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-Q for the period ended September 30, 2005 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Bevil J. Hogg, President and 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: November 14, 2005	/s/ BEVIL J. HOGG
	Bevil J. Hogg
	President and Chief Executive Officer
	Stereotaxis, Inc.

A signed original of this written statement or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement has been provided to Stereotaxis, Inc. and will be retained by Stereotaxis, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.