Exhibit 10.4
                                                                    ------------


THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR
ANY STATE SECURITIES LAWS. THEY MAY NOT BE SOLD OR OFFERED FOR SALE EXCEPT
PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT AS TO THE SECURITIES UNDER SAID
ACT AND ANY APPLICABLE STATE SECURITIES LAWS OR AN APPLICABLE EXEMPTION FROM
SUCH REGISTRATION REQUIREMENTS.

                                  Right to Purchase Shares of Common Stock
                                  of GRC International, Inc.


                        ------------------------------- 
                         Common Stock Purchase Warrant


          GRC International, Inc., a Delaware corporation having an address at
1900 Gallows Road, Vienna, VA 22182, (the "Company"), hereby certifies that for
$10.00 and other good and valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, Halifax Fund, L.P., having an address c/o Citco
Fund Services Ltd., Corporate Centre, West Bay Road, P.O. Box 311 06SMB, Grand
Cayman, Cayman Islands, ("Purchaser") or any other Warrant Holder is entitled,
on the terms and conditions set forth below, to purchase from the company at any
time after the date hereof and ending eighty-four (84) months after the date
hereof 320,000 of fully paid and nonassessable shares of Common Stock, $0.10 par
value, of the Company together with any associated Common Stock Purchase Rights
(the "Common Stock") at the Purchase Price (hereinafter defined), as the same
may be adjusted pursuant to Section 5 herein.

     1.   Definitions.
          ----------- 

          (a)  the term "Warrant Holder" shall mean the Purchaser or any 
          assignee of all or any portion of this Warrant at any given time 
          who, at the time of assignment, acquired the right to purchase at
          least 1000 Warrant Shares, (such number being subject to adjustment
          after the date hereof pursuant to Section 5 herein.)

          (b)  the term "Warrant Shares" shall mean the Shares of Common Stock
          or other securities issuable upon exercise of this Warrant.
 
          (c)  the term "Purchase Price" shall mean $8.47./1/

          (d)  other terms used herein which are defined in the Convertible
          Securities Subscription Agreement dated as of January 21, 1997 (the
          "Agreement") or the Registration Rights Agreement, dated as of January
          30, 1997 (the "Registration Rights Agreement"), or in the Debentures
          issued by the Company to the Purchaser pursuant to the Agreement (the
          "Debentures"), shall have the same meanings herein as therein.

- ------------------------
/1/ To be 140% of the average of the closing sales prices of the Common Stock on
the NYSE from (and including) January 21, 1997 through (and including) 
January 29, 1997.

 
     2.   Exercise of Warrant.
          ------------------- 

          This Warrant may be exercised by Warrant Holder, in whole or in part,
     at any time and from time to time, on or after the date which is eighteen
     (18) months following the Closing Date, by surrender of this Warrant,
     together with the Purchase Price and form of subscription at the end hereof
     duly executed by Warrant Holder, to the Company at its principal office;
     provided that in the event that prior to such date there is a definitive
     --------                                                                
     agreement executed for a Paragraph 5 Transaction (as defined in the
     Debentures) (if such transaction is a merger, acquisition, sale of Common
     Stock, sale of assets or similar transaction) or a declaration of a record
     date for a material special dividend or distribution in respect of the
     Common Stock (in cash or securities or other assets, other than Common
     Stock), the Warrant shall become exercisable thereafter in full at the
     Adjusted Purchase Price. The Adjusted Purchase Price shall equal the lesser
     of (i) $8.47/1/ (as adjusted from time to time pursuant to Section 5
     hereof) and (ii) 80.0% (as adjusted from time to time pursuant to Sections
     5(c) and 5(f) hereof) of the Transaction Value per share of Common Stock
     issuable upon exercise of the Warrant.  The term "Transaction Value" means,
     in the case of a merger, acquisition, sale of Common Stock, sale of assets
     or similar transaction, the fair market value of the consideration to be
     received per share of Common Stock, as evidenced by the average of the
     closing sale price for the Common Stock during the ten trading days
     following the announcement of such definitive agreement and in the case of
     a material special dividend or distribution (which material special
     dividend or distribution shall not include any grant of any "poison pill"
     or any amendment or modification of the terms of any "poison pill" that
     does not involve any increase in the consideration payable thereunder upon
     redemption of the "poison pill"), the sum of (i) the fair market value of
     the dividend or distribution as determined in good faith by the Company's
     Board of Directors; provided that if the dividend or distribution is in the
     form of an instrument that trades "when issued" the fair market value
     thereof shall be determined by reference to the average of the closing sale
     price for such instrument in the when issued market (or in the absence of a
     closing sale price, the average of the closing bid and asked price) during
     the ten trading days following such record date. In the event that the
     Warrant is not exercised in full, the number of Warrant Shares shall be
     reduced by the number of Warrant Shares for which this Warrant is exercised
     and the Company, at its expense, shall forthwith issue and deliver to or
     upon the order of Warrant Holder a new Warrant of like tenor in the name of
     Warrant Holder or as Warrant Holder (upon payment by Warrant Holder of any
     applicable transfer taxes) may request, reflecting such adjusted Warrant
     Shares.

