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                                                                    Exhibit 31.1

                            Certification Pursuant To
                               18 U.S.C. ss. 1350,
                             As Adopted Pursuant To
                  Section 302 of the Sarbanes-Oxley Act of 2002

I, Richard E. Bornhoft, certify that:

1.   I have reviewed this quarterly report of The Frontier Fund;

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(s) 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)) 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)  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

          (c)  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(s) 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.


May 16, 2005                            /s/ Richard E. Bornhoft
                                        ----------------------------------------
                                        Richard E. Bornhoft
                                        President and Chief Executive Officer of
                                        Equinox Fund Management, LLC, the
                                        Managing Owner of The Frontier Fund