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:        November 30


Date of reporting period:       May 31, 2003






                                  FORM N-CSR


ITEM 1. REPORTS TO STOCKHOLDERS.

      General Government

      Securities Money

      Market Fund

      SEMIANNUAL REPORT May 31, 2003

YOU, YOUR ADVISOR AND
DREYFUS
A MELLON FINNACIAL 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

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

                                 Back Cover

                                                                       The Fund

                                                  General Government Securities

                                                              Money Market Fund

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This  semiannual  report  for  General  Government  Securities Money Market Fund
covers the six-month period from December 1, 2002, through May 31, 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.

We  have recently seen some signs of stability in the financial markets. Perhaps
most  important,  the  war  in  Iraq  wound down quickly, without disrupting oil
supplies  or  major  incidents of terrorism. While the U.S. economy has remained
weak,  growth  has  been positive overall. Many stock market indices have posted
encouraging gains since the start of 2003, suggesting greater investor optimism,
although  it  is  uncertain  whether such gains will continue. At the same time,
yields  of  U.S.  Treasury  securities  and money market instruments continue to
hover  near  historical  lows, and inflationary pressures have remained subdued

What are the implications for your investments? An accommodative monetary policy
and  a  stimulative fiscal policy suggest that money market yields should remain
relatively  low  for  the foreseeable future, even if the economy begins to gain
strength.  We  currently  see  opportunities for potentially higher returns from
longer-term  assets  in  the  stock  and  bond  markets,  but  selectivity among
individual  securities  should  remain a key factor. However, no one can say for
certain  what  direction the markets will take over time. Your financial advisor
can  help  you  to  ensure  that  your portfolio reflects your investment needs,
long-term 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
June 16, 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  six-month  period  ended May 31, 2003, the fund produced annualized
yields  of  0.64%  for  Class A shares and 0.40% for Class B shares. Taking into
account  the  effects  of  compounding,  the  fund produced annualized effective
yields of 0.64% for Class A shares and 0.40% for Class B shares.(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 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?

When  the  reporting period began in December 2002, the U.S. economy appeared to
be  gathering  momentum  in  the wake of the Federal Reserve Board's (the "Fed")
November  interest-rate  reduction  of  50 basis points, which drove the federal
funds  rate  down  to  1.25%. Retail sales came in higher than most analysts had
expected,  and the stock market began to rally. In addition, consumer confidence
improved during December. Nonetheless, the fourth quarter's GDP growth rate came
in at an estimated annualized rate of just 1.4%.

During the first quarter of 2003, the economy sent mixed signals, and hopes of a
more  robust  economic  rebound  faded. Home sales rose in January, but consumer
confidence  fell  to  new  lows.  Manufacturing  expanded in January but fell in
February. For its part, the Fed kept the federal funds rate unchanged at 1.25%.

                                                             The Fund


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

In March, the outbreak of hostilities in Iraq clouded the economic picture.  The
Fed  indicated at the time that  uncertainty  regarding the war with Iraq was so
great that it could not adequately  assess the economic risks.  Nonetheless,  as
the  conflict  progressed,   the  market's  focus  appeared  to  shift  toward
expectations  of a quick  resolution to the war,  causing money market yields to
rise at the longer end of the curve.

After the war began to wind down in April,  investors' attention returned to the
problems underlying the weak U.S. economy.  The manufacturing  sector contracted
in April, and the unemployment  rate rose to 6%,  suggesting  lingering  caution
among  businesses  reluctant  to resume  hiring  and  production.  In  addition,
uncertainty remained as to the prospects for continued spending among consumers,
as revised  estimates of U.S. economic growth for the first quarter of 2003 came
in at a relatively disappointing 1.9%.

In  May, the economy showed signs of gradual improvement. A key purchasing index
rose  significantly  over  the  previous  month's  levels,  suggesting that the
manufacturing  sector  may  be  improving  and  the  worst may be over. Consumer
confidence  rebounded  to  its  highest levels in almost a year, indicating that
consumers  were becoming increasingly optimistic after reining in their spending
during the Iraq war. These encouraging signs were supported by other potentially
constructive  factors,  including  gains  in  the  stock  market, low inflation,
declining  oil  prices,  gains in productivity and pending tax cuts. However, at
its  meeting  in early May, the Fed adopted a relatively cautious stance, citing
disappointing  numbers related to employment and production. The Fed also stated
that economic risks were "weighted toward weakness for the foreseeable future."


What is the fund's current strategy?

