**Exhibit
31.1**
  **CERTIFICATION
OF CHIEF EXECUTIVE OFFICER**
 
 I, Paul
H. Fischer, Ph.D., certify that:
 
 1.  I have
reviewed this annual report on Form 10-K of GenVec, Inc.
 
 2.  Based on
my knowledge, this annual 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 officer 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 the 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 ,
2005
 
 /s/
Paul H Fischer Ph.D.
 Paul H.
Fischer, Ph.D.
 President
and Chief Executive Officer