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                                                                    EXHIBIT 31.1

                    CERTIFICATION PURSUANT TO SECTION 302 OF
                         THE SARBANES-OXLEY ACT OF 2002

                                 CERTIFICATION

I, Robert F. Orlich, certify that:

    1. I have reviewed this report on Form 10-K of Transatlantic Holdings, 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 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)) 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) Omitted pursuant to SEC Release No. 33-8238;

        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: March 12, 2004

                                                   /s/ ROBERT F. ORLICH
                                           .....................................
                                                     Robert F. Orlich
                                          President and Chief Executive Officer