##### 



Exhibit 31.1 Certification
Pursuant to Section 302 of the Sarbanes-Oxley Act of 2002 I, John E. Jackson, certify that: 1. I have reviewed this Quarterly Report on Form 10-Q of Hanover Compressor Company; 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 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-15f
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; and 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: May 4, 2005By:
    
    /s/ John E. JacksonName:
    
    John E. JacksonTitle:
    
    President and Chief Executive Officer(Principal Executive Officer)