SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549

                                   FORM 8-K


                                Current Report
                    Pursuant to Section 13 or 15(d) of the
                        Securities Exchange Act of 1934

        Date of Report (Date of earliest event reported) - June 1, 1998


                               DATA RACE,  INC.
            (Exact name of registrant as specified in its charter)

                                     TEXAS
                (State or other jurisdiction of incorporation)

             0-20706                                 74-2272363
    (Commission File Number)             (I.R.S. Employer  Identification No.)


                              12400 NETWORK BLVD.
                           SAN ANTONIO, TEXAS 78249
                                (210) 263-2000
         (Address of Principal Executive Offices and Telephone Number,
                             Including Area Code)

 
ITEM 5.  OTHER EVENTS.

     On November 12, 1997, the Company completed the first closing of a private
placement of its 1997 Series C Convertible Participating Preferred Stock
("Preferred Stock") and Stock Purchase Warrants ("Warrants") with four
investment firms (the "Investors"), at an aggregate price of $5,000,000.  At
such time, the Investors agreed, subject to certain conditions, to purchase at a
second closing additional shares of Preferred Stock and Warrants at an aggregate
price of $3,000,000.  Subject to prior extensions, the second closing was
scheduled to occur on June 1, 1998. Although the Company believes that it has
met all of the conditions necessary for the second closing, the Company and the
Investors have agreed to defer the second closing to June 10, 1998, in order to
permit the Company to fully explore other financing alternatives.


ITEM 7.  FINANCIAL STATEMENTS AND EXHIBITS.


         (c)  Exhibits
              --------

         Exhibit                            Description
         -------                            -----------  

           10.1        Amendment dated June 1, 1998 to the Securities Purchase
                       Agreement dated November 7, 1997

                                       2

 
                                  SIGNATURES


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                     DATA RACE, Inc.


Date:  June 1, 1998                  By: /s/ GREGORY T. SKALLA
                                        -------------------------------
                                        Gregory T. Skalla,
                                        Vice President-Finance, Chief Financial
                                        Officer, Treasurer and Secretary

                                       3

 
                                 EXHIBIT INDEX



         Exhibit                            Description
         -------                            -----------  

           10.1        Amendment dated June 1, 1998 to the Securities Purchase
                       Agreement dated November 7, 1997

                                       4