Despite  the  encouraging  signs  that  arose  during  May,  we  remain cautious
regarding  the  prospects for a quick pickup in economic growth. We believe that
more  solid  evidence  is  required to support a sustainable rebound in economic
activity among consumers and businesses. In fact, by the reporting period's end,
market  expectations  had begun to build that the Fed was likely to cut interest
rates further if the economy did not expand more robustly by its meeting in late
June.  These  expectations  have  recently  been reflected by lower yields among
short-term U.S. government securities.

Because the current money market yield curve is  relatively  flat, we have begun
to allow the fund's weighted average maturity to shorten gradually. Accordingly,
the fund ended the  reporting  period  with a  weighted  average  maturity  that
remained  longer  than its peer group  average,  but less so than it had been in
previous months.

June 16, 2003

(1)  ANNUALIZED EFFECTIVE YIELD IS BASED UPON DIVIDENDS DECLARED DAILY AND
REINVESTED MONTHLY. PAST PERFORMANCE IS NO GUARANTEE OF FUTURE RESULTS. YIELDS
FLUCTUATE. AN INVESTMENT IN THE FUND IS NOT INSURED OR GUARANTEED BY THE FDIC OR
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

May 31, 2003 (Unaudited)

                                                                    Annualized
                                                                    Yield on
                                                                    Date of                   Principal
U.S. GOVERNMENT AGENCIES--108.3%                                    Purchase (%)              Amount ($)               Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

Federal Farm Credit Bank, Consolidated

  Systemwide Notes

                                                                                                             
   11/4/2003                                                                1.42              1,500,000               1,521,475

Federal Farm Credit Bank, Consolidated

  Systemwide Floating Rate Notes

   6/2/2003                                                                 1.25  (a)         50,000,000             49,999,967

   6/2/2004                                                                 1.28  (a)         45,000,000             45,004,521

Federal Home Loan Banks, Discount Notes

   6/2/2003                                                                 1.26             225,000,000            224,992,125

   6/11/2003                                                                1.18              50,000,000             49,983,611

   8/14/2003                                                                1.78              19,000,000             18,931,653

   8/20/2003                                                                1.15             100,000,000             99,744,445

   12/30/2003                                                               1.25              25,000,000             24,818,033

Federal Home Loan Banks, Floating Rate Notes

   6/27/2002                                                                1.27  (a)         50,000,000             49,999,121

   9/8/2003                                                                 1.27  (a)         50,000,000             50,000,000

   10/24/2003                                                               1.20  (a)        100,000,000            100,000,000

   7/30/2004                                                                1.26  (a)        150,000,000            150,000,000

   12/2/2004                                                                1.27  (a)        100,000,000            100,016,000

Federal Home Loan Banks, Notes

   5/14/2004                                                                1.38              50,000,000             50,000,000

   6/22/2004                                                                1.24              50,000,000             50,000,000

Federal Home Loan Mortgage Corporation,

  Discount Notes

   8/25/2003                                                                1.39              52,589,000             52,417,648

   9/11/2003                                                                1.72              25,000,000             24,880,292

   11/6/2003                                                                1.41              50,000,000             49,694,972

   12/19/2003                                                               1.27              50,000,000             49,648,250

Federal Home Loan Mortgage Corporation,

  Notes

   11/17/2003                                                               1.35              75,000,000             76,671,233

Federal National Mortgage Association,

  Discount Notes

   8/29/2003                                                                1.15              46,860,000             46,726,774

   9/24/2003                                                                1.20              50,000,000             49,810,090

   10/17/2003                                                               1.40              25,000,000             24,867,750

   11/14/2003                                                               1.25              50,000,000             49,714,111

   12/12/2003                                                               1.25              50,000,000             49,665,889


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

Federal National Mortgage Association,

  Floating Rate Notes

   7/22/2003                                                                1.25  (a)         50,000,000             49,999,299

   10/7/2004                                                                1.28  (a)        100,000,000             99,959,400

   10/28/2004                                                               1.27  (a)        150,000,000            149,957,555

Federal National Mortgage Association, Notes

   11/14/2003                                                               1.39              23,500,000             23,847,733

   3/15/2004                                                                1.24              12,352,000             12,686,767

Student Loan Marketing Association,

  Discount Notes

   6/2/2003                                                                 1.26              30,117,000             30,115,946

TOTAL U.S. GOVERNMENT AGENCIES

   (cost $1,905,674,660)                                                                                           1,905,674,660
- ------------------------------------------------------------------------------------------------------------------------------------

REPURCHASE AGREEMENT--.2%
- ------------------------------------------------------------------------------------------------------------------------------------

Barclays Capital Inc.

  dated 5/30/2003, due 6/2/2003 in the
  amount of $3,000,250 (fully collateralized
  by $3,055,000 U.S. Treasury Bills,
  due 8/28/2003, value $3,044,918)

