Exhibit 23.1

                       CONSENT OF INDEPENDENT ACCOUNTANTS

   We consent to the incorporation by reference in the registration statements
of ACE Limited on Form S-3 (File Nos. 333-78841, 333-60985), Form S-4 (File No.
333-90927) and Form S-8 (File Nos. 33-86146, 333-1400, 333-1402, 333-1404, 33-
46301, 333-72299, 333-82175, 333-93867, 333-72301) of our reports dated
February 16, 2000, on our audits of the consolidated financial statements and
financial statement schedules of ACE Limited as of December 31, 1999 and 1998,
and for the year ended December 31, 1999, the three months ended December 31,
1998 and the years ended September 30, 1998 and 1997, which reports are
included and incorporated by reference in this Annual Report on Form 10-K.

                                          PricewaterhouseCoopers LLP

New York, New York
March 24, 2000