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                                                                    EXHIBIT 10.3


                              AMENDMENT NO. 1 TO
                             CONSULTING AGREEMENT

     This Amendment No. 1 (this "Amendment") is entered into as of November 19,
1998, between DATA RACE, Inc., a Texas corporation (the "Company"); and Liviakis
Financial Communications, Inc., a California corporation ("Consultant").

                                   RECITALS

     WHEREAS, the Company and Consultant are parties to that certain Consulting
Agreement dated July 13, 1998 (the "Agreement"); and

     WHEREAS, the Company and Consultant desire to extend the term and modify
certain provisions of the Agreement.

     NOW THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties to this Amendment
agree as follows:

                                   AGREEMENT

     1.  Unless the context requires otherwise, capitalized terms used, but not
         defined herein, shall have the applicable meanings given to them in the
         Agreement.

     2.  The parties agree to amend the term of the Agreement, extending the
         expiration date of the Agreement to January 1, 2000 from March 15,
         1999. As amended, Section 1 of the Agreement will read as follows:

     "1. Term of Consultancy.  Company hereby agrees to retain the Consultant
         -------------------                                                 
     to act in a consulting capacity to the Company, and the Consultant hereby
     agrees to provide services to the Company commencing immediately and ending
     on January 1, 2000.  The Agreement may be terminated by the Company with a
     written notice of such desire to terminate the Agreement."

     3.  The Company agrees to issue and deliver to Consultant 200,000 shares
         (the "Extension Bonus") of the Company's common stock ("Common Stock"),
         provided that such issuance is contingent upon an increase in number of
         the Company's authorized shares of Common Stock at the special meeting
         of the Company's shareholders scheduled to be held on or about January
         15, 1999.

     4.  The parties agree that, except as provided herein, the shares issued 
         as the Extension Bonus are treated as shares issued as part of the
         "Commencement Bonus" for purposes of the Agreement. Without limiting
         the foregoing (i) the Company acknowledges that the Bonus Shares are a
         nonrefundable, non-
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             apportionable, and non-ratable retainer and that such shares are
             not a prepayment for future services and (ii) the Consultant
             reaffirms the representations, warranties and covenants contained
             in Sections 4.2 and 4.3 of the Agreement.

         5.  Company agrees that the shares issued as Additional Bonus will 
             carry piggy-back registration rights whereby such shares will be
             included in the next resale registration statement filed under the
             Securities Act of 1933, as amended (the "Securities Act") after the
             issuance of the shares.

         6.  Notwithstanding Section 5 above, the Company agrees to file a 
             resale registration statement covering the shares issued as
             Additional Bonus under the Securities Act no later than October 31,
             1999.

         7.  Consultant agrees that it shall not sell or transfer any of the 
             shares issued as the Commencement Bonus (including the Extension
             Bonus) during the term of the Agreement, as extended. Robert B.
             Prag ("Prag") also agrees that he will not sell or transfer any of
             the shares issued to him as a Commencement Bonus during the term of
             the Agreement, as extended, as long as he is an officer and/or
             director of the Consultant. Notwithstanding the preceding sentence,
             Prag may sell or transfer, subject to compliance with applicable
             securities laws, any of the shares issued to him as a Commencement
             Bonus beginning on, but not prior to, March 16, 1999, provided that
             he is no longer an officer or director of the Consultant at the
             time of such transfer or sale.

         8.  The Agreement, as modified by this Amendment, sets forth the entire
             understanding between the parties hereto concerning the subject
             matter contained herein and, except as specifically modified
             herein, all other provisions of the Agreement are hereby ratified
             and affirmed. Provisions of the Agreement may be amended or waived
             only by written instrument executed by the party against whom
             enforcement is sought. The parties agree to execute such additional
             documents and take such additional actions as may be reasonably
             necessary to give effect to the purposes and the intent of the
             Agreement, as modified by this Amendment.

         9.  This Amendment may be executed in one or more counterparts, any of
             which shall be deemed to be an original, all of which taken
             together shall constitute one and the same instrument.


                         [signatures on following page]
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     IN WITNESS WHEREOF, each party has duly executed this Amendment as of the
date first written above.


     COMPANY                              CONSULTANT
     -------                              ----------
 
DATA RACE, INC.                           LIVIAKIS FINANCIAL COMMUNICATIONS INC.

By: /s/ Gregory T. Skalla                 By: /s/ John M. Liviakis
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    Gregory T. Skalla, Senior Vice            John M. Liviakis
    President-Financeand Chief                Presidnet
    Financial Officer