     3.  Delivery of Stock Certificates.
         ------------------------------ 

         (a)  Subject to the terms and conditions of this Warrant, as soon as
practicable after the exercise of this Warrant in full or in part, and in any
event within three (3) trading days thereafter, the Company at its expense
(including, without limitation, the payment by it of any applicable issue taxes)
will cause to be issued in the name of and delivered to Warrant Holder, or as
Warrant Holder (upon payment by

- ------------------------
/1/ To be 140% of the average of the closing sales prices of the Common Stock on
the NYSE from (and including) January 21, 1997 through (and including)
January 29, 1997.

                                       2

 
     Warrant Holder of any applicable transfer taxes) may lawfully direct, a
     certificate or certificates for the number of fully paid and non-assessable
     shares of Common Stock to which Warrant Holder shall be entitled on such
     exercise, together with any other stock or other securities or property
     (including cash, where applicable) to which Warrant Holder is entitled upon
     such exercise.

          (b)  This Warrant may not be exercised as to fractional shares of
     Common Stock. In the event that the exercise of this Warrant, in full or in
     part, would result in the issuance of any fractional share of Common Stock,
     then in such event Warrant Holder shall be entitled to cash equal to the
     Fair Market Value of such fractional share.  For purposes of this Warrant,
     Fair Market Value equals the closing trading price of the Common Stock on
     the NASDAQ Stock Market, the American Stock Exchange or the New York Stock
     Exchange, whichever is the principal trading exchange or market for the
     Common Stock (the "Principal Market") on the date of determination or, if
     the Common Stock is not listed or admitted to trading on any national
     securities exchange or quoted in the NASDAQ Stock Market, the average of
     the closing bid and asked prices on the over-the-counter market as
     furnished by any New York Stock Exchange member firm reasonably selected
     from time to time by the Company for that purpose, or, if the Common Stock
     is not listed or admitted to trading on any national securities exchange or
     quoted on the NASDAQ Stock market or traded over-the-counter and the
     average price cannot be determined as contemplated above, the Fair Market
     Value of the Common Stock shall be as reasonably determined in good faith
     by the Company's Board of Directors.

     4.   Covenants of the Company.
          ------------------------ 

          (a)  The Company shall use its reasonable best efforts to insure 
that a Registration Statement under the Act covering the issuance of the Warrant
Shares and the resale or other disposition thereof by Warrant Holder is
effective as provided in the Registration Rights Agreement.

          (b)  The Company shall take all necessary actions and proceedings as
may be required and permitted by applicable law, rule and regulation, including,
without limitation the notification of the New York Stock Exchange, for the
legal and valid issuance of this Warrant and the Warrant Shares to the Warrant
Holder under this Warrant.

          (c)  From the date hereof through the last date on which this Warrant
is exercisable, the Company shall take all steps reasonably necessary and within
its control to insure that the Common Stock remains listed on the Principal
Market and shall not amend its Certificate of Incorporation or Bylaws so as to
constitute a breach of the Company's obligations hereunder.

          (d)  The Company shall at all times reserve and keep available, solely
for issuance and delivery as Warrant Shares hereunder, such shares of Common
Stock as shall from time to time be issuable as Warrant Shares.

