:

Investment income--net                                           .003            .011          .037           .052            .041

Distributions:

Dividends from investment income--net                           (.003)          (.011)        (.037)         (.052)          (.041)

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

TOTAL RETURN (%)                                                 .29            1.14          3.81           5.29            4.17
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                         1.00            1.00          1.00           1.00            1.00

Ratio of net investment income
   to average net assets                                         .29            1.13          3.60           5.15            4.09

Decrease reflected in above expense
   ratios due to undertakings by
   The Dreyfus Corporation                                       .03             .03           .04            .03             .03
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ x 1,000)                        933,041        1,014,283       826,720       552,238         659,185

SEE NOTES TO FINANCIAL STATEMENTS.



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 wholly-owned subsidiary of Mellon
Bank, N.A., which is a wholly-owned subsidiary of Mellon Financial Corporation.

Dreyfus  Service  Corporation  (the "Distributor"), a wholly-owned subsidiary of
the  Manager, is the distributor of the fund's shares. 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 (10 billion shares authorized) and Class B
(6  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 Class A and
Class  B shares are subject to a Shareholder Services Plan. 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.  During  the  period  ended  November  30,  2003,
sub-accounting  service  fees  amounted  to  $539,346 for Class B shares and are
included in shareholder servicing cost.

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 a pro rata basis.

                                                             The Fund

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 accounting
principles generally accepted in the United States, 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
in accordance with Rule 2a-7 of the Act, 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,
adjusted  for amortization of discount and premium on investment, is earned from
settlement  date  and  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 $153 during the period ended November 30, 2003,
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.

(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, if any, are normally declared
and  paid annually, but the fund may make distributions on a more frequent basis
to  comply  with  the  distribution requirements of the Internal Revenue Code 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.

At  November 30, 2003, the components of accumulated earnings on a tax basis was
substantially the same as for financial reporting purposes.

The  accumulated  capital  loss  carryover of $93,109 is available to be applied
against  future  net securities profits, if any, realized subsequent to November
30,  2003.  If  not  applied,  $21,009  of the carryover expires in fiscal 2005,
$17,123  expires  in  fiscal  2007,  $41,869  expires in fiscal 2008 and $13,108
expires in fiscal 2011.

The  tax  character  of  distributions  paid  to  shareholders during the fiscal
periods  ended  November  30, 2003 and November 30, 2002, respectively, were all
ordinary income.

At  November  30,  2003, 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).

                                                             The Fund

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

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

(a)  Pursuant  to  a  management  agreement  ("Agreement") with the Manager, the
management  fee  is computed at the annual rate of .50 of 1% of the 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 fees, interest on borrowings and extraordinary expenses, exceed
1 1/2% of  the  value of the fund's average net assets, the fund may deduct from
payments  to  be  made  to  the  Manager,  or the Manager will bear, such excess
expense.  During  the  period  ended  November  30,  2003,  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 bear directly the costs of
preparing,  printing  and distributing prospectuses and statements of additional
information  and  implementing and operating the Plan, such aggregate amount not
to  exceed  in any fiscal year of the fund the greater of $100,000 or .005 of 1%
of  the average daily net assets of Class A. In addition, Class A shares pay the
Distributor  for  distributing  their  shares,  servicing  shareholder  accounts
("Servicing") and  advertising  and marketing relating to Class A shares at an
aggregate  annual rate of .20 of 1% of the value of the average daily net assets
of  Class A. The Distributor may pay one or more 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 Distributor. If a holder of
Class  A  shares ceases to be a client of a Service Agent, but continues to hold
Class  A  shares, the Distributor will be permitted to act as a Service Agent in
respect  of  such  fund  shareholders  and  receive  payments under the Plan for
Servicing.  The  fees payable for Servicing are payable without regard to actual
expenses  incurred.  During  the  period ended November 30, 2003, Class A shares
were charged $1,260,418 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   bear  directly  the  costs  of  preparing,  printing  and  distributing
prospectuses  and  statements  of additional information and of implementing and
operating  the Class B Distribution Plan, such aggregate amount not to exceed in
any fiscal year of the fund the greater of $100,000 or .005 of 1% of the average
daily  net  assets  of  Class  B.  In  addition,  Class  B  shares reimburse the
Distributor  for  payments made to third parties for distributing Class B shares
at  an aggregate annual rate not to exceed .20 of 1% of the value of the average
daily  net assets of Class B. During the period ended November 30, 2003, Class B
shares were charged $2,166,721 pursuant to the Class B Distribution Plan.

(c)  Under  the  Shareholder  Services  Plan  with  respect to Class A ("Class A
Shareholder  Services Plan"), Class A shares reimburse the Distributor an amount
not  to exceed an annual rate of .25 of 1% of the value of the average daily net
assets  of Class A for certain allocated expenses of providing personal services
and/or  maintaining  shareholder  accounts.  The  services  provided may include
personal   services   relating   to  shareholder  accounts,  such  as  answering
shareholder  inquiries  regarding  the  fund  and  providing  reports  and other
information,  and  services  related to the maintenance of shareholder accounts.
During  the period ended November 30, 2003, Class A shares were charged $227,145
pursuant to the Class A Shareholder Services Plan.

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

                                                             The Fund

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

The  Manager  had  undertaken  from December 1, 2002 through June 30, 2003, from
July  1,  2003  through July 7, 2003, and from July 8, 2003 through November 30,
2003,  to  reduce  the  expenses  of  Class  B shares to the extent that, if the
aggregate  expenses  of  Class  B  shares,  exclusive  of taxes, brokerage fees,
interest  on  borrowings  and  extraordinary  expenses, exceed an annual rate of
1.01%, .90%, and  1.01%, respectively,  of the value of the average daily net
assets  of  Class B. In addition, the Manager may, at times, limit certain money
market  fund  expenses in an effort to enhance yields of a fund, or a particular
class  of  a  fund, as applicable, because of low interest rates. Effective July
14,  2003, the Manager limited fund expenses on the fund (Class B) to maintain a
minimum  yield  of  15  basis  points.  Such  expense limitations are voluntary,
temporary  and  may be revised or terminated at anytime. During the period ended
November  30, 2003, Class B shares were charged $2,696,728 pursuant to the Class
B Shareholder Services Plan, of which $320,598 was reimbursed by the Manager.