   (cost $3,000,000)                                                        1.00                3,000,000              3,000,000
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $1,908,674,660)                                                           108.5%           1,908,674,660

LIABILITIES, LESS CASH AND RECEIVABLES                                                            (8.5%)           (149,904,125)

NET ASSETS                                                                                        100.0%           1,758,770,535

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


SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

STATEMENT OF ASSETS AND LIABILITIES

May 31, 2003 (Unaudited)

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

ASSETS ($):

Investments in securities--
   See Statement of Investments--Note 1(b)          1,908,674,660  1,908,674,660

Interest receivable                                                    1,777,157

Prepaid expenses and other assets                                         59,095

                                                                   1,910,510,912
- --------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                         1,292,801

Cash overdraft due to Custodian                                         252,560

Payable for investment securities purchased                         150,016,000

Payable for shares of Common Stock redeemed                              75,532

Accrued expenses                                                        103,484

                                                                    151,740,377
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                    1,758,770,535
- --------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                   1,758,844,377

Accumulated net realized gain (loss) on investments                    (73,842)
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                    1,758,770,535

NET ASSET VALUE PER SHARE

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

Net Assets ($)                                       633,990,214  1,124,780,321

Shares Outstanding                                   634,081,225  1,124,763,152
- --------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                               1.00           1.00

SEE NOTES TO FINANCIAL STATEMENTS.


STATEMENT OF OPERATIONS

Six Months Ended May 31, 2003 (Unaudited)

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

INVESTMENT INCOME ($):

INTEREST INCOME                                                     11,956,647

EXPENSES:

Management fee--Note 2(a)                                            4,228,611

Shareholder servicing costs--Note 2(c)                               1,797,173

Distribution fees, service fees and prospectus--Note 2(b)            1,697,231

Registration fees                                                       79,986

Custodian fees                                                          56,845

Directors' fees and expenses--Note 2(d)                                 23,888

Professional fees                                                       20,971

Shareholders' reports                                                    4,010

Miscellaneous                                                           10,074

TOTAL EXPENSES                                                       7,918,789

Less--reduction in shareholder servicing costs due to
  undertaking--Note 2(c)                                              (87,680)

NET EXPENSES                                                         7,831,109

INVESTMENT INCOME--NET                                               4,125,538
- --------------------------------------------------------------------------------

NET REALIZED GAIN (LOSS) ON INVESTMENTS--NOTE 1(B) ($)                     915

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                 4,126,453

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

STATEMENT OF CHANGES IN NET ASSETS

                                         Six Months Ended
                                             May 31, 2003           Year Ended
                                              (Unaudited)    November 30, 2002
- --------------------------------------------------------------------------------

OPERATIONS ($):

Investment income--net                          4,125,538          20,947,155

Net realized gain (loss) on investments               915              28,539

NET INCREASE (DECREASE) IN NET ASSETS
   RESULTING FROM OPERATIONS                    4,126,453          20,975,694
- --------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A shares                                (1,996,953)         (10,213,063)

Class B shares                                (2,128,585)         (10,734,092)

TOTAL DIVIDENDS                               (4,125,538)         (20,947,155)
- --------------------------------------------------------------------------------

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

Net proceeds from shares sold:

Class A shares                              2,223,242,688       4,554,368,708

Class B shares                              1,217,769,622       2,332,493,736

Dividends reinvested:

Class A shares                                  1,983,125         10,053,123

Class B shares                                  1,823,700          8,765,998

Cost of shares redeemed:

Class A shares                            (2,253,211,870)      (4,707,413,531)

Class B shares                            (1,109,096,344)      (2,153,713,780)

INCREASE (DECREASE) IN NET ASSETS FROM
   CAPITAL STOCK TRANSACTIONS                82,510,921            44,554,254

TOTAL INCREASE (DECREASE) IN NET ASSETS      82,511,836            44,582,793
- --------------------------------------------------------------------------------

NET ASSETS ($):

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

END OF PERIOD                               1,758,770,535        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.