          (e)  The Warrant Shares, when issued in accordance with the terms
hereof, will be duly authorized and, when paid for or issued in accordance with
the terms hereof, shall be validly issued, fully paid and non-assessable. The
Company has
                                       3

 
     authorized and reserved for issuance to Warrant Holder the requisite number
     of shares of Common Stock to be issued pursuant to this Warrant.

          (f)  With a view to making available to Warrant Holder the benefits of
     Rule 144 promulgated under the Act and any other rule or regulation of the
     SEC that may at any time permit Warrant Holder to sell securities of the
     Company to the public without registration, the Company agrees to use its
     reasonable best efforts to:

               (i)    make and keep public information available, as those terms
          are understood and defined in Rule 144, at all times;

               (ii)   file with the SEC in a timely manner all reports and other
          documents required of the Company under the Act and the Exchange Act;
          and

               (iii)  furnish to any Warrant Holder forthwith upon request a
          written statement by the Company that it has complied with the
          reporting requirements of Rule 144 and of the Act and the Exchange
          Act, a copy of the most recent annual or quarterly report of the
          Company, and such other reports and documents so filed by the Company
          as may be reasonably requested to permit any such Warrant Holder to
          take advantage of any rule or regulation of the SEC permitting the
          selling of any such securities without registration.

     5.   Adjustment of Exercise Price and Number of Share.
          ------------------------------------------------ 

          The number of, and kind of, securities purchasable upon exercise of
     this Warrant and the Purchase Price shall be subject to adjustment from
     time to time as follows:

          (a)  Subdivisions. Combinations and Other Issuances.  If the Company
               ----------------------------------------------                 
     shall at any time after the date hereof but prior to the expiration of this
     Warrant subdivide its outstanding securities as to which purchase rights
     under this Warrant exist, by split-up, spin-off, or otherwise, or combine
     its outstanding securities as to which purchase rights under this Warrant
     exist, the number of Warrant Shares as to which this Warrant is exercisable
     as of the date of such subdivision, split-up, spin-off or combination shall
     forthwith be proportionately increased in the case of a subdivision, or
     proportionately decreased in the case of a combination.  Appropriate
     adjustments shall also be made to the purchase price payable per share, but
     the aggregate purchase price payable for the total number of Warrant Shares
     purchasable under this Warrant as of such date shall remain the same.

          (b)  Stock Dividend.  If at any time after the date hereof the Company
               --------------                                                   
     declares a dividend or other distribution on Common Stock payable in Common
     Stock or other securities or rights convertible into Common Stock ("Common
     Stock Equivalents") without payment of any consideration by holders of
     Common Stock for the additional shares of Common Stock or the Common Stock
     Equivalents (including the additional shares of Common Stock issuable upon
     exercise or conversion thereof), then the number of shares of Common Stock
     for which this Warrant may be exercised shall be increased as of the record
     date (or the date of such dividend distribution if not record date is set)
     for determining which holders of Common Stock shall be entitled to receive
     such dividends, in proportion to the increase in the number of outstanding

                                       4

 
     shares (and shares of Common Stock issuable upon conversion of all such
     securities convertible into Common Stock) of Common Stock as a result of
     such dividend, and the Purchase Price shall be adjusted so that the
     aggregate amount payable for the purchase of all the Warrant Shares
     issuable hereunder immediately after the record date (or on the date of
     such distribution, if applicable), for such dividend shall equal the
     aggregate amount so payable immediately before such record date (or on the
     date of such distribution, if applicable).

          (c) Other Distributions.  If at any time after the date hereof the
              -------------------                                           
     Company distributes to holders of its Common Stock, other than as part of
     its dissolution, liquidation or the winding up of its affairs, any shares
     of its capital stock, any evidence of indebtedness or any of its assets
     (other than cash, Common Stock or securities convertible into Common
     Stock), then the Company shall decrease the per share Purchase Price of
     this Warrant by an appropriate amount based upon the value distributed on
     each share of Common Stock as determined in good faith by the Company's
     Board of Directors.

