Exhibit 99.2

[LOGO] Endurance

                                           Contact
                                           Massa B. Cressall, Investor Relations
                                           Phone: (441) 278-0988
                                           Email: mcressall@endurance.bm

        ENDURANCE SPECIALTY ANNOUNCES TWO CAPITAL MANAGEMENT INITIATIVES

PEMBROKE, Bermuda - May 24, 2004 - Endurance Specialty Holdings Ltd. (NYSE:ENH)
announced today that its Board of Directors has authorized the Company to engage
in two capital management initiatives.

The Company announced today that it has repurchased 2,036,834 of its ordinary
shares owned by Lightyear Capital, initial investors at the formation of the
Company. The purchase price was $31.779 per share, representing a 1% discount to
the closing price for the ordinary shares on May 21, 2004. The purchase price
totaled $64.7 million. Endurance used existing cash on hand to fund the
repurchases.

In addition, Endurance has initiated a share repurchase program. Under this
program, the Company will repurchase up to 2,000,000 of its ordinary shares and
share equivalents. The repurchases will be accomplished in open market or
privately negotiated transactions, from time to time, depending on market
conditions. The share repurchase program is currently authorized to continue
until May 2006.

Kenneth J. LeStrange, Chairman and Chief Executive Officer, commented, "We are
pleased do announce these capital management initiatives. Capital management has
and will continue to be a cornerstone of our strategy. The repurchase of shares
allows Endurance to reduce significant potential overhang from one of our
initial investors at an attractive valuation. Our new share repurchase program
gives us the flexibility to enhance our return on equity through selective
repurchases of our ordinary shares from time to time consistent with our capital
management goals."

About Endurance Specialty Holdings

Endurance Specialty Holdings Ltd. is a global provider of property and casualty
insurance and reinsurance. Through its operating subsidiaries, Endurance
currently writes property per risk treaty reinsurance, property catastrophe
reinsurance, casualty treaty reinsurance, property individual risks, casualty
individual risks, and other specialty lines. Endurance's operating subsidiaries
have been assigned a group rating of A (Excellent) from A.M. Best and A- from
Standard & Poor's. Endurance's headquarters are located at Wellesley House, 90
Pitts Bay Road, Pembroke HM 08, Bermuda and its mailing address is Endurance
Specialty Holdings, Suite No. 784, No. 48 Par-la-Ville Road, Hamilton HM 11,
Bermuda. For more information about Endurance, please visit
http://www.endurance.bm.