                                         Six Months Ended
                                             May 31, 2003                               Year Ended November 30,
                                                                  ------------------------------------------------------------------
CLASS A SHARES                                  (Unaudited)         2002         2001          2000           1999          1998
- ------------------------------------------------------------------------------------------------------------------------------------

PER SHARE DATA ($):

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

Investment Operations:

Investment income--net                                 .003          .014         .040          .054           .043          .048

Distributions:

Dividends from investment
   income--net                                        (.003)        (.014)       (.040)        (.054)         (.043)        (.048)

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

TOTAL RETURN (%)                                       .64(a)       1.38         4.05          5.54           4.42          4.88
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses
   to average net assets                               .78(a)        .77          .77           .76            .76           .77

Ratio of net investment income
   to average net assets                               .64(a)       1.38         3.85          5.40           4.35          4.77
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period
   ($ x 1,000)                                     633,990       661,976      804,956       574,630        610,511       539,878

(A) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

FINANCIAL HIGHLIGHTS (CONTINUED)

                                       Six Months Ended
                                           May 31, 2003                                    Year Ended November 30,
                                                                  ------------------------------------------------------------------
CLASS B SHARES                               (Unaudited)            2002          2001          2000           1999          1998
- ------------------------------------------------------------------------------------------------------------------------------------

PER SHARE DATA ($):

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

Investment Operations:

Investment income--net                               .002            .011          .037          .052           .041          .046

Distributions:

Dividends from investment
   income--net                                      (.002)          (.011)        (.037)        (.052)         (.041)        (.046)

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

TOTAL RETURN (%)                                     .40(a)         1.14          3.81          5.29           4.17          4.66
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses
   to average net assets                            1.01(a)         1.00          1.00          1.00           1.00           .97

Ratio of net investment income
   to average net assets                             .40(a)         1.13          3.60          5.15           4.09          4.55

Decrease reflected in above
   expense ratios due to
   undertakings by
   The Dreyfus Corporation                           .02(a)          .03           .04           .03            .03           .05
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period
   ($ x 1,000)                                 1,124,780        1,014,283       826,720      552,238        659,185       645,984



(A) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.


NOTES TO FINANCIAL STATEMENTS (Unaudited)

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.

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 (Unaudited) (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
receives net earnings credits based on available cash balances left on deposit.

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.

The  fund  has an unused capital loss carryover of $80,001 available for federal
income tax purposes to be applied against future net securities profits, if any,
realized  subsequent  to  November  30,  2002.  If  not  applied, $21,009 of the
carryover  expires  in  fiscal  2005, $17,123 expires in fiscal 2007 and $41,869
expires in fiscal 2008.

The  tax  character of distributions paid to shareholders during the fiscal year
ended  November  30,  2002 was all ordinary income. The tax character of current
year distributions will be determined at the end of the current fiscal year.

At  May  31,  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 (Unaudited) (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  May  31,  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 of 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 fund's Board of Directors. If
a  holder  of  Class  A  shares  ceases  to  be a client of a Service Agent, but
continues  to  hold  Class  A  shares, the Manager 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 May 31, 2003, Class
A shares were charged $629,155 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 May 31, 2003, Class B
shares were charged $1,068,076 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  May  31,  2003, Class A shares were charged $139,795
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 (Unaudited) (CONTINUED)

The Manager had undertaken  from December 1, 2002 through May 31, 2003,  that if
the  aggregate  expenses  of Class B shares  of the  fund,  exclusive  of taxes,
brokerage fees, interest on borrowings and extraordinary expenses,  exceed 1.01%
of the value of the  average  daily net  assets  of Class B, the  Manager  would
reimburse the expenses of the fund under the Class B  Shareholder  Services Plan
to the extent of any excess  expense  and up to the full fee  payable  under the
Class B Shareholder Services Plan. During the period ended May 31, 2003, Class B
shares were charged,  $1,330,498  pursuant to the Class B  Shareholder  Services
Plan, of which $87,680 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  May  31,  2003,  the  fund  was charged $32,251, pursuant to the transfer
agency agreement.

(D)  Each  Board  member also serves as a Board member of other funds within the
Dreyfus  complex  (collectively, the "Fund Group"). Each Board member who is not
an  "affiliated  person" as defined in the Act receives an annual fee of $50,000
and  an  attendance  fee  of  $6,500  for  each  in-person  meeting and $500 for
telephone  meetings.  These fees are allocated among the funds in the Fund Group
in  proportion  to relative to each fund's net assets. The Chairman of the Board
receives  an  additional  25%  of  such  compensation.  Subject to the Company's
Emeritus  Program Guidelines, Emeritus Board members, if any, receive 50% of the
annual  retainer  fee  and  per  meeting  fee  paid at the time the Board member
achieves emeritus status.



NOTES

                                                           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) 2003 Dreyfus Service Corporation                                  975SA0503



      General

      Treasury Prime

      Money Market Fund

      SEMIANNUAL REPORT May 31, 2003

YOU, YOUR ADVISOR AND
DREYFUS
A MELLON FINNACIAL 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

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

                                 Back Cover

                                                                       The Fund

                                                         General Treasury Prime

                                                              Money Market Fund

LETTER FROM THE CHAIRMAN

Dear Shareholder:

This  semiannual report for General Treasury Prime Money Market Fund, covers the
six-month  period  from  December  1, 2002, through May 31, 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.