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, 2003, the fund was charged $61,622 pursuant to the transfer
agency agreement.

(d)  Each  Board  member also serves as a Board member of other funds within the
Dreyfus  complex. Annual retainer fees and attendance fees are allocated to each
fund    based    on    net    assets.


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 of General
Government  Securities  Money  Market  Fund (one of the funds comprising General
Government  Securities  Money  Market Funds, Inc.), as of November 30, 2003, 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 auditing standards generally accepted
in the United States. 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, 2003 by correspondence with
the  custodian.  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, 2003, 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 accounting principles generally
accepted in the United States.

                                        [ERNST & YOUNG LLP SIGNATURE LOGO]

New York, New York
January 8, 2004

                                                             The Fund


IMPORTANT TAX INFORMATION (Unaudited)

For  state  individual income tax purposes, the fund hereby designates 47.70% of
the  ordinary  income  dividends  paid during its fiscal year ended November 30,
2003  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.


BOARD MEMBERS INFORMATION (Unaudited)

JOSEPH S. DIMARTINO (60)

CHAIRMAN OF THE BOARD (1995)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Corporate Director and Trustee

OTHER BOARD MEMBERSHIPS AND AFFILIATIONS:

* The Muscular Dystrophy Association, Director

* Levcor International, Inc., an apparel fabric processor, Director

* Century Business Services, Inc., a provider of outsourcing functions for small
and medium size companies, Director

* The Newark Group, a provider of a national market of paper recovery
facilities, paperboard mills and paperboard converting plants, Director

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 191

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

CLIFFORD L. ALEXANDER, JR. (70)

BOARD MEMBER (1982)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

*  President  of  Alexander  & Associates,  Inc.,  a  management consulting firm
(January 1981-present)

* Chairman of the Board of Moody's Corporation (October 2000-October 2003)

* Chairman of the Board and Chief Executive Officer of The Dun and Bradstreet
Corporation (October 1999-September 2000)

OTHER BOARD MEMBERSHIPS AND AFFILIATIONS:

* Wyeth (formerly, American Home Products Corporation), a global leader in
pharmaceuticals, consumer healthcare products and animal health products,
Director

* Mutual of America Life Insurance Company, Director

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 70

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

PEGGY C. DAVIS (60)

BOARD MEMBER (1990)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Shad Professor of Law, New York University School of Law (1983-present)

* She writes and teaches in the fields of evidence, constitutional theory,
family law,  social sciences and the law, legal process and professional
methodology and training

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 26

                                                             The Fund

BOARD MEMBERS INFORMATION (Unaudited) (CONTINUED)

ERNEST KAFKA (71)

BOARD MEMBER (1982)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Physician engaged in private practice specializing in the psychoanalysis of
adults and  adolescents (1962-present)

* Instructor, The New York Psychoanalytic Institute (1981-present)

* Associate Clinical Professor of Psychiatry at Cornell Medical School
(1987-2002)

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 26

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

NATHAN LEVENTHAL (60)

BOARD MEMBER (1989)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Chairman of the Avery-Fisher Artist Program (November 1997-present)

* President of Lincoln Center for the Performing Arts, Inc. (March 1984-December
2000)

OTHER BOARD MEMBERSHIPS AND AFFILIATIONS:

* Movado Group, Inc., Director

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 26

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

ONCE ELECTED ALL BOARD MEMBERS SERVE FOR AN INDEFINITE TERM. ADDITIONAL
INFORMATION ABOUT THE BOARD MEMBERS, INCLUDING THEIR ADDRESS IS AVAILABLE IN THE
FUND'S STATEMENT OF ADDITIONAL INFORMATION WHICH CAN BE OBTAINED FROM DREYFUS
FREE OF CHARGE BY CALLING THIS TOLL FREE NUMBER: 1-800-554-4611.

SAUL B. KLAMAN, EMERITUS BOARD MEMBER


OFFICERS OF THE FUND (Unaudited)

STEPHEN E. CANTER, PRESIDENT SINCE MARCH 2000.

     Chairman of the Board, Chief Executive Officer and Chief Operating Officer
of the Manager, and an officer of 95 investment companies (comprised of 186
portfolios) managed by the Manager. Mr. Canter also is a Board member and, where
applicable, an Executive Committee Member of the other investment management
subsidiaries of Mellon Financial Corporation, each of which is an affiliate of
the Manager. He is 58 years old and has been an employee of the Manager since
May 1995.

STEPHEN R. BYERS, EXECUTIVE VICE PRESIDENT SINCE NOVEMBER 2002.

     Chief Investment Officer, Vice Chairman and a Director of the Manager, and
an officer of 95 investment companies (comprised of 186 portfolios) managed by
the Manager. Mr. Byers also is an officer, director or an Executive Committee
Member of certain other investment management subsidiaries of Mellon Financial
Corporation, each of which is an affiliate of the Manager. He is 50 years old
and has been an employee of the Manager since January 2000. Prior to joining the
Manager, he served as an Executive Vice President-Capital Markets, Chief
Financial Officer and Treasurer at Gruntal & Co., L.L.C.

MARK N. JACOBS, VICE PRESIDENT SINCE MARCH 2000.

     Executive Vice President, Secretary and General Counsel of the Manager, and
an officer of 96 investment companies (comprised of 202 portfolios) managed by
the Manager. He is 57 years old and has been an employee of the Manager since
June 1977.

STEVEN F. NEWMAN, SECRETARY SINCE MARCH 2000.

     Associate General Counsel and Assistant Secretary of the Manager, and an
officer of 96 investment companies (comprised of 202 portfolios) managed by the
Manager. He is 54 years old and has been an employee of the Manager since July
1980.

JANETTE E. FARRAGHER, ASSISTANT SECRETARY SINCE MARCH 2000.

     Associate General Counsel of the Manager, and an officer of 15 investment
companies (comprised of 26 portfolios) managed by the Manager. She is 41 years
old and has been an employee of the Manager since February 1984.

MICHAEL A. ROSENBERG, ASSISTANT SECRETARY SINCE MARCH 2000.

     Associate General Counsel of the Manager, and an officer of 93 investment
companies (comprised of 195 portfolios) managed by the Manager. He is 43 years
old and has been an employee of the Manager since October 1991.

JAMES WINDELS, TREASURER SINCE NOVEMBER 2001.