          (d) Merger, Etc.  If at any time after the date hereof there shall be
              -----------                                                      
     a merger or consolidation of the Company with or into or a transfer of all
     or substantially all of the assets of the Company to another entity, then
     the Warrant Holder shall be entitled to receive upon such transfer, merger
     or consolidation becoming effective, and upon payment of the aggregate
     Purchase Price then in effect, the number of shares or other securities or
     property of the company or of the successor corporation resulting from such
     merger or consolidation, which would have been received by Warrant Holder
     for the shares of stock subject to this Warrant had this Warrant been
     exercised just prior to such transfer, merger or consolidation becoming
     effective or to the applicable record date thereof, as the case may be.

          (e) Reclassification, Etc.  If at any time after the date hereof there
              ---------------------                                             
     shall be a reorganization or reclassification of the securities as to which
     purchase rights under this Warrant exist into the same or a different
     number of securities of any other class or classes, then the Warrant Holder
     shall thereafter be entitled to receive upon exercise of this Warrant,
     during the period specified herein and upon payment of the Purchase Price
     then in effect, the number of shares or other securities or property
     resulting from such reorganization or reclassification, which would have
     been received by the Warrant Holder for the shares of stock subject to this
     Warrant had this Warrant at such time been exercised.

          (f) Purchase Price Adjustment.  In the event that the Company issues
              -------------------------                                       
     or sells any Common Stock or securities which are convertible into or
     exchangeable for its Common Stock or any convertible securities, or any
     warrants or other rights to subscribe for or to purchase or any options for
     the purchase of its Common Stock or any such convertible securities (other
     than issuance of Debentures or of shares of Common Stock upon conversion
     thereof, securities issued or which may be issued pursuant to the Company's
     employee, officer, director or consultant stock or option or similar
     equity-based compensation plans now or hereafter established or shares
     issued upon exercise of options, warrants or rights outstanding on the date
     of the Agreement and listed in the Exchange Act Reports) at an effective
     purchase price per share which is less than ninety-five percent (95%) of
     the Fair Market Value (including any applicable underwriting discounts
     and/or commissions) of the Common Stock on the trading day 

                                       5

 
     next preceding such issue or sale, then in each such case, the Purchase
     Price in effect immediately prior to such issue or sale shall be reduced
     effective concurrently with such issue or sale to an amount determined by
     multiplying the Purchase Price then in effect by a fraction, (x) the
     numerator of which shall be the sum of (1) the number of shares of Common
     Stock outstanding immediately prior to such issue or sale, including,
     without duplication, those deemed to have been issued under any provision
     of the Debentures and the Warrants plus (2) the number of shares of Common
     Stock which the aggregate consideration received by the Company for such
     additional shares would purchase at such Fair Market Value and (y) the
     denominator of which shall be the number of shares of Common Stock of the
     Company outstanding immediately after such issue or sale including, without
     duplication, those deemed to have been issued under any provision of the
     Debentures and Warrants. For purposes of the foregoing fraction, Common
     Stock outstanding shall include, without limitation, any Equity Offerings
     (as defined in the Debentures) then outstanding, whether or not they are
     exercisable or convertible when such fraction is to be determined.

          The number of shares which may be purchased hereunder shall be
     increased proportionately to any reduction in Purchase Price pursuant to
     this paragraph 5(f), so that after such adjustments the aggregate Purchase
     Price payable hereunder for the increased number of shares shall be the
     same as the aggregate Purchase Price in effect just prior to such
     adjustments.

     6.   No Impairment.
          ------------- 

          The Company will not, by amendment of its Certificate of Incorporation
     or through any reorganization, transfer of assets, consolidation, merger,
     dissolution, issue or sale of securities or any other voluntary action,
     avoid or seek to avoid the observance or performance of any of the terms of
     this Warrant, but will at all times in good faith assist in the carrying
     out of all such terms and in the taking of all such action as may be
     necessary or appropriate in order to protect the rights of the Warrant
     Holder against impairment.  Without limiting the generality of the
     foregoing, the Company (a) will not increase the par value of any Warrant
     Shares above the amount payable therefor on such exercise, and (b) will
     take all such action as may be reasonably necessary or appropriate in order
     that the Company may validly and legally issue fully paid and nonassessable
     Warrant Shares on the exercise of this Warrant.  By acceptance hereof, the
     Holder of this Debenture acknowledges and agrees that a Paragraph 5
     Transaction (as defined in the Debentures) shall not constitute an
     impairment of the rights of the Warrant Holder hereunder.