We  have recently seen some signs of stability in the financial markets. Perhaps
most  important,  the  war  in  Iraq  wound down quickly, without disrupting oil
supplies  or  major  incidents of terrorism. While the U.S. economy has remained
weak,  growth  has  been positive overall. Many stock market indices have posted
encouraging gains since the start of 2003, suggesting greater investor optimism,
although  it  is  uncertain  whether such gains will continue. At the same time,
yields  of  U.S.  Treasury  securities  and money market instruments continue to
hover  near  historical  lows, and inflationary pressures have remained subdued.

What are the implications for your investments? An accommodative monetary policy
and  a  stimulative fiscal policy suggest that money market yields should remain
relatively  low  for  the foreseeable future, even if the economy begins to gain
strength.  We  currently  see  opportunities for potentially higher returns from
longer-term  assets  in  the  stock  and  bond  markets,  but  selectivity among
individual  securities  should  remain a key factor. However, no one can say for
certain  what  direction the markets will take over time. Your financial advisor
can  help  you  to  ensure  that  your portfolio reflects your investment needs,
long-term 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
June 16, 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  six-month  period  ended May 31, 2003, the fund produced annualized
yields of 0.53% for Class A shares, 0.33% for Class B shares and 0.27% for Class
X  shares.  Taking  into  account  the effects of compounding, the fund produced
annualized  effective  yields  of  0.53%  for  Class A shares, 0.33% for Class B
shares and 0.28% 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?

When  the  reporting period began in December 2002, the U.S. economy appeared to
be  gathering  momentum  in  the wake of the Federal Reserve Board's (the "Fed")
November  interest-rate  reduction  of  50 basis points, which drove the federal
funds  rate  down  to  1.25%. Retail sales came in higher than most analysts had
expected,  and the stock market began to rally. In addition, consumer confidence
improved during December. Nonetheless, the fourth quarter's GDP growth rate came
in at an estimated annualized rate of just 1.4%.

During the first quarter of 2003, the economy sent mixed signals, and hopes of a
more  robust  economic  rebound  faded. Home sales rose in January, but consumer
confidence  fell  to  new  lows.  Manufacturing  expanded in January but fell in
February. For its part, the Fed kept the federal funds rate unchanged at 1.25%.

                                                             The Fund


DISCUSSION OF FUND PERFORMANCE (CONTINUED)

In March, the outbreak of hostilities in Iraq clouded the economic picture.  The
Fed  indicated at the time that  uncertainty  regarding the war with Iraq was so
great that it could not adequately  assess the economic risks.  Nonetheless,  as
the  conflict  progressed,   the  market's  focus  appeared  to  shift  toward
expectations  of a quick  resolution to the war,  causing money market yields to
rise at the longer end of the curve.

After the war began to wind down in April,  investors' attention returned to the
problems underlying the weak U.S. economy.  The manufacturing  sector contracted
in April, and the unemployment  rate rose to 6%,  suggesting  lingering  caution
among  businesses  reluctant  to resume  hiring  and  production.  In  addition,
uncertainty remained as to the prospects for continued spending among consumers,
as revised  estimates of U.S. economic growth for the first quarter of 2003 came
in at a relatively disappointing 1.9%.

In  May, the economy showed signs of gradual improvement. A key purchasing index
rose  significantly  over  the  previous  month's  levels,  suggesting that the
manufacturing  sector  may  be  improving  and  the  worst may be over. Consumer
confidence  rebounded  to  its  highest levels in almost a year, indicating that
consumers  were becoming increasingly optimistic after reining in their spending
during the Iraq war. These encouraging signs were supported by other potentially
constructive  factors,  including  gains  in  the  stock  market, low inflation,
declining  oil  prices,  gains in productivity and pending tax cuts. However, at
its  meeting  in early May, the Fed adopted a relatively cautious stance, citing
disappointing  numbers related to employment and production. The Fed also stated
that economic risks were "weighted toward weakness for the foreseeable future."


What is the fund's current strategy?

Despite  the  encouraging  signs  that  arose  during  May,  we  remain cautious
regarding  the  prospects for a quick pickup in economic growth. We believe that
more  solid  evidence  is  required to support a sustainable rebound in economic
activity among consumers and businesses. In fact, by the reporting period's end,
market  expectations  had begun to build that the Fed was likely to cut interest
rates further if the economy did not expand more robustly by its meeting in late
June.  These  expectations  have  recently  been reflected by lower yields among
short-term U.S. Treasury securities.

