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 * H&F CORP INVESTORS IV BERMUDA LTD   2. Issuer Name and Ticker or Trading Symbol ARCH CAPITAL GROUP LTD. [ACGL] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director __X__ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) C/O A.S. & K. SERVICES, LTD., CEDAR HOUSE, 41 CEDAR AVENUE 3. Date of Earliest Transaction (Month/Day/Year) 05/15/2007 (Street) HAMILTON HM 12 BERMUDA  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 Common Shares, $0.01 par value per share (1) 05/15/2007   J(2)   4,674,022 (2) D (2) 0 (3) I Partnership (1)

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

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
H&F CORP INVESTORS IV BERMUDA LTD C/O A.S. & K. SERVICES, LTD. CEDAR HOUSE, 41 CEDAR AVENUE HAMILTON HM 12 BERMUDA		X

Signatures

/s/ Georgia Lee, Vice President		05/16/2007
**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)	THE REPORTING PERSONS ARE, AND THIS FORM 4 IS FILED ON BEHALF OF, HFCP IV (BERMUDA), L.P. ("HFCP IV BERMUDA"), H&F INTERNATIONAL PARTNERS IV-A (BERMUDA), L.P. ("HFIP IV-A BERMUDA"), H&F INTERNATIONAL PARTNERS IV-B (BERMUDA), L.P. ("HFIP IV-B BERMUDA") AND H&F EXECUTIVE FUND IV (BERMUDA), L.P. ("HFEF BERMUDA" AND COLLECTIVELY, THE "PARTNERSHIPS"). H&F INVESTORS IV (BERMUDA), L.P. ("HFI IV BERMUDA") IS THE SOLE GENERAL PARTNER OF EACH OF THE PARTNERSHIPS. H&F CORPORATE INVESTORS IV (BERMUDA), LTD. ("HFCI BERMUDA") IS THE SOLE GENERAL PARTNER OF HFI IV BERMUDA. A FIVE MEMBER INVESTMENT COMMITTEE OF HFCI BERMUDA FORMED BY THE SHAREHOLDERS OF HFCI BERMUDA ("THE INVESTMENT COMMITTEE") HAS INVESTMENT DISCRETION OVER THE SECURITIES. AS A RESULT, HFCI BERMUDA AND HFI IV BERMUDA MAY BE DEEMED TO CONTROL THE PARTNERSHIPS. THE MEMBERS OF THE INVESTMENT COMMITTEE DISCLAIM BENEFICIAL OWNERSHIP, EXCEPT TO THE EXTENT OF THEIR RESPECTIVE INDIRECT PECUNIARY INTERESTS IN THE ISSUER.
(2)	ON MAY 15, 2007, HFCP IV BERMUDA, HFIP IV-A BERMUDA, HFIP IV-B BERMUDA AND HFEF BERMUDA DISTRIBUTED TO THEIR RESPECTIVE LIMITED PARTNERS 3,766,638, 618,132, 204,201 AND 85,051 COMMON SHARES, RESPECTIVELY (COLLECTIVELY 4,674,022 COMMON SHARES), OF THE ISSUER IN ACCORDANCE WITH THEIR APPLICABLE PARTNERSHIP AGREEMENTS.
(3)	FOLLOWING THE DISTRIBUTION DESCRIBED IN NOTE 2, HFCP IV BERMUDA, HFIP IV-A BERMUDA, HFIP IV-B BERMUDA AND HFEF BERMUDA BENEFICIALLY OWN NO COMMON SHARES OF THE ISSUER. SHARE COUNT EXCLUDES 11,916 COMMON SHARES AND 3,300 OPTIONS TO ACQUIRE COMMON SHARES GRANTED TO DESIGNEES OF THE PARTNERSHIPS TO THE BOARD OF DIRECTORS OF THE ISSUER, WHICH SHARES AND OPTIONS ARE HELD PROPORTIONATELY FOR THE BENEFIT OF THE PARTNERSHIPS.

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