SECURITIES AND EXCHANGE COMMISSION
                     Washington D.C.  20549



                            FORM 8-K



                         Current Report

             Pursuant to Section 13 or 15(d) of the
                 Securities Exchange Act of 1934







Date of Report (Date of earliest event reported) June 4, 1996    
                                                 -------------


                           ACE LIMITED                           
- ---------------------------------------------------------------
     (Exact name of registrant as specified in its charter)


Cayman Islands             1-11778              Not Applicable
- -----------------------------------------------------------------
(State or other          (Commission           (I.R.S. Employer
jurisdiction of          File Number)         Identification No.)
incorporation) 




           The ACE Building
         30 Woodbourne Street
           Hamilton, Bermuda                          HM 08  
- -----------------------------------------------------------------
(Address of principal executive offices)           (Zip Code)


Registrant's telephone number, including are code: (441) 295-5200
                                                   --------------

                        Not Applicable
- -----------------------------------------------------------------
  (Former name or former address, if changed since last report)


Item  5.  Other Events.

     On June 4, 1996, ACE Limited (NYSE: ACL) ("ACE") issued a
press release relating to the unsolicited offer by IPC Holdings,
Ltd. to acquire Tempest Reinsurance Company Limited.

     Included as Exhibit 99.1 to this Current Report on Form 8-K is
a copy of the press release referred to above.

Item 7.   Exhibits.

99.1      Press Release, dated June 4, 1996.

                           SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of
1934, the registrant has duly caused this report to be signed on
its behalf by the undersigned thereunto duly authorized.

                                ACE LIMITED

Dated: June 4, 1996

                                By: /s/ Christopher Z. Marshall
                                    ---------------------------
                                    Christopher Z. Marshall
                                    Executive Vice President and
                                    Chief Financial Officer

                          EXHIBIT INDEX


Exhibit                                                Sequential
Number        Description                              Page No.  
- --------      -------------                            -----------
99.1          Press Release, dated June 4, 1996