     7.   Notice of Adjustments: Notices.
          ------------------------------ 

          Whenever the Purchase Price or number of shares purchasable hereunder
     shall be adjusted pursuant to Section 5 hereof, the Company shall execute
     and deliver to the Warrant Holder a certificate setting forth, in
     reasonable detail, the event requiring the adjustment, the amount of the
     adjustment, the method by which such adjustment was calculated and the
     Purchase Price and number of shares purchasable hereunder after giving
     effect to such adjustment, and shall cause a copy of such certificate to be
     mailed (by first class mail, postage prepaid) to the Warrant Holder.

                                       6

 
     8.   Rights As Stockholder.
          --------------------- 

          Prior to exercise of this Warrant, the Warrant Holder shall not be
     entitled to any rights as a stockholder of the company with respect to the
     Warrant Shares, including (without limitation) the right to vote such
     shares, receive dividends or other distributions thereon or be notified of
     stockholder meetings.  However, in the event of any taking by the Company
     of a record of the holders of any class of securities for the purpose of
     determining the holders thereof who are entitled to receive any dividend
     (other than a cash dividend) or other distribution, any right to subscribe
     for, purchase or otherwise acquire any shares of stock of any class or any
     other securities or property, or to receive any other right, the Company
     shall mail to each Warrant Holder, at least 10 days prior to the date
     specified, therein, a notice specifying the date on which any such record
     is to be taken for the purpose of such dividend, distribution or right, and
     the amount and character of such dividend, distribution or right.

     9.   Replacement of Warrant.
          ---------------------- 

          On receipt of evidence reasonably satisfactory to the Company of the
     loss, theft, destruction or mutilation of the Warrant and, in the case of
     any such loss, theft or destruction of the Warrant, on delivery of an
     indemnity agreement or security reasonably satisfactory in form and amount
     to the Company or, in the case of any such mutilation, on surrender and
     cancellation of such Warrant, the Company at its expense will execute and
     deliver, in lieu thereof, a new Warrant of like tenor.

     10.  Specific Enforcement; Consent to Jurisdiction; Waiver of Jury Trial.
          ------------------------------------------------------------------- 

          (a) The Company and the Warrant Holder acknowledge and agree that
     irreparable damage would occur in the event that any of the provisions of
     this Warrant were not performed in accordance with their specific terms or
     were otherwise breached.  It is accordingly agreed that the parties shall
     be entitled to an injunction or injunctions to prevent or cure breaches of
     the provisions of this Warrant and to enforce specifically the terms and
     provisions hereof, this being in addition to any other remedy to which
     either of them may be entitled by law or equity.

          (b) Each of the Company and the Warrant Holder hereby (i) agree that
     all actions or proceedings arising directly or indirectly from or in
     connection with this Warrant shall be litigated only in the Supreme Court
     of the State of New York or the United States District Court for the
     Southern District of New York located in New York County, New York and (ii)
     to the extent permitted by applicable law, consent to the jurisdiction and
     venue of the foregoing courts and consent that any process or notice of
     motion or other application to either of said courts or a judge thereof may
     be served inside or outside the State of New York or the Southern District
     of New York by registered mail, return receipt requested, directed to the
     such party at its address set forth in this Warrant (and service so made
     shall be deemed complete five (5) days after the same has been posted as
     aforesaid) or by personal service or in such other manner as may be
     permissible under the rules of said courts.  The parties hereto hereby
     waive any right to a jury trial in connection with any litigation pursuant
     to this Warrant.

                                       7

 
     11.  Entire Agreement: Amendments.
          ---------------------------- 

          This Warrant, the Exhibits hereto and the provisions contained in the
     Agreement, the Registration Rights Agreement or the Debentures and
     incorporated into this Warrant and the Warrant Shares contain the entire
     understanding of the parties with respect to the matters covered hereby and
     thereby and except as specifically set forth herein and therein, neither
     the Company nor the Warrant Holder makes any representation, warranty,
     covenant or undertaking with respect to such matters.  No provision of this
     Agreement may be waived or amended other than by a written instrument
     signed by the party against whom enforcement of any such amendment or
     waiver is sought.