Because the current money market yield curve is  relatively  flat, we have begun
to allow the fund's weighted average maturity to shorten gradually. Accordingly,
the fund ended the  reporting  period  with a  weighted  average  maturity  that
remained  longer  than its peer group  average,  but less so than it had been in
previous months.

June 16, 2003

(1)  ANNUALIZED EFFECTIVE YIELD IS BASED UPON DIVIDENDS DECLARED DAILY AND
REINVESTED MONTHLY. PAST PERFORMANCE IS NO GUARANTEE OF FUTURE RESULTS. YIELDS
FLUCTUATE. AN INVESTMENT IN THE FUND IS NOT INSURED OR GUARANTEED BY THE FDIC OR
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

May 31, 2003 (Unaudited)

STATEMENT OF INVESTMENTS

                                                                           Annualized
                                                                             Yield on
                                                                              Date of             Principal
U.S. TREASURY BILLS--86.3%                                                Purchase (%)            Amount ($)            Value ($)
- ------------------------------------------------------------------------------------------------------------------------------------

                                                                                                                
   6/12/2003                                                                     1.14               493,000              492,828

   6/19/2003                                                                     1.18               874,000              873,484

   6/26/2003                                                                     1.17            12,000,000           11,990,292

   7/3/2003                                                                      1.06             9,831,000            9,821,704

   7/10/2003                                                                     1.20               203,000              202,737

   7/17/2003                                                                     1.17            10,070,000           10,055,030

   7/24/2003                                                                     1.12             3,400,000            3,394,394

   7/31/2003                                                                     1.09             7,639,000            7,625,070

   8/21/2003                                                                     1.05             3,467,000            3,458,822

   8/28/2003                                                                     1.06             2,406,000            2,399,790

   10/9/2003                                                                     1.11             5,000,000            4,980,139

   11/13/2003                                                                    1.09             2,000,000            1,990,100

TOTAL U.S. TREASURY BILLS

   (cost $57,284,390)                                                                                                 57,284,390
- ------------------------------------------------------------------------------------------------------------------------------------

U.S. TREASURY NOTES--13.7%
- ------------------------------------------------------------------------------------------------------------------------------------

   3.875%, 6/30/2003                                                             2.28             2,000,000            2,002,411

   3.875%, 7/31/2003                                                             1.72             2,000,000            2,006,966

   3.625%, 3/31/2004                                                             1.22             5,000,000            5,097,006

TOTAL U.S. TREASURY NOTES

   (cost $9,106,383)                                                                                                   9,106,383
- ------------------------------------------------------------------------------------------------------------------------------------

TOTAL INVESTMENTS (cost $66,390,773)                                                                  100.0%          66,390,773

CASH AND RECEIVABLES (NET)                                                                              0.0%              23,120

NET ASSETS                                                                                            100.0%          66,413,893

SEE NOTES TO FINANCIAL STATEMENTS.



STATEMENT OF ASSETS AND LIABILITIES

May 31, 2003 (Unaudited)

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

ASSETS ($):

Investments in securities--See Statement of Investments  66,390,773  66,390,773

Cash                                                                        217

Interest receivable                                                      89,149

Prepaid expenses                                                          3,345

                                                                     66,483,484
- --------------------------------------------------------------------------------

LIABILITIES ($):

Due to The Dreyfus Corporation and affiliates                            45,594

Accrued expenses                                                         23,997

                                                                         69,591
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                       66,413,893
- --------------------------------------------------------------------------------

COMPOSITION OF NET ASSETS ($):

Paid-in capital                                                      66,411,180

Accumulated net realized gain (loss) on investments                       2,713
- --------------------------------------------------------------------------------

NET ASSETS ($)                                                       66,413,893

NET ASSET VALUE PER SHARE





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

                                                                                                               
Net Assets ($)                                                             30,580,401             35,820,992            12,500

Shares Outstanding                                                         30,578,625             35,820,055            12,500
- ------------------------------------------------------------------------------------------------------------------------------------

NET ASSET VALUE PER SHARE ($)                                                    1.00                   1.00              1.00




SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

STATEMENT OF OPERATIONS

Six Months Ended May 31, 2003 (Unaudited)

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

INVESTMENT INCOME ($):

INTEREST INCOME                                                        385,512

EXPENSES:

Management fee--Note 2(a)                                              145,854

Shareholder servicing costs--Note 2(c)                                  66,072

Distribution fees, service fees  and prospectus--Note 2(b)              59,364

Professional fees                                                       12,958

Custodian fees                                                           4,656

Registration fees                                                        4,589

Shareholders' reports                                                    2,327

Miscellaneous                                                            1,252

Directors' fees and expenses--Note 2(d)                                    969

TOTAL EXPENSES                                                         298,041

Less--reduction in service plan fees and shareholder servicing costs
  due to undertaking--Note 2 (b,c)                                     (32,124)

NET EXPENSES                                                           265,917

INVESTMENT INCOME--NET                                                 119,595
- --------------------------------------------------------------------------------

NET REALIZED GAIN (LOSS) ON INVESTMENTS--NOTE 1(B) ($)                   2,777

NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                   122,372

SEE NOTES TO FINANCIAL STATEMENTS.


