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 * Duer Walter M   2. Issuer Name and Ticker or Trading Symbol HCC INSURANCE HOLDINGS INC/DE/ [HCC] 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 HCC INSURANCE HOLDINGS, INC., 13403 NORTHWEST FREEWAY 3. Date of Earliest Transaction (Month/Day/Year) 05/27/2010 (Street) HOUSTON, TX 77040 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 Stock               11,211 D   Common Stock 05/27/2010   A   3,158 (1) A $ 25.33 14,369 D   Common Stock               2,006.483 I By Family LP

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

Option to Purchase (2)

$ 19.47

(3)

08/26/2012

Common Stock

37,500

37,500

D

Option to Purchase (4)

$ 30.85

01/05/2007

01/05/2011

Common Stock

12,500

12,500

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
Duer Walter M C/O HCC INSURANCE HOLDINGS, INC. 13403 NORTHWEST FREEWAY HOUSTON, TX 77040	X

Signatures

Randy D. Rinicella as Attorney in Fact for Walter M. Duer		06/01/2010
**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)	As part of the HCC Board of Directors compensation package, each non-employee Director receives a grant of HCC Common Stock in the amount of the number of shares determined by dividing $80,000 by the closing price on the date of the Annual Meeting of Shareholders. The Annual Meeting of Shareholders was Thursday, May 27, 2010.
(2)	Option to purchase granted pursuant to the 2001 Flexible Incentive Plan.
(3)	The options vest over a 60 month period; the aggregate number of shares purchasable are as follows: 7,500 on 08/26/2005; 15,000 on 08/26/2006; 22,500 on 08/26/2007; 30,000 on 08/26/2008; 37,500 on 08/26/2009.
(4)	Option to purchase granted pursuant to the 2004 Flexible Incentive Plan.

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