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): July 2, 1999


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


                                                           
          Cayman Islands                   1-11778                          98-0091805
     (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
     (Address of principal executive offices)             (Zip Code)

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

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


Item 2.  Acquisition or Disposition of Assets.

     On July 2, 1999, ACE Limited (the "Company"), through its wholly owned
subsidiary ACE INA Holdings, Inc. ("Holdings"), completed the acquisition of the
domestic and international property and casualty business (the "Acquired
Business") of CIGNA Corporation ("CIGNA") for the previously announced price of
$3.45 billion in cash. The transaction is initially being financed with $1.025
billion of available cash, $400 million from a hybrid trust preferred security
and the remainder with commercial paper issuance. Ultimately, the commercial
paper will be replaced with a combination of newly issued equity, senior debt
and trust preferred securities. A copy of the Acquisition Agreement and
Amendments Nos. 1 and 2 thereto are filed as Exhibits 2.1, 2.2 and 2.3 to this
Form 8-K.

     Also put in place at the closing was the previously announced reinsurance
arrangement with National Indemnity Company (a subsidiary of Berkshire Hathaway)
providing $1.25 billion in protection against adverse development in the run-
off operations and certain asbestos and environmental exposures of ACE INA.

     The Company has also entered into a 10-year agreement with IBM Global
Services ("IBM") to manage the transition and integration of the information
technology ("IT") infrastructure for the Acquired Business and to provide
ongoing IT support for these operations. The outsourcing agreement will transfer
approximately 350 employees to IBM together with the software, hardware and
other facilities necessary to provide these services.  A copy of the agreement
with IBM is filed as Exhibit 99.1.

     Included as Exhibit 99.2 to this Current Report on Form 8-K is a copy of
the press release dated July 2, 1999 announcing such completion.

Item 5.    Other Events

     In connection with the completion of the acquisition of the Acquired
Business, ACE RHINOS Trust, a Delaware statutory business trust (the "Trust"),
sold in a private placement $400 million of Auction Rate Reset Preferred
Securities (the "Preferred Securities").  All of the common securities of the
Trust are owned by Holdings.

     The Preferred Securities mature on September 30, 2002.  Distribution on the
Preferred Securities are payable quarterly at LIBOR plus 125 basis points,
adjusted quarterly, provided that the Trust may defer such payments (but no
later than September 30, 2001 or earlier Redemption Date), with such deferred
payments compounded quarterly, if Holdings defers interest on the Subordinated
Notes (as defined below).  If the trading price of ACE's Ordinary Shares
declines to 66-2/3% of the closing price of ACE's ordinary shares on June 30,
1999, the holders of a majority of the Preferred Securities will have the
option to require Banc of America Securities LLC ("BAS") as the Remarketing
Agent to remarket the Preferred Securities. If remarketed, the maturity of the
remarketed securities will be reset as the later of September 30,

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2001 or one year from the date on which the remarketed securities are issued.
The coupon will be reset pursuant to a bid process to value the remarketed
securities at 100.25% of the face amount thereof. A copy of the Remarketing and
Contingent Purchase Agreement is filed as Exhibit 99.3 to this Form 8-K.

     The sole assets of the Trust consist of a $412,372,000 Auction Rate Reset
Subordinated Notes Series A (the "Subordinated Notes") issued by Holdings. The
Subordinated Notes mature on September 30, 2001. Interest on the Subordinated
Notes is payable quarterly at LIBOR plus 125 basis points, adjusted quarterly,
provided that Holdings may defer such interest payments (but no later than the
September 30, 2001 or earlier Redemption Date), with such deferred payments
compounded quarterly. If under certain circumstances the Trust is dissolved and
the holders of the Preferred Securities directly holds the Subordinated Notes,
then the remarketing provisions described above will be applicable to the
Subordinated Notes. A copy of the Indenture and Supplemental Indenture is filed
as Exhibits 99.5 and 99.6 to this Form 8-K.

     In connection with the issuance of the Preferred Securities, the Company
has agreed with BAS to use its reasonable best efforts to complete one or more
firm commitment underwritings with an aggregate public offering price of $400
million on or before June 30, 2002.  The Company has agreed to maintain an
effective shelf registration statement with availability for the issuance of up
to $400 million ordinary shares (exclusive of any amounts to cover over-
allotments).  A copy of the letter agreement is filed as Exhibit 99.4 to this
Form 8-K.

Item 7.   Financial Statements and Exhibits.

           (a)  Audited Financial Statements of the Acquired Business

                See Exhibit 99.7

           (b)  Pro Forma Financial Information

                The required pro forma financial information will be filed by
                amendment to the Form 8-K as soon as practicable, but in any
                event not later than 60 days after July 2, 1999.

           (c)  Exhibits.