STATEMENT OF CHANGES IN NET ASSETS

                                         Six Months Ended
                                             May 31, 2003            Year Ended
                                               (Unaudited)    November 30, 2002
- --------------------------------------------------------------------------------

OPERATIONS ($):

Investment income--net                            119,595               490,980

Net realized gain (loss) on investments             2,777                 6,141

NET INCREASE (DECREASE) IN NET ASSETS
   RESULTING FROM OPERATIONS                      122,372               497,121
- --------------------------------------------------------------------------------

DIVIDENDS TO SHAREHOLDERS FROM ($):

Investment income--net:

Class A shares                                    (68,337)             (372,855)

Class B shares                                    (51,241)             (118,076)

Class X shares                                        (17)                  (49)

TOTAL DIVIDENDS                                  (119,595)             (490,980)
- --------------------------------------------------------------------------------

CAPITAL STOCK TRANSACTIONS ($1.00 per share):

Net proceeds from shares sold:

Class A shares                                 29,859,782            90,612,542

Class B shares                                 58,943,599            81,092,618

Class X shares                                         --                11,500

Dividends reinvested:

Class A shares                                     67,972               369,481

Class B shares                                     51,281               117,978

Cost of shares redeemed:

Class A shares                                (29,776,850)         (127,253,599)

Class B shares                                (46,053,664)          (70,319,942)

INCREASE (DECREASE) IN NET ASSETS
   FROM CAPITAL STOCK TRANSACTIONS             13,092,120           (25,369,422)

TOTAL INCREASE (DECREASE) IN NET ASSETS        13,094,897           (25,363,281)
- --------------------------------------------------------------------------------

NET ASSETS ($):

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

END OF PERIOD                                  66,413,893            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.





                                                               Six Months Ended
                                                                   May 31, 2003                    Year Ended November 30,
                                                                                        --------------------------------------------
CLASS A SHARES                                                       (Unaudited)           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                                                     .003             .011             .034             .051

Distributions:

Dividends from investment income--net                                     (.003)           (.011)           (.034)           (.051)

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

TOTAL RETURN (%)                                                            .52(c)          1.07             3.49             5.21
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                     .80(c)           .78              .80              .80

Ratio of net investment income
   to average net assets                                                    .53(c)          1.13             3.25             5.49

Decrease reflected in above
   expense ratios due to undertaking
   by The Dreyfus Corporation                                               .09(c)           .00(b)           .08              .43
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ X 1,000)                                    30,580           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.

(C) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.


                                                               Six Months Ended
                                                                   May 31, 2003                     Year Ended November 30,
                                                                                        --------------------------------------------
CLASS B SHARES                                                       (Unaudited)           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 (%)                                                            .32(b)            .86             3.27             5.00
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                    1.00(b)           1.00             1.00             1.00

Ratio of net investment income
   to average net assets                                                    .31(b)            .84             2.94             5.14

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

Net Assets, end of period ($ X 1,000)                                    35,821            22,878           11,987            5,385

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

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.

                                                             The Fund

FINANCIAL HIGHLIGHTS (CONTINUED)

                                                               Six Months Ended
                                                                   May 31, 2003                     Year Ended November 30,
                                                                                       ---------------------------------------------
CLASS X SHARES                                                       (Unaudited)          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                                                     .001              .008             .032             .048

Distributions:

Dividends from investment income--net                                     (.001)            (.008)           (.032)           (.048)

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

TOTAL RETURN (%)                                                            .28(b)            .82             3.22             4.94
- ------------------------------------------------------------------------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA (%):

Ratio of expenses to average net assets                                    1.05(b)           1.05             1.05             1.05

Ratio of net investment income
   to average net assets                                                    .27(b)            .74             3.03             4.55

Decrease reflected in above
   expense ratios due to undertaking
   by The Dreyfus Corporation                                               .26(b)            .42             3.24            20.13
- ------------------------------------------------------------------------------------------------------------------------------------

Net Assets, end of period ($ X 1,000)                                        13                12                1                1




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

(B) ANNUALIZED.

SEE NOTES TO FINANCIAL STATEMENTS.


