**EXHIBIT 31.1****CERTIFICATION PURSUANT TO SECTION 302 OF THESARBANES-OXLEY ACT OF 2002**I, Andrew A. Barnard, President and Chief Executive Officer ofOdyssey Re Holdings Corp., certify that:     1. I have reviewed this quarterly report on Form 10-Qof the registrant, Odyssey Re Holdings Corp.;     2. Based on my knowledge, this quarterly report does notcontain any untrue statement of a material fact or omit to statea material fact necessary to make the statements made, in lightof the circumstances under which such statements were made, notmisleading with respect to the period covered by this quarterlyreport;     3. Based on my knowledge, the financial statements, andother financial information included in this quarterly 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 quarterly report;     4. The registrant’s other certifying officer and I areresponsible for establishing and maintaining disclosure controlsand procedures (as defined in Exchange Act Rules 13a-15(e)and 15d-15(e)) and internal control over financial reporting (asdefined in Exchange Act Rules 13a-15(f) and 15d-15(f)) forthe registrant and we 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 quarterly    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    quarterly report our conclusions about the effectiveness of the    disclosure controls and procedures, as of the end of the period    covered by this quarterly report based on such    evaluation; and           (d) disclosed in this quarterly report any change in the    registrant’s internal control over financial reporting that    occurred during the registrant’s most recent fiscal quarter    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 Ihave disclosed, based on our most recent evaluation of internalcontrol over financial reporting, to the registrant’sauditors and the audit committee of the registrant’s boardof 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. By     /s/ Andrew A. Barnard           Andrew A. Barnard     President and Chief Executive OfficerDate: August 8, 2005