          2.1  Acquisition Agreement, dated as of January 11, 1999, among CIGNA
Corporation, CIGNA Holdings, Inc. and ACE Limited

          2.2  Amendment No. 1 to Acquisition Agreement, dated as of July 2,
1999, CIGNA Corporation, CIGNA Holdings, Inc. and ACE Limited

          2.3  Amendment No. 2 to Acquisition Agreement, dated as of July 2,
1999, CIGNA Corporation, CIGNA Holdings, Inc. and ACE Limited

                                      -3-


     99.1  Information Technology Services Agreement, dated as of June 29, 1999,
among Holdings and International Business Machines Corporation

     99.2  Press release, dated July 9, 1999

     99.3  Remarketing and Contingent Purchase Agreement, dated June 30, 1999,
among ACE Limited, Holdings, ACE RHINOS Trust and Banc of America Securities LLC

     99.4  Letter agreement, dated as of June 29, 1999, between Bank of America
Securities LLC and ACE Limited

     99.5  Indenture, dated as of June 15, 1999, between ACE RHINOS Trust,
Holdings and The First National Bank of Chicago, as Trustee

     99.6  Supplemental Indenture, dated as of June 30, 1999, between ACE RHINOS
Trust, Holdings and The First National Bank of Chicago, as Trustee

     99.7  Audited financial statements for the Acquired Business for each of
the years in the three-year period ended December 31, 1998


Item 8.  Change in Fiscal Year

     Effective July 2, 1999, the Company changed its fiscal year so that its
fiscal year will now commence on January 1 and end on December 31.  This change
was made to align the Company's fiscal year end with the statutory year ends of
the majority of its subsidiaries.  A Quarterly Report on Form 10-Q for the
transition period from September 30, 1998 through December 31, 1998 will be
filed.

     Because of the change in fiscal year, the 2000 annual general meeting of
stockholders will be held on June 9, 2000. Accordingly, the deadline for
stockholders who wish to submit a proposal to be considered for inclusion in the
proxy statement for such annual meeting has been extended. Stockholders wishing
to submit such a proposal should send it to the Secretary, ACE Limited, The ACE
Building, 30 Woodbourne Avenue, Hamilton HM 08 Bermuda so that it is received no
later than December 31, 1999 and such proposal must otherwise comply with the
requirements of the U.S. Securities and Exchange Commission to be eligible for
inclusion in the Company's 2000 annual general meeting proxy statement and form
of proxy. Under the Company's Articles of Association, the deadline for advance
notice to submit a proposal for consideration at the 2000 annual meeting, or to
nominate persons for election as directors, did not change. Such written  notice
must be received by the Secretary of the Company on or prior to December 7,
1999. The notice must meet the requirements set forth in the Company's Articles
of Association. Under the circumstances described in, and upon compliance with,
Rule 14a-4(c) under the Exchange Act, management proxies would be allowed to use
their discretionary voting authority to vote on any proposal with respect to
which the foregoing requirements have been met.

                                      -4-


                                   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: July 19, 1999             ACE LIMITED


                                 By:  Christopher Z. Marshall
                                      -----------------------
                                      Christopher Z. Marshall
                                      Chief Financial Officer

                                      -5-


                                 EXHIBIT INDEX


Exhibit
Number                Description
- ------                -----------
       
2.1       Acquisition Agreement, dated as of January 11, 1999, among CIGNA
          Corporation, CIGNA Holdings, Inc. and ACE Limited

2.2       Amendment No. 1 to Acquisition Agreement, dated as of July 2,
          1999, CIGNA Corporation, CIGNA Holdings, Inc. and ACE Limited

2.3       Amendment No. 2 to Acquisition Agreement, dated as of July 2,
          1999, CIGNA Corporation, CIGNA Holdings, Inc. and ACE Limited

99.1      Information Technology Services Agreement, dated as of June 29,
          1999, among Holdings and International Business Machines Corporation

99.2      Press release, dated July 9, 1999

99.3      Remarketing and Contingent Purchase Agreement, dated June 30, 1999,
          among ACE Limited, Holdings, ACE RHINOS Trust and Banc of America
          Securities LLC

99.4      Letter agreement, dated as of June 29, 1999, between Bank of America
          Securities LLC and ACE Limited

99.5      Indenture, dated as of June 15, 1999, between ACE RHINOS Trust,
          Holdings and The First National Bank of Chicago, as Trustee

99.6      Supplemental Indenture, dated as of June 30, 1999, between ACE
          RHINOS Trust, Holdings and The First National Bank of Chicago, as
          Trustee

99.7      Audited financial statements for the Acquired Business for each
          of the years in the three-year period ended December 31, 1998
          (Incorporated by reference to Exhibit 99.2 to Current Report on Form
          8-K (Date of Earliest Event Reported May 18, 1999))