     Director - Mutual Fund Accounting of the Manager, and an officer of 96
investment companies (comprised of 202 portfolios) managed by the Manager. He is
45 years old and has been an employee of the Manager since April 1985.

                                                             The Fund

OFFICERS OF THE FUND (Unaudited) (CONTINUED)

ROBERT ROBOL, ASSISTANT TREASURER SINCE AUGUST 2003.

     Senior Accounting Manager - Money Market Funds of the Manager, and an
officer of 37 investment companies (comprised of 79 portfolios) managed by the
Manager. He is 39 years old and has been an employee of the Manager since
October 1988.

KENNETH J. SANDGREN, ASSISTANT TREASURER SINCE NOVEMBER 2001.

     Mutual Funds Tax Director of the Manager, and an officer of 96 investment
companies (comprised of 202 portfolios) managed by the Manager. He is 49 years
old and has been an employee of the Manager since June 1993.

WILLIAM GERMENIS, ANTI-MONEY LAUNDERING COMPLIANCE OFFICER SINCE SEPTEMBER 2002

     Vice President and Anti-Money Laundering Compliance Officer of the
Distributor, and the Anti-Money Laundering Compliance Officer of 91 investment
companies (comprised of 197 portfolios) managed by the Manager. He is 33 years
old and has been an employee of the Distributor since October 1998. Prior to
joining the Distributor, he was a Vice President of Compliance Data Center, Inc


                      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.
                        200 Park Avenue
                        New York, NY 10166

                      Distributor

                        Dreyfus Service Corporation
                        200 Park Avenue
                        New York, NY 10166

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 info@dreyfus.com

ON THE INTERNET  Information can be viewed online or downloaded from:

http://www.dreyfus.com

(c) 2004 Dreyfus Service Corporation                                  975AR1103


      General
      Treasury Prime
      Money Market Fund

      ANNUAL REPORT November 30, 2003


YOU, YOUR ADVISOR AND
DREYFUS
A MELLON FINANCIAL COMPANY(SM)


The  views  expressed in this report reflect those of the portfolio manager only
through the end of the period covered and do not necessarily represent the views
of  Dreyfus  or any other person in the Dreyfus organization. Any such views are
subject  to change at any time based upon market or other conditions and Dreyfus
disclaims any responsibility to update such views. These views may not be relied
on as investment advice and, because investment decisions for a Dreyfus fund are
based  on  numerous  factors,  may  not be relied on as an indication of trading
intent on behalf of any Dreyfus fund.

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


                                 Contents

                                 THE FUND
- --------------------------------------------------

                             2   Letter from the Chairman

                             3   Discussion of Fund Performance

                             6   Statement of Investments

                             7   Statement of Assets and Liabilities

                             8   Statement of Operations

                             9   Statement of Changes in Net Assets

                            10   Financial Highlights

                            13   Notes to Financial Statements

                            19   Report of Independent Auditors

                            20   Important Tax Information

                            21   Board Members Information

                            23   Officers of the Fund

                                 FOR MORE INFORMATION
- ---------------------------------------------------------------------------

                                 Back Cover

                                                                       The Fund

                                                         General Treasury Prime
                                                              Money Market Fund

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This  annual  report  for  General  Treasury  Prime Money Market Fund covers the
12-month period from December 1, 2002, through November 30, 2003. 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.

Recent  reports  of  marked  improvement  in  the  growth of U.S. Gross Domestic
Product  suggest to us that the economy has started to turn the corner. Tax cuts
and  low  mortgage  rates  have put cash in consumers' pockets, and corporations
have begun to increase spending and investment. As a result, after several years
of  falling  interest rates, longer-term bond yields have begun to creep upward.
However, the Federal Reserve Board repeatedly has affirmed its commitment to low
short-term  interest rates, and yields of money market instruments have remained
near historical lows.

Of  course,  we  have  seen  upturns before, only to be disappointed when growth
proved unsustainable over the longer term. However, based on recent data, we are
cautiously optimistic about the current economic environment. As always, we urge
you  to  speak  regularly  with  your  financial advisor, who may be in the best
position  to  suggest  the  Dreyfus  funds  designed to meet your current needs,
future goals and attitudes toward risk.

Thank you for your continued confidence and support.

Sincerely,

/s/ Stephen E. Canter

Stephen E. Canter
Chairman and Chief Executive Officer
The Dreyfus Corporation
December 15, 2003




DISCUSSION OF FUND PERFORMANCE

Bernard W. Kiernan, Jr., Portfolio Manager

How did General Treasury Prime Money Market Fund perform during the period?

During  the 12-month period ended November 30, 2003, the fund produced yields of
0.39% for Class A shares, 0.24% for Class B shares and 0.21% for Class X shares.
Taking  into  account  the  effects  of compounding, the fund produced effective
yields of 0.39% for Class A shares, 0.24% for Class B shares and 0.21% for Class
X shares for the same period.(1)

What is the fund's investment 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  normally  invests  substantially  all  of its assets in U.S. Treasury
securities.

What other factors influenced the fund's performance?

Although the Federal Reserve Board (the "Fed") reduced short-term interest rates
by  50  basis  points in early November 2002, just weeks before the start of the
reporting  period,  the  economy  remained  persistently  sluggish, growing at a
disappointing  1.4%  annualized  rate  in  the  fourth quarter of 2002 as rising
geopolitical tensions, corporate scandals and a declining stock market continued
to take their toll on economic activity.

During  the opening months of 2003, hopes of a more sustainable economic rebound
faded when the impending war in Iraq caused businesses and consumers to postpone
spending.  However,  after it became clear in late March that major combat would
be  over  quickly, investors became more optimistic, and yields of U.S. Treasury
bills and notes began
                                                                      The Fund


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

to  rise.  Nonetheless,  the rate of economic expansion failed to improve during
the  first  quarter,  with  U.S.  GDP growing at an annualized 1.4% rate for the
second consecutive quarter during the reporting period.

The  manufacturing  sector  showed signs of more sustainable improvement in May,
and  consumer  confidence  rebounded.  These encouraging signs were supported by
gains  in  the  stock  market,  low  inflation,  moderating  oil  prices, rising
productivity  and legislation enacting new tax cuts. However, the Fed maintained
its  relatively  cautious  stance at its May meeting, saying economic risks were
"weighted toward weakness for the foreseeable future."

