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 8, 1996
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                                  ACE LIMITED
                                        
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             (Exact name of registrant as specified in its charter)


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

The ACE Building
30 Woodbourne Avenue
Hamilton, Bermuda                               HM 08

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(Address of principal executive offices)      (Zip Code)

Registrant's telephone number, including are code: (441) 295-5200
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                                 Not Applicable
                                        
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 (Former name or former address, if changed since last report)

 
Item 5.   Other Events.

     On June 8, 1996, ACE Limited (NYSE: ACL) ("ACE") sent a letter to Donald
Kramer, Co-Chairman of Tempest Reinsurance Company Limited ("Tempest"),
proposing an increase in the consideration to be paid to Tempest shareholders in
connection with its previously announced agreement to acquire Tempest.

     On June 9, ACE issued a press release relating to the increased offer to
acquire Tempest.

     Included as Exhibit 99.1 and 99.2 to this Current Report on Form 8-K is a
copy of the letter sent to Donald Kramer and the press release, respectively.

Item 7.   Exhibits.

99.1      Letter, dated June 8, 1996, from Brian Duperreault, Chairman,
          President and Chief Executive Officer of ACE Limited, to Donald
          Kramer, Co-Chairman of Tempest Reinsurance Company Limited.

99.2      Press Release, dated June 9, 1996.

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                                  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.


Dated: June 10, 1996

                              ACE LIMITED


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

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                                 EXHIBIT INDEX
 
 


Exhibit                                                               Sequential
Number                   Description                                   Page No.
- -------                  -----------                                  ----------
                                                                    
99.1      Letter, dated June 8, 1996, from Brian Duperreault,
          Chairman, President and Chief Executive Officer
          of ACE Limited, to Donald Kramer, Co-Chairman of
          Tempest Reinsurance Company Limited.

99.2      Press Release, dated June 9, 1996