EXHIBIT 99.1

                     HCC ANNOUNCES CONVERTIBLE NOTE OFFERING

HOUSTON (March 25, 2003) . . .

HCC INSURANCE HOLDINGS, INC. (NYSE SYMBOL: HCC) announced today that it is
making a public offering of convertible notes (the "Notes") under its previously
filed shelf registration statement. Salomon Smith Barney will be acting as sole
book-running manager for this offering.

The Notes will be convertible into shares of HCC's common stock, when the market
price of the shares reaches certain specified thresholds. The Notes cannot be
called for six years after issuance and mature in 20 years, although the holders
can require HCC to repurchase the Notes on certain dates and upon the occurrence
of certain change in control events.

The gross proceeds from the sale will be $125 million before the underwriters'
over-allotment option. HCC intends to use the proceeds of the offering to repay
outstanding debt, for general corporate purposes and to fund future acquisitions
and strategic investments.

This press release does not constitute an offer to sell or the solicitation of
an offer to purchase these securities. The Notes may be offered only by means of
a prospectus, including a prospectus supplement. A copy of the prospectus may be
obtained from Salomon Smith Barney.

HCC is an international insurance holding company and a leading specialty
insurance group. HCC has assets of $3.7 billion and its shares trade on the NYSE
(symbol: HCC), with a market capitalization of over $1.6 billion. HCC is rated
AA (Very Strong) by Standard & Poor's and A+ (Superior) by A.M. Best Company.

For more information, visit our website at www.hcch.com.
                                           ------------
Contact:    L. Byron Way, Vice President
            HCC Insurance Holdings, Inc.
            Telephone:  (713) 690-7300

Forward-looking statements contained in this press release are made under "safe
harbor" provisions of the Private Securities Litigation Reform Act of 1995 and
involve a number of risks and uncertainties. The types of risks and
uncertainties which may affect the Company are set forth in its periodic reports
filed with the Securities and Exchange Commission.

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