Economic  indicators continued to improve in June, and the economy expanded at a
greater   than  expected  3.3%  annualized  rate  during  the  second  quarter.
Unfortunately,  the unemployment rate climbed to 6.4%, its highest level in nine
years,  and  most investors expected the Fed to reduce interest rates further at
its  meeting  in late June. The Fed did not disappoint them, driving the federal
funds rate down another 25 basis points to 1%, a 45-year low.

In  July,  new  signs  of  economic  strength created a sudden shift in investor
sentiment  amid  concerns  that rising inflation and a ballooning federal budget
deficit  might lead to higher interest rates. As a result, prices of longer-term
bonds plunged, producing one of the most severe six-week declines in the history
of  the  bond market. Although heightened volatility roiled the longer-term bond
markets,  money  market yields remained relatively steady, anchored at the short
end of the curve by the 1% federal funds rate.

The  economy continued to improve in the fall as it became clearer that business
investment  and  consumer  spending  were rebounding, even as inflation remained
well under control. Jobless claims dropped in September to their lowest level in
eight  months,  and sales at department stores rose as consumers spent their tax
refunds.  It  was  later  estimated  that  the  economy  grew  at  a robust 8.2%
annualized rate during the third quarter of 2003.


Economic  indicators  in  October  and  November  provided  more  evidence of an
improving  economy,  including  an encouraging increase in the number of jobs in
the  U.S.  economy  and  a decrease in the unemployment rate to 6.0%. Orders for
durable   goods  rose  more  strongly  in  November,  suggesting  that  business
investment  was  finally  contributing  in a meaningful way to the recovery, and
consumer  confidence  advanced  to  its  highest level in more than a year. As a
result,  yields  of  U.S. Treasury securities began to rise at the longer end of
the  fund's  maturity  range. However, as was widely expected, the Fed held the
overnight  federal  funds rate steady at its December meeting just after the end
of the reporting period and reiterated its commitment to keeping borrowing rates
low for "a considerable period."

What is the fund's current strategy?

We  generally have maintained the fund's weighted average maturity in a range we
consider longer than average. This strategy is designed to capture higher yields
at  the  longer  end of the fund's maturity range. Of course, we are prepared to
adjust our strategies as economic and market conditions evolve.

December 15, 2003

(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 THE U.S.
GOVERNMENT. 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. YIELDS
PROVIDED FOR THE FUND'S CLASS B AND CLASS X 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 AND CLASS X YIELDS WOULD HAVE BEEN LOWER.

                                                             The Fund

STATEMENT OF INVESTMENTS

November 30, 2003

STATEMENT OF INVESTMENTS


                                                                                                             

                                                                      Annualized
                                                                        Yield on
                                                                         Date of                Principal
U.S. TREASURY BILLS--83.8%                                           Purchase (%)              Amount ($)              Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

   12/4/2003                                                                  .94               3,714,000              3,713,709

   12/11/2003                                                                 .92               8,989,000              8,986,706

   12/18/2003                                                                 .89               3,487,000              3,485,535

   12/26/2003                                                                 .91               5,331,000              5,327,637

   1/2/2004                                                                   .91              11,516,000             11,506,680

   2/5/2004                                                                   .91                 363,000                362,394

   2/12/2004                                                                 1.00              12,459,000             12,433,958

   4/22/2004                                                                  .91               1,803,000              1,796,483

TOTAL U.S. TREASURY BILLS

   (cost $47,613,102)                                                                                                 47,613,102
- ------------------------------------------------------------------------------------------------------------------------------------

U.S. TREASURY NOTES--17.7%
- ------------------------------------------------------------------------------------------------------------------------------------

  3.625%, 3/31/2004

   (cost $10,081,382)                                                        1.12              10,000,000             10,081,382
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $57,694,484)                                                               101.5%             57,694,484

LIABILITIES, LESS CASH AND RECEIVABLES                                                             (1.5%)              (830,657)

NET ASSETS                                                                                         100.0%             56,863,827

SEE NOTES TO FINANCIAL STATEMENTS.



STATEMENT OF ASSETS AND LIABILITIES

November 30, 2003

                                                             Cost         Value
- --------------------------------------------------------------------------------

ASSETS ($):

Investments in securities--See Statement of Investments  57,694,484  57,694,484

Interest receivable                                                      61,407

Prepaid expenses                                                          1,750

                                                                     57,757,641
- --------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                            35,536

Cash overdraft due to custodian                                         828,810

Payable for shares of common stock redeemed                                  83

Accrued expenses                                                         29,385

                                                                        893,814
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                       56,863,827
- --------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                      56,864,480

Accumulated net realized gain (loss) on investments                       (653)
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                       56,863,827


                                                                                                                
NET ASSET VALUE PER SHARE

                                                                              Class A                Class B               Class X
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets ($)                                                             26,314,661              30,536,667                12,499

Shares Outstanding                                                         26,314,541              30,537,439                12,500
- ------------------------------------------------------------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                                                    1.00                    1.00                  1.00

SEE NOTES TO FINANCIAL STATEMENTS.


                                                             The Fund

STATEMENT OF OPERATIONS

Year Ended November 30, 2003

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

INVESTMENT INCOME ($):

INTEREST INCOME                                                        699,892

EXPENSES:

Management fee--Note 2(a)                                              296,831

Distribution fees, service fees and and prospectus--Note 2(b)          121,197

Shareholder servicing costs--Note 2(c)                                 120,447

Professional fees                                                       25,063

Custodian fees                                                          10,740

Registration fees                                                        6,704

Shareholders' reports                                                    6,014

Directors' fees and expenses--Note 2(d)                                  2,035

Miscellaneous                                                            2,168

TOTAL EXPENSES                                                         591,199

Less--reduction in service plan fees and shareholder
  servicing costs due to undertaking--Note 2(b,c)                     (71,462)

NET EXPENSES                                                           519,737

INVESTMENT INCOME--NET                                                 180,155
- --------------------------------------------------------------------------------

NET REALIZED GAIN (LOSS) ON INVESTMENTS--NOTE 1(B) ($)                   (589)

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                   179,566

SEE NOTES TO FINANCIAL STATEMENTS.


