EXHIBIT 31.1

Certification of Principal Executive Officer

I, Bevil J. Hogg, certify that:

1.       I have reviewed this annual report on Form 10-K of Stereotaxis,
         Inc.;

2.       Based on my knowledge, this report does not contain any untrue
         statement of a material fact or omit to state a material fact
         necessary to make the statements made, in light of the
         circumstances under which such statements were made, not misleading
         with respect to the period covered by this report;

3.       Based on my knowledge, the financial statements, and other
         financial information included in this report, fairly present in
         all material respects the financial condition, results of
         operations and cash flows of the registrant as of, and for, the
         periods presented in this report;

4.       The registrant's other certifying officers and I are responsible
         for establishing and maintaining disclosure controls and procedures
         (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and
         internal control over financial reporting (as defined in Exchange
         Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:

                  (a) Designed such disclosure controls and procedures, or
                  caused such disclosure controls and procedures to be
                  designed under our supervision, to ensure that material
                  information relating to the registrant, including its
                  consolidated subsidiaries, is made known to us by others
                  within those entities, particularly during the period in
                  which this report is being prepared;

                  (b) Designed such internal control over financial
                  reporting, or caused such internal control over financial
                  reporting to be designed under our supervision, to provide
                  reasonable assurance regarding the reliability of
                  financial reporting and the preparation of financial
                  statements for external purposes in accordance with
                  generally accepted accounting principles;

                  (c) Evaluated the effectiveness of the registrant's
                  disclosure controls and procedures and presented in this
                  report our conclusions about the effectiveness of the
                  disclosure controls and procedures, as of the end of the
                  period covered by this report based on such evaluation;
                  and

                  (d) Disclosed in this report any change in the
                  registrant's internal control over financial reporting
                  that occurred during the registrant's most recent fiscal
                  quarter (the registrant's fourth fiscal quarter in the
                  case of an annual report) that has materially affected, or
                  is reasonably likely to materially affect, the
                  registrant's internal control over financial reporting.

5.       The registrant's other certifying officer and I have disclosed,
         based on our most recent evaluation of internal control over
         financial reporting, to the registrant's auditors and the audit
         committee of the registrant's board of directors (or persons
         performing the equivalent functions):

                  (a) All significant deficiencies and material weaknesses
                  in the design or operation of internal control over
                  financial reporting which are reasonably likely to
                  adversely affect the registrant's ability to record,
                  process, summarize and report financial information; and

                  (b) Any fraud, whether or not material, that involves
                  management or other employees who have a significant role
                  in the registrant's internal control over financial
                  reporting.

Date: March 15, 2006                    /s/ BEVIL J. HOGG
                                        -----------------------
                                        Bevil J. Hogg
                                        President and Chief Executive Officer
                                        Stereotaxis, Inc.
                                        (Principal Executive Officer)