FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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(Print or Type Responses)

1. Name and Address of Reporting Person * FORRESTER W THOMAS   2. Issuer Name and Ticker or Trading Symbol AXIS CAPITAL HOLDINGS LTD [AXS] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) C/O AXIS CAPITAL HOLDINGS LIMITED, 106 PITTS BAY ROAD 3. Date of Earliest Transaction (Month/Day/Year) 12/31/2004 (Street) PEMBROKE, D0 HM 08 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Phantom Stock

(1)

12/31/2004

A

539

(2)

(2)

Common Shares

539

(1)

539

D

Phantom Stock

(3)

01/03/2005

A

728

(2)

(2)

Common Shares

728

(3)

728

D

Stock Option for Common Shares

$ 27.45

01/03/2005

A

8,000

01/03/2006(4)

01/03/2015

Common Shares

8,000

(5)

8,000

D

Phantom Stock

(6)

01/03/2005

A

2,150

(2)

(2)

Common Shares

2,150

(6)

2,150

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
FORRESTER W THOMAS C/O AXIS CAPITAL HOLDINGS LIMITED 106 PITTS BAY ROAD PEMBROKE, D0 HM 08	X

Signatures

Carol S. Rivers, Attorney in Fact		01/04/2005
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	Phantom stock represents common shares issued in lieu of directors' fees that have been deferred using the closing sale price on December 31, 2004 of $27.35 per share.
(2)	Phantom stock is generally distributed when service as a director ceases.
(3)	Phantom stock represents restricted shares issued in lieu of directors' fees that have been deferred using the closing sale price on January 3, 2005 of $27.45 per share.
(4)	Option vests in three equal installments on the first, second and third anniversaries of the dte of grant.
(5)	Option issued as directors' fees.
(6)	Phantom stock represents common shares issued in lieu of directors' fees that have been deferred using the closing sale price on January 3, 2005 of $27.45 per share.

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