STATEMENT OF CHANGES IN NET ASSETS

                                                     Year Ended November 30,
                                             -----------------------------------
                                                     2003               2002
- --------------------------------------------------------------------------------

OPERATIONS ($):

Investment income--net                            180,155              490,980

Net realized gain (loss) on investments             (589)                6,141

NET INCREASE (DECREASE) IN NET ASSETS
   RESULTING FROM OPERATIONS                     179,566               497,121
- --------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A shares                                  (103,233)            (372,855)

Class B shares                                   (76,896)            (118,076)

Class X shares                                       (26)                 (49)

TOTAL DIVIDENDS                                 (180,155)            (490,980)
- --------------------------------------------------------------------------------

CAPITAL STOCK TRANSACTIONS (1.00 per share):

Net proceeds from shares sold:

Class A shares                                 48,879,828          90,612,542

Class B shares                                154,799,623          81,092,618

Class X shares                                         --              11,500

Dividends reinvested:

Class A shares                                    101,992             369,481

Class B shares                                     76,896             117,978

Cost of shares redeemed:

Class A shares                               (53,095,000)        (127,253,599)

Class B shares                              (147,217,919)         (70,319,942)

INCREASE (DECREASE) IN NET ASSETS
   FROM CAPITAL STOCK TRANSACTIONS             3,545,420          (25,369,422)

TOTAL INCREASE (DECREASE) IN NET ASSETS        3,544,831          (25,363,281)
- --------------------------------------------------------------------------------

NET ASSETS ($):

Beginning of Period                            53,318,996           78,682,277

END OF PERIOD                                  56,863,827           53,318,996

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

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.


                                                                                                              

                                                                                              Year Ended November 30,
                                                                         -----------------------------------------------------------
CLASS A SHARES                                                           2003             2002             2001           2000(a)
- ------------------------------------------------------------------------------------------------------------------------------------

PER SHARE DATA ($):

Net asset value, beginning of period                                     1.00             1.00             1.00              1.00

Investment Operations:

Investment income--net                                                    .004             .011             .034              .051

Distributions:

Dividends from investment income--net                                    (.004)           (.011)           (.034)            (.051)

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

TOTAL RETURN (%)                                                          .39             1.07             3.49              5.21
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                   .80              .78              .80               .80

Ratio of net investment income
   to average net assets                                                  .38             1.13             3.25              5.49

Decrease reflected in above expense
   ratios due to undertaking
   by The Dreyfus Corporation                                             .05              .00(b)           .08               .43
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ X 1,000)                                  26,315           30,428           66,694            20,179

(A) FROM DECEMBER 1, 1999 (COMMENCEMENT OF OPERATIONS) TO NOVEMBER 30, 2000.

(B) AMOUNT REPRESENTS LESS THAN .01% PER SHARE.

SEE NOTES TO FINANCIAL STATEMENTS.


                                                                                               Year Ended November 30,
                                                                         -----------------------------------------------------------
CLASS B SHARES                                                           2003             2002             2001           2000(a)
- ------------------------------------------------------------------------------------------------------------------------------------

PER SHARE DATA ($):

Net asset value, beginning of period                                     1.00             1.00             1.00              1.00

Investment Operations:

Investment income--net                                                    .002             .009             .032              .049

Distributions:

Dividends from investment income--net                                    (.002)           (.009)           (.032)            (.049)

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

TOTAL RETURN (%)                                                          .24              .86             3.27              5.00
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                   .94             1.00             1.00              1.00

Ratio of net investment income
   to average net assets                                                  .24              .84             2.94              5.14

Decrease reflected in above expense
   ratios due to undertaking
   by The Dreyfus Corporation                                             .18              .08              .13              4.97
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ X 1,000)                                  30,537           22,878           11,987             5,385

(A) FROM DECEMBER 1, 1999 (COMMENCEMENT OF OPERATIONS) TO NOVEMBER 30, 2000.

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

FINANCIAL HIGHLIGHTS (CONTINUED)

                                                                                            Year Ended November 30,
                                                                         -----------------------------------------------------------

CLASS X SHARES                                                           2003             2002             2001           2000(a)
- ------------------------------------------------------------------------------------------------------------------------------------

PER SHARE DATA ($):

Net asset value, beginning of period                                     1.00             1.00             1.00              1.00

Investment Operations:

Investment income--net                                                    .002             .008             .032              .048

Distributions:

Dividends from investment income--net                                    (.002)           (.008)           (.032)            (.048)

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

TOTAL RETURN (%)                                                          .21              .82             3.22              4.94
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                   .96             1.05             1.05              1.05

Ratio of net investment income
   to average net assets                                                  .21              .74             3.03              4.55

Decrease reflected in above expense
   ratios due to undertaking
   by The Dreyfus Corporation                                             .33              .42             3.24             20.13
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ X 1,000)                                      12               12             1                 1

(A) FROM DECEMBER 1, 1999 (COMMENCEMENT OF OPERATIONS) TO NOVEMBER 30, 2000.

SEE NOTES TO FINANCIAL STATEMENTS.



NOTES TO FINANCIAL STATEMENTS

NOTE 1--Significant Accounting Policies:

General Treasury Prime 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 wholly-owned subsidiary of Mellon
Bank, N.A., which is a wholly-owned subsidiary of Mellon Financial Corporation.

Dreyfus  Service  Corporation  (the "Distributor"), a wholly-owned subsidiary of
the  Manager, is the distributor of the fund's shares. The fund is authorized to
issue  3  billion  shares  of  $.001  par value Common Stock. The fund currently
offers  three  classes of shares: Class A (1 billion shares authorized), Class B
(1  billion  shares authorized) and Class X (1 billion shares authorized). Class
A,  Class  B and Class X 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  and Class X shares are subject to a Distribution Plan adopted pursuant
to  Rule 12b-1 under the Act and Class A, Class B and Class X shares are subject
to  Shareholder  Services Plan. 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. During the
period  ended November 30, 2003, sub-accounting service fees amounted to $16,183
for Class B shares and are included in shareholder servicing cost.

The  Company  accounts  separately for the assets, liabilities and operations of
each  series.  Expenses  directly  attributable  to  each  series  are

                                                                      The Fund

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

charged  to that series' operations; expenses which are applicable to all series
are allocated among them on a pro rata basis.

