EXHIBIT 32.1

         Certification Pursuant to Section 906 of the Sarbanes-Oxley Act



                                                                 March 28, 2005



Securities and Exchange Commission
450 Fifth Street, N.W.
Washington, D.C. 20549

Ladies and Gentlemen:

         The certifications set forth below are being submitted in connection
with the annual report on Form 10-K (the "Report") of Zix Corporation for the
purpose of complying with Rule 13a-14(b) or Rule 15d-14(b) of the Securities
Exchange Act of 1934 (the "Exchange Act") and Section 1350 of Chapter 63 of
Title 18 of the United States Code.

         Richard D. Spurr, the acting chief executive officer, and Bradley C.
Almond, the chief financial officer of Zix Corporation, each certifies that to
the best of their knowledge and in their respective capacities as officers of
Zix Corporation:

         1. the Report fully complies with the requirements of Section 13(a) or
15(d) of the Exchange Act; and

         2. the information contained in the Report fairly presents, in all
material respects, the financial condition and results of operations of Zix
Corporation as of the dates and for the periods expressed in the Report.



                                                 /s/ Richard D. Spurr
                                ------------------------------------------------
                                Name:             Richard D. Spurr
                                         ---------------------------------------
                                Title:   Chief Executive Officer,
                                         President & Chief Operating Officer
                                         ---------------------------------------

                                                /s/ Bradley C. Almond
                                ------------------------------------------------
                                Name:             Bradley C. Almond
                                         ---------------------------------------
                                Title:   Vice President, Chief Financial
                                         Officer, and Treasurer
                                         ---------------------------------------