Exhibit 99.1

[LOGO] Endurance

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

                                        Marianne Walsh, Corporate Communications
                                        Phone: (441) 278-0420
                                        Email: mwalsh@endurance.bm

ENDURANCE SPECIALTY REPORTS HURRICANE LOSSES FOR 3RD QUARTER OF 2004

PEMBROKE, Bermuda--(BUSINESS WIRE)--Oct. 4, 2004--Endurance Specialty Holdings
Ltd. (NYSE:ENH) today reported that estimated aggregate potential claims from
hurricanes Charley, Frances, Ivan, and Jeanne, net of reinsurance recoverables,
reinstatement premiums, and taxes, is expected to be approximately $115 million.
The $115 million reported loss amount includes Endurance's previously reported
loss estimates for hurricanes Charley and Frances and encompasses loss estimates
for Endurance's U.S. and Caribbean exposures. Endurance's loss estimates for
hurricanes Charley and Frances remain consistent with the company's previous
public announcements. The company's property catastrophe, property treaty,
direct property, and other specialty lines segments were impacted by the
hurricane losses.

Endurance's loss estimate is based on currently available information derived
from our proprietary catastrophe modeling, standard industry models and
assessments of exposure and claims information obtained from our clients. Due to
the unusually high frequency of hurricanes, estimation of losses remains
especially uncertain. Endurance made significant adjustments to model outputs to
factor the potential for additional material demand surge in claims; however
such adjustments may prove to be inaccurate. Accordingly, actual losses from
these events may vary materially from estimated losses.

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, A2 by Moody's
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 Ltd., Suite No. 784, No. 48 Par-la-Ville Road,
Hamilton HM 11, Bermuda. For more information about Endurance, please visit
http://www.endurance.bm.

Safe Harbor for Forward-Looking Statements

Some of the statements in this press release may include forward-looking
statements which reflect our current views with respect to future events and
financial performance. Such statements may include forward-looking statements
both with respect to us in general and the insurance and reinsurance sectors
specifically, both as to underwriting and investment matters. Statements which
include the words "expect," "intend," "plan," "believe," "project,"
"anticipate," "seek," "will," and similar statements of a future or
forward-looking nature identify forward-looking statements in this press release
for purposes of the U.S. federal securities laws or otherwise. We intend these
forward-looking statements to be covered by the safe harbor provisions for
forward-looking statements in the Private Securities Litigation Reform Act of
1995.

All forward-looking statements address matters that involve risks and
uncertainties. Accordingly, there are or may be important factors that could
cause actual results to differ from those indicated in the forward-looking
statements. These factors include, but are not limited to, competition, possible
terrorism or the outbreak of war, the frequency or severity of unpredictable
catastrophic events, changes in demand for insurance or reinsurance, rating
agency actions, uncertainties in our reserving process, a change in our tax
status, acceptance of our products, the availability of reinsurance or
retrocessional coverage, retention of key personnel, political conditions,
changes in accounting policies, changes in general economic conditions and other
factors described in our Annual Report on Form 10-K for the year ended December
31, 2003.

Forward-looking statements speak only as of the date on which they are made, and
we undertake no obligation publicly to update or revise any forward-looking
statement, whether as a result of new information, future developments or
otherwise.

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