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 accounting
principles generally accepted in the United States, 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
in accordance with Rule 2a-7 of the Act, 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,
adjusted for amortization of discount and premium on investments, is earned from
settlement  date  and  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 $418 during the period ended November 30, 2003
based  on  available  cash  balances  left  on deposit. Income earned under this
arrangement    is    included    in    interest    income.

(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, if any, are normally declared
and  paid annually, but the fund may make distributions on a more frequent basis
to  comply  with  the  distribution requirements of the Internal Revenue Code 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.

At November 30, 2003, the components of accumulated earnings on a tax basis were
substantially the same as for financial reporting purposes.

The  accumulated  capital loss carryover of $653 is available for federal income
tax  purposes  to  be  applied  against  future  net securities profits, if any,
realized  subsequent  to November 30, 2003. If not applied, $64 of the carryover
expires in fiscal 2009 and $589 expires in fiscal 2011.

The  tax character of distributions paid to shareholders during the fiscal years
ended  November  30, 2003 and November 30, 2002, respectively, were all ordinary
income.

At  November  30,  2003, 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 fees, interest on borrowings and extraordinary expenses, exceed
1 1/2%  of the value of the fund's average net assets, the fund may deduct from
payments  to  be  made  to  the  Manager,  or the Manager will bear, such excess
expense.  During  the  period  ended  November  30,  2003,  there was no expense
reimbursement pursuant to the undertaking.

(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 bear directly the cost of
preparing,    printing    and    distributing   prospectuses   and

                                                                     The Fund

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

statements  of  additional  information and implementing and operating the Plan,
such  aggregate  amount  not  to  exceed in any full fiscal year of the fund the
greater of $100,000 or .005 of 1% of the average daily net assets of Class A. In
addition,  Class  A  shares  pay  the Distributor for distributing their shares,
servicing  shareholder  accounts  ("Servicing") and  advertising and marketing
relating to Class A shares at an aggregate annual rate of .20 of 1% of the value
of  the average daily net assets of Class A. The Distributor may pay one or more
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
Distributor.  If  a  holder of Class A shares ceases to be a client of a Service
Agent,  but  continues to hold Class A shares, the Distributor will be permitted
to  act  as  a  Service  Agent  in respect of such fund shareholders and receive
payments  under  the  Plan  for  Servicing.  The  fees payable for Servicing are
payable  without  regard  to  actual  expenses incurred. During the period ended
November  30, 2003, Class A shares were charged $55,106 pursuant to the Plan, of
which $5,263 was reimbursed by the Manager, due to an undertaking, see Note
2(c).

Under  the  Distribution  Plan  with  respect  to Class B ("Class B Distribution
Plan") adopted  pursuant  to  Rule  12b-1  under  the  Act, Class B shares bear
directly  the  costs  of  preparing,  printing and distributing prospectuses and
statements of additional information and of implementing and operating the Class
B  Distribution  Plan, such aggregate amount not to exceed in any fiscal year of
the  fund  the greater of $100,000 or .005 of 1% of the average daily net assets
of  Class  B. In addition, Class B shares reimburse the Distributor for payments
made  to  third parties for distributing Class B shares at an annual rate not to
exceed .20 of 1% of the value of the average daily net assets of Class B. During
the period ended November 30, 2003, Class B shares were charged $66,059 pursuant
to the Class B Distribution Plan.


Under  the  Distribution  Plan  with  respect  to Class X ("Class X Distribution
Plan") adopted  pursuant  to  Rule  12b-1 under the Act, Class X shares pay the
Distributor  for  distributing  Class X shares at an annual rate of .25 of 1% of
the  value  of  the average daily net assets of Class X. During the period ended
November  30,  2003,  Class  X  shares  were charged $32 pursuant to the Class X
Distribution Plan.

(c)  Under  the  Shareholder  Services  Plan  with  respect to Class A ("Class A
Shareholder  Services Plan"), Class A shares reimburse the Distributor an amount
not  to exceed an annual rate of .25 of 1% of the value of the average daily net
assets  of Class A for certain allocated expenses of providing personal services
and/or  maintaining  shareholder  accounts.  The  services  provided may include
personal   services   relating   to  shareholder  accounts,  such  as  answering
shareholder  inquiries  regarding Class A shares and providing reports and other
information,  and  services  related to the maintenance of shareholder accounts.
The Manager has undertaken from December 1, 2002 through November 30, 2003, that
if the aggregate expenses of Class A shares, exclusive of taxes, brokerage fees,
interest on borrowings and extraordinary expenses, exceed .80 of 1% of the value
of  the  average  daily  net  assets of Class A, the Manager would reimburse the
expenses  of the fund under the Class A Shareholder Services Plan, to the extent
of  any  excess  expense  and  up  to  the  full  fee  payable under the Class A
Shareholder  Services  Plan.  During the period ended November 30, 2003, Class A
shares  were  charged  $8,740 pursuant to the Class A Shareholder Services Plan,
all of which was reimbursed by the Manager.

Under  the  Shareholder  Services  Plan  with  respect  to  Class  B and Class X
("Shareholder Services Plan"), Class B and Class X shares pay the Distributor at
an  annual  rate  of  .25  of 1% of the value of the average daily net assets of
Class  B  and  Class  X  shares for servicing shareholder accounts. The services
provided may include personal services relating to shareholder accounts, such as
answering shareholder inquiries regarding Class B and

                                                                       The Fund

NOTES TO FINANCIAL STATEMENTS (CONTINUED)

Class X 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, 2002 through June 30, 2003, from
July  1,  2003  through July 7, 2003, and from July 8, 2003 through November 30,
2003,  to  reduce  the  expenses  of  Class  B shares to the extent that, if the
aggregate  expenses  of  Class  B  shares,  exclusive  of taxes, brokerage fees,
interest  on borrowings and extraordinary expenses, exceed an annual rate of 1%,
..90%, and  1%, respectively. The Manager had undertaken from December 1, 2002
through June 30, 2003 and from July 1, 2003 through November 30, 2003, to reduce
the  expenses of Class X shares to the extent that, if the aggregate expenses of
Class  X  shares, exclusive of taxes, brokerage fees, interest on borrowings and
extraordinary  expenses,  exceed an annual rate of 1.05% and .90%, respectively,
of the value of the average daily net assets of Class X shares. In addition, the
Manager  may, at times, limit certain money market fund expenses in an effort to
enhance  yields  of  a  fund,  or  a  particular class of a fund, as applicable,
because of low interest rates. Effective July 14, 2003, the Manager limited fund
expenses  on  the  fund  (Class B and Class X) to maintain a minimum yield of 15
basis  points.   Such  expense  limitations  are voluntary, temporary and may be
revised  or  terminated  at  anytime. During the period ended November 30, 2003,
Class  B  and Class X shares were charged $80,914 and $32 respectively, pursuant
to  the  Shareholder Services Plan, of which $57,427 and $32, respectively, were
reimbursed by the Manager.

