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                                                       OMB APPROVAL
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           UNITED STATES                       OMB Number:          3235-0145
SECURITIES AND EXCHANGE COMMISSION             Estimated average burden hours
      WASHINGTON, D.C. 20549                   per response.............14.90
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SCHEDULE 13G
INFORMATION STATEMENT PURSUANT TO RULES 13d-1 (b) AND (c) AND AMENDMENTS THERETO
FILED PURSUANT TO 13d-2 (b)
(AMENDMENT NO.___)*
ACE LIMITED

(Name of Issuer)

COMMON STOCK
 (Title of Class of Securities)

G0070K103
 (CUSIP Number)
*The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter the disclosures provided in a prior cover page.
The information required in the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

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CUSIP NO. G0070K103                          13G                          PAGE 2  OF  5 PAGES
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   1    NAME OF REPORTING PERSON
        S.S. or I.R.S. IDENTIFICATION OF ABOVE PERSON

          OPPENHEIMER CAPITAL  (IRS NO. 13-3413767)
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   2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                             (a)[ ]
                                                                                      (b)[x]

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   3    SEC USE ONLY

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   4    CITIZENSHIP OR PLACE OF ORGANIZATION

        DELAWARE
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  NUMBER OF SHARES      5   SOLE VOTING POWER
    BENEFICIALLY
      OWNED BY
                            -0-
                      -----------------------------------------------------------------------
        EACH            6   SHARED VOTING POWER
      REPORTING
       PERSON
          WITH              9,784,039
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                        7   SOLE DISPOSITIVE POWER

                            -0-
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                        8   SHARED DISPOSITIVE POWER

                            9,784,039
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   9    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

        9,784,039
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  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*         [ ]

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  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

        17.7
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  12    TYPE OF REPORTING PERSON*

        IA
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*SEE INSTRUCTION BEFORE FILLING OUT!
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ITEM 1 (a) NAME OF ISSUER:
ACE LIMITED
(b) ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

30 Woodbourne Avenue
Hamilton HM08, Bermuda
ITEM 2 (a) NAME OF PERSON FILING:
OPPENHEIMER CAPITAL
(b) ADDRESS OF PRINCIPAL BUSINESS OFFICE:
Oppenheimer Tower, World Financial Center New York, New York 10281
(c) CITIZENSHIP:

Not Applicable.
(d) TITLE OF CLASS OF SECURITIES:

Common Stock
(e) CUSIP NUMBER:
G0070K103
ITEM 3 IF THIS STATEMENT IS FILED PURSUANT TO RULE 13d-1(b), OR 13d-2(b),
CHECK WHETHER THE PERSON FILING IS A:
(a) [ ] Broker or Dealer registered under Section 15 of the Act.
(b) [ ] Bank as defined in Section 3(a)(6) of the Act.
(c) [ ] Insurance Company as defined in Section 3(a)(19) of the Act.
(d) [ ] Investment Company registered under Section 8 of the Investment Company Act.
(e) [X] Investment Adviser registered under Section 203 of the Investment Advisors Act of 1940.
(f) [ ] Employee Benefit Plan, Pension Fund which is subject to the provisions of the Employee Retirement Income Security Act of 1974 or Endowment Fund; see
[Paragraph] 240.13d-1(b)(1)(ii)(F).
(g) [ ] Parent Holding Company, in accordance with [Paragraph] 13d-1(b)(ii)(G).
(h) [ ] Group, in accordance with [Paragraph] 13d-1(b)(1)(ii)(H).
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ITEM 4 OWNERSHIP.
(a) Amount beneficially owned: 9,784,039 **
(b) Percent of Class: 17.7
(c) Number of shares as to which such person has:
(i) Sole power to vote or direct the vote: -0-
(ii) Shared power to vote: 9,784,039 **
(iii) Sole power to dispose or direct the disposition of: -0-
(iv) Shared power to dispose or direct the disposition of:

9,784,039 **
**This report is being filed on behalf of Oppenheimer Capital, a Delaware general partnership and/or certain investment advisory clients or discretionary accounts relating to their collective beneficial ownership of shares of common stock of the Issuer. Oppenheimer Capital is a registered investment adviser under Section 203 of the Investment Advisers Act of 1940. As a result of its role as investment adviser Oppenheimer may be deemed may be deemed to be the beneficial owner of the securities of the Issuer. Oppenheimer Capital has the sole power to dispose of the shares and to vote the shares under its written guidelines established by its Management Board.
ITEM 5 OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS.
If this statement is being filed to report the fact that as of the date hereof the reporting person has ceased to be the beneficial owner of more than five percent of the class of securities, check the following
[ ].
ITEM 6 OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON.
Our clients have the right to receive or the power to direct the receipt of dividends or the profits from the sale of such securities. No one client owns more than five percent of the securities of the Issuer.
ITEM 7 IDENTIFICATION AND CLARIFICATION OF THE SUBSIDIARY WHICH ACQUIRED
THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY.
Not Applicable.
ITEM 8 IDENTIFICATION AND CLARIFICATION OF MEMBERS OF THE GROUP.
Not Applicable.
ITEM 9 NOTICE OF DISSOLUTION OF GROUP.
Not Applicable.
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ITEM 10 CERTIFICATION.
By signing below I certify that, to the best of my knowledge and belief, the securities referred to above were acquired in the ordinary course of business and were not acquired for the purpose of and do not have the effect of changing or influencing the control of the issuer of such securities and were not acquired in connection with or as a participant in any transaction having such purposes or effect.
SIGNATURE
After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Date: February 27, 1998

/s/ Thomas Duggan
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    General Counsel	

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