NOTES TO FINANCIAL STATEMENTS (Unaudited)

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.

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 (Unaudited) (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 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
receives net earnings credits based on available cash balances left on deposit.

(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.


The  fund  has  an  unused  capital  loss carryover of $64 available for federal
income tax purposes to be applied against future net securities profits, if any,
realized  subsequent to November 30, 2002. If not applied, the carryover expires
in fiscal 2009.

The  tax  character of distributions paid to shareholders during the fiscal year
ended  November  30,  2002 was all ordinary income. The tax character of current
year distributions will be determined at the end of the current fiscal year.

At  May  31,  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 May 31, 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 cost 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

                                                                      The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

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 fund's Board of Directors. If
a  holder  of  Class  A  shares  ceases  to  be a client of a Service Agent, but
continues  to  hold  Class  A  shares, the Manager 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 May 31, 2003, Class
A  shares  were  charged  $26,254  pursuant  to  the  Plan,  of which $3,488 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 May 31, 2003, Class B shares were charged $33,094 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
May  31,  2003,  Class  X  shares  were  charged  $16  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 o 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 had undertaken  from December 1, 2002 through May 31, 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 May 31, 2003, Class A shares
were charged  $8,172  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  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 May 31,
2003, that if the aggregate expenses of Class B and Class X shares, exclusive of
taxes,  brokerage fees, interest on borrowings and extraordinary expenses exceed
1%  for  Class  B  shares and 1.05% for Class X shares, of the average daily net
assets of such class, the Manager would reimburse the expenses of the fund under
the Shareholder Services Plan, to the extent of any excess expense and up to the
full fee
                                                                The Fund

NOTES TO FINANCIAL STATEMENTS (Unaudited) (CONTINUED)

payable  under  the  Shareholder  Services Plan. During the period ended May 31,
2003,  Class  B  and  Class X shares were charged $40,671 and $16, respectively,
pursuant   to  the  Shareholder  Services  Plan,  of  which  $20,448  and  $16,
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  May 31, 2003, the fund was charged $1,292 pursuant to the transfer agency
agreement.

(d)  Each  Board  member also serves as a Board member of other funds within the
Dreyfus  complex  (collectively, the "Fund Group"). Each Board member who is not
an  "affiliated  person" as defined in the Act receives an annual fee of $50,000
and  an  attendance  fee  of  $6,500  for  each  in-person  meeting and $500 for
telephone  meetings.  These fees are allocated among the funds in the Fund Group
in  proportion  to  each  fund's relative net assets. The Chairman of the Board
receives  an  additional  25%  of  such  compensation.  Subject to the Company's
Emeritus  Program Guidelines, Emeritus Board members, if any, receive 50% of the
annual  retainer  fee  and  per  meeting  fee  paid at the time the Board member
achieves emeritus status.


NOTES

                                                           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) 2003 Dreyfus Service Corporation                                  387SA0503




ITEM 2. CODE OF ETHICS.

                Not applicable.

ITEM 3. AUDIT COMMITTEE FINANCIAL EXPERT.

                Not applicable.

ITEM 4. PRINCIPAL ACCOUNTANT FEES AND SERVICES.

                Not applicable.

ITEM 5. [RESERVED]

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)   Based on an evaluation of the Disclosure Controls and Procedures (as
defined in Rule 30a-2(c) under the Investment Company Act of 1940, the
"Disclosure Controls") as of a date within 90 days prior to the filing date
(the "Filing Date") of this Form N-CSR (the "Report"), the Disclosure
Controls are effectively designed to ensure that information required to be
disclosed by the Registrant in the Report is recorded, processed, summarized
and reported by the Filing Date, including ensuring that information required
to be disclosed in the Report is accumulated and communicated to the
Registrant's management, including the Registrant's principal executive
officer and principal financial officer, as appropriate to allow timely
decisions regarding required disclosure.

(b)   There were no significant changes in the Registrant's internal controls
or in other factors that could significantly affect these controls subsequent
to the date of their evaluation, and there were no corrective actions with
regard to significant deficiencies and material weaknesses.

ITEM 10.  EXHIBITS.

(a)   Not applicable.

(b)(1)      Certifications of principal executive officer and principal
financial officer as required by Rule 30a-2 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:  July 30, 2003

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:  July 30, 2003

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

Date:  July 30, 2003


                                EXHIBIT INDEX

            (b)(1)   Certifications of principal executive officer and
            principal financial officer as required by Rule 30a-2 under the
            Investment Company Act of 1940.

            (b)(2)   Certification of principal executive officer and
            principal financial officer as required by Section 906 of the
            Sarbanes-Oxley Act of 2002.