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,  2003, the fund was charged $2,549 pursuant to the transfer
agency agreement.

(d)  Each  Board  member also serves as a Board member of other funds within the
Dreyfus  complex. Annual retainer fees and attendance fees are allocated to each
fund based on net assets.


REPORT OF INDEPENDENT AUDITORS

Shareholders and Board of Directors
General Treasury Prime Money Market Fund

We  have audited the accompanying statement of assets and liabilities, including
the  statement  of investments, of General Treasury Prime Money Market Fund (one
of  the  funds  constituting  General  Government Securities Money Market Funds,
Inc.)  as  of November 30, 2003, 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 auditing standards generally accepted
in  the United States.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, 2003 by correspondence with
the  custodian.  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  Treasury  Prime Money Market Fund, at November 30, 2003, the results of
its  operations  for the year then ended, the changes in its 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 accounting principles generally
accepted in the United States.

                                        [ERNST & YOUNG LLP SIGNATURE LOGO]

New York, New York
January 8, 2004

                                                             The Fund


IMPORTANT TAX INFORMATION (Unaudited)

For State individual income tax purposes, the fund hereby designates 100% of the
ordinary income dividends paid during its fiscal year ended November 30, 2003 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.


BOARD MEMBERS INFORMATION (Unaudited)

JOSEPH S. DIMARTINO (60)

CHAIRMAN OF THE BOARD (1995)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Corporate Director and Trustee

OTHER BOARD MEMBERSHIPS AND AFFILIATIONS:

* The Muscular Dystrophy Association, Director

* Levcor International, Inc., an apparel fabric processor, Director

* Century Business Services, Inc., a provider of outsourcing functions for small
and medium size companies, Director

* The Newark Group, a provider of a national market of paper recovery
facilities,

 paperboard mills and paperboard converting plants, Director

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 191

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

CLIFFORD L. ALEXANDER, JR. (70)

BOARD MEMBER (1982)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

*  President  of  Alexander  & Associates,  Inc.,  a  management consulting firm
(January 1981-present)

* Chairman of the Board of Moody's Corporation (October 2000-October 2003)

* Chairman of the Board and Chief Executive Officer of The Dun and Bradstreet
Corporation (October 1999-September 2000)

OTHER BOARD MEMBERSHIPS AND AFFILIATIONS:

* Wyeth (formerly, American Home Products Corporation), a global leader in
pharmaceuticals, consumer healthcare products and animal health products,
Director

* Mutual of America Life Insurance Company, Director

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 70

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

PEGGY C. DAVIS (60)

BOARD MEMBER (1990)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Shad Professor of Law, New York University School of Law (1983-present)

* She writes and teaches in the fields of evidence, constitutional theory,
family law, social  sciences and the law, legal process and professional
methodology and training

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 26

                                                             The Fund

BOARD MEMBERS INFORMATION (Unaudited) (CONTINUED)

ERNEST KAFKA (71)

BOARD MEMBER (1982)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Physician engaged in private practice specializing in the psychoanalysis of
adults and  adolescents (1962-present)

* Instructor, The New York Psychoanalytic Institute (1981-present)

* Associate Clinical Professor of Psychiatry at Cornell Medical School
(1987-2002)

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 26

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

NATHAN LEVENTHAL (60)

BOARD MEMBER (1989)

PRINCIPAL OCCUPATION DURING PAST 5 YEARS:

* Chairman of the Avery-Fisher Artist Program (November 1997-present)

* President of Lincoln Center for the Performing Arts, Inc. (March 1984-December
2000)

OTHER BOARD MEMBERSHIPS AND AFFILIATIONS:

* Movado Group, Inc., Director

NO. OF PORTFOLIOS FOR WHICH BOARD MEMBER SERVES: 26

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

ONCE ELECTED ALL BOARD MEMBERS SERVE FOR AN INDEFINITE TERM. ADDITIONAL
INFORMATION ABOUT THE BOARD MEMBERS, INCLUDING THEIR ADDRESS IS AVAILABLE IN THE
FUND'S STATEMENT OF ADDITIONAL INFORMATION WHICH CAN BE OBTAINED FROM DREYFUS
FREE OF CHARGE BY CALLING THIS TOLL FREE NUMBER: 1-800-554-4611.

SAUL B. KLAMAN, EMERITUS BOARD MEMBER


OFFICERS OF THE FUND (Unaudited)

STEPHEN E. CANTER, PRESIDENT SINCE MARCH 2000.

     Chairman of the Board, Chief Executive Officer and Chief Operating Officer
of the Manager, and an officer of 95 investment companies (comprised of 186
portfolios) managed by the Manager. Mr. Canter also is a Board member and, where
applicable, an Executive Committee Member of the other investment management
subsidiaries of Mellon Financial Corporation, each of which is an affiliate of
the Manager. He is 58 years old and has been an employee of the Manager since
May 1995.

STEPHEN R. BYERS, EXECUTIVE VICE PRESIDENT SINCE NOVEMBER 2002.

     Chief Investment Officer, Vice Chairman and a Director of the Manager, and
an officer of 95 investment companies (comprised of 186 portfolios) managed by
the Manager. Mr. Byers also is an officer, director or an Executive Committee
Member of certain other investment management subsidiaries of Mellon Financial
Corporation, each of which is an affiliate of the Manager. He is 50 years old
and has been an employee of the Manager since January 2000. Prior to joining the
Manager, he served as an Executive Vice President-Capital Markets, Chief
Financial Officer and Treasurer at Gruntal & Co., L.L.C.

MARK N. JACOBS, VICE PRESIDENT SINCE MARCH 2000.