     12.  Restricted Securities.
          --------------------- 

          Sections 5.6, 6.1, 6.2 and 6.3 of the Agreement are incorporated
     herein by reference and hereby made a part hereof.

     13.  Notices.
          ------- 

          Any notice or other communication required or permitted to be given
     hereunder shall be in writing and shall be effective (a) upon hand delivery
     or delivery by telex (with correction answer back received), telecopy or
     facsimile at the address or number designated below (if delivered on a
     business day during normal business hours where such notice is to be
     received), or the first business day following such delivery (if delivered
     other than on a business day during normal business hours where such notice
     is to be received) or (b) on the second business day following the date of
     mailing by express courier service, fully prepaid, addressed to such
     address, or upon actual receipt of such mailing, whichever shall first
     occur.  The addresses for such communications shall be:

               to the Company:

                    Chairman, President & CEO
                    GRC International, Inc.
                    1900 Gallows Road
                    Vienna, VA 22182

               with copies to:
                    Arnold & Porter
                    555 12th Street, N.W.
                    Washington, D.C. 20004
                    Attention:  Steve Parker, Esq.
                                      and
                                Cathy McCoy, Esq.

                                       8

 
               to the Warrant Holder:

                    Halifax Fund, L.P.
                    c/o Citco Fund Services Ltd.
                    Corporate Centre
                    West Bay Road
                    P.O. Box 31106 SMB
                    Grand Cayman, Cayman Islands
                    Attn:
                    Fax: (809) 949-3877

               with copies to:

                    The Palladin Group, L.P.
                    40 West 57th Street
                    Suite 1500
                    New York, NY 10019
                    Attn: Andrew Kaplan
                    Fax: (212) 698-0599

     Either party hereto may from time to time change its address for notices
     under this Section 13 by giving at least 10 days prior written notice of
     such changed address to the other party hereto.

     14.  Miscellaneous.
          ------------- 

          This Warrant and any term hereof may be changed, waived, discharged or
     terminated only by an instrument in writing signed by the party against
     which enforcement of such change, waiver, discharge or termination is
     sought.  This Warrant shall be construed and enforced in accordance with
     and governed by the laws of the State of New York.  The headings in this
     Warrant are for purposes of reference only, and shall not limit or
     otherwise affect any of the terms hereof. The invalidity or
     unenforceability of any provision hereof shall in no way affect the
     validity or enforceability of any other provisions.

                                       9

 
     15.  Expiration
          ----------

          The right to exercise this Warrant shall expire eighty-four (84)
     months after the date hereof.

Dated:  January 30, 1997            GRC INTERNATIONAL, INC.

                                    By:
                                       ------------------------------
                                    Title:

[CORPORATE SEAL]

Attest:

By:
   ---------------------------
Its:

                                      10

 
                            FORM OF WARRANT EXERCISE

                   (To be signed only on exercise of Warrant)

TO
  -----------------------

          The undersigned, the holder of the within Warrant, hereby irrevocably
elects to exercise this Warrant for, and to purchase thereunder, ____ shares of
Common Stock of GRC International, Inc., a Delaware corporation (the "Company"),
and herewith makes payment of $_________ therefor, and requests that the
certificates for such shares be issued in the name of, and delivered to 
__________________, whose address is _____________________________________.

Dated:
      --------------------------------------
                    (Signature must conform to name of holder as specified on
                    the face of the Warrant)


- -------------------------------- 
                    (Address)

 
                               FORM OF ASSIGNMENT

                   (To be signed only on transfer of Warrant)

For value received, the undersigned hereby sells, assigns, and transfers unto
__________ the right represented by the within Warrant to purchase ______ shares
of Common Stock of GRC International, Inc., a ______________ corporation, to
which the within Warrant relates, and appoints ____________ Attorney to transfer
such right on the books of GRC International, Inc., a Delaware corporation, with
full power of substitution the premises.

Dated:
                                    -----------------------------------
                                    (Signature must conform to name of holder as
                                    specified on the face of the Warrant)


                                     -----------------------------------
                                              (Address)

Signed in the presence of:

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