Exhibit 32.1


                CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


      In connection with the annual report of Stereotaxis,  Inc. (the "Company")
on Form 10-K for the period ended December 31, 2006 as filed with the Securities
and Exchange  Commission  on the date hereof (the  "Report"),  I, Bevil J. Hogg,
Chief Executive Officer of the Company,  certify, pursuant to Rule 13a-14(b) and
Section  1350 of Chapter 63 of Title 18 of the United  States  Code,  as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

      (1) The Report fully  complies with the  requirements  of Section 13(a) or
15(d) of the Securities Exchange Act of 1934; and

      (2) The  information  contained  in the  Report  fairly  presents,  in all
material  respects,  the  financial  condition  and results of operations of the
Company.


Date:   March 13, 2007                 /s/ BEVIL J. HOGG
                                       -----------------------
                                       Bevil J. Hogg
                                       Chief Executive Officer
                                       Stereotaxis, Inc.