     Executive Vice President, Secretary and General Counsel of the Manager, and
an officer of 96 investment companies (comprised of 202 portfolios) managed by
the Manager. He is 57 years old and has been an employee of the Manager since
June 1977.

STEVEN F. NEWMAN, SECRETARY SINCE MARCH 2000.

     Associate General Counsel and Assistant Secretary of the Manager, and an
officer of 96 investment companies (comprised of 202 portfolios) managed by the
Manager. He is 54 years old and has been an employee of the Manager since July
1980.

JANETTE E. FARRAGHER, ASSISTANT SECRETARY SINCE MARCH 2000.

     Associate General Counsel of the Manager, and an officer of 15 investment
companies (comprised of 26 portfolios) managed by the Manager. She is 41 years
old and has been an employee of the Manager since February 1984.

MICHAEL A. ROSENBERG, ASSISTANT SECRETARY SINCE MARCH 2000.

     Associate General Counsel of the Manager, and an officer of 93 investment
companies (comprised of 195 portfolios) managed by the Manager. He is 43 years
old and has been an employee of the Manager since October 1991.

JAMES WINDELS, TREASURER SINCE NOVEMBER 2001.

     Director - Mutual Fund Accounting of the Manager, and an officer of 96
investment companies (comprised of 202 portfolios) managed by the Manager. He is
45 years old and has been an employee of the Manager since April 1985.

                                                             The Fund

OFFICERS OF THE FUND (Unaudited) (CONTINUED)

ROBERT ROBOL, ASSISTANT TREASURER SINCE AUGUST 2003.

     Senior Accounting Manager - Money Market Funds of the Manager, and an
officer of 37 investment companies (comprised of 79 portfolios) managed by the
Manager. He is 39 years old and has been an employee of the Manager since
October 1988.

KENNETH J. SANDGREN, ASSISTANT TREASURER SINCE NOVEMBER 2001.

     Mutual Funds Tax Director of the Manager, and an officer of 96 investment
companies (comprised of 202 portfolios) managed by the Manager. He is 49 years
old and has been an employee of the Manager since June 1993.

WILLIAM GERMENIS, ANTI-MONEY LAUNDERING COMPLIANCE OFFICER SINCE SEPTEMBER 2002

     Vice President and Anti-Money Laundering Compliance Officer of the
Distributor, and the Anti-Money Laundering Compliance Officer of 91 investment
companies (comprised of 197 portfolios) managed by the Manager. He is 33 years
old and has been an employee of the Distributor since October 1998. Prior to
joining the Distributor, he was a Vice President of Compliance Data Center, Inc


                      For More Information

                        General Treasury Prime 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.
                        200 Park Avenue
                        New York, NY 10166

                      Distributor

                        Dreyfus Service Corporation
                        200 Park Avenue
                        New York, NY 10166

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 info@dreyfus.com

ON THE INTERNET  Information can be viewed online or downloaded from:

http://www.dreyfus.com

(c) 2004 Dreyfus Service Corporation                                  387AR1103


ITEM 2.         CODE OF ETHICS.

      The Registrant has adopted a code of ethics that applies to the
Registrant's principal executive officer, principal financial officer, principal
accounting officer or controller, or persons performing similar functions.

ITEM 3.         AUDIT COMMITTEE FINANCIAL EXPERT.

      The Registrant's Board has determined that Joseph S. DiMartino, a member
of the Audit Committee of the Board, is an audit committee financial expert as
defined by the Securities and Exchange Commission (the "SEC"). Mr. DiMartino is
"independent" as defined by the SEC for purposes of audit committee financial
expert determinations.

ITEM 4.         PRINCIPAL ACCOUNTANT FEES AND SERVICES.

               Not applicable.

ITEM 5.         AUDIT COMMITTEE OF LISTED REGISTRANTS.

               Not applicable.

ITEM 6.         [RESERVED]

ITEM 7.  DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END
         MANAGEMENT INVESTMENT COMPANIES.

               Not applicable.

ITEM 8.         [RESERVED]

ITEM 9.         CONTROLS AND PROCEDURES.

(a) The Registrant's principal executive and principal financial officers have
concluded, based on their evaluation of the Registrant's disclosure controls and
procedures as of a date within 90 days of the filing date of this report, that
the Registrant's disclosure controls and procedures are reasonably designed to
ensure that information required to be disclosed by the Registrant on Form N-CSR
is recorded, processed, summarized and reported within the required time periods
and that information required to be disclosed by the Registrant in the reports
that it files or submits on Form N-CSR is accumulated and communicated to the
Registrant's management, including its principal executive and principal
financial officers, as appropriate to allow timely decisions regarding required
disclosure.

(b) There were no changes to the Registrant's internal control over financial
reporting that occurred during the Registrant's most recently ended fiscal
half-year that has materially affected, or is reasonably likely to materially
affect, the Registrant's internal control over financial reporting.

ITEM 10.  EXHIBITS.

(a)(1) Code of ethics referred to in Item 2.

(a)(2) Certifications of principal executive and principal financial officers as
required by Rule 30a-2(a) under the Investment Company Act of 1940.

(b) Certification of principal executive and principal financial officers as
required by Rule 30a-2(b) under the Investment Company Act of 1940.


                                   SIGNATURES



Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the Registrant has duly caused this Report to be
signed on its behalf by the undersigned, thereunto duly authorized.

GENERAL GOVERNMENT SECURITIES MONEY MARKET FUNDS, INC.

By:     /S/ STEPHEN E. CANTER
        ---------------------
        Stephen E. Canter
        President

Date:     January 23, 2004

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this Report has been signed below by the
following persons on behalf of the Registrant and in the capacities and on the
dates indicated.

By:     /S/ STEPHEN E. CANTER
        -----------------------
        Stephen E. Canter
        Chief Executive Officer

Date:     January 23, 2004

By:     /S/ JAMES WINDELS
        ---------------------
        James Windels
        Chief Financial Officer

Date:     January 23, 2004







                                  EXHIBIT INDEX

      (a)(1) Code of ethics referred to in Item 2.

      (a)(2) Certifications of principal executive and principal financial
      officers as required by Rule 30a-2(a) under the Investment Company Act of
      1940. (EX-99.CERT)

      (b) Certification of principal executive and principal financial officers
      as required by Rule 30a-2(b) under the Investment Company Act of 1940.
      (EX-99.906CERT)