Ownership Submission
FORM 3
UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

INITIAL STATEMENT OF 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 *
  Lyons Mark Donald
2. Date of Event Requiring Statement (Month/Day/Year)
07/02/2008
3. Issuer Name and Ticker or Trading Symbol
ARCH CAPITAL GROUP LTD. [ACGL]
(Last)
(First)
(Middle)
ONE LIBERTY PLAZA, 53RD FLOOR
4. Relationship of Reporting Person(s) to Issuer
(Check all applicable)
_____ Director _____ 10% Owner
__X__ Officer (give title below) _____ Other (specify below)
Chairman & CEO Arch Insur Gr
5. If Amendment, Date Original Filed(Month/Day/Year)
(Street)

NEW YORK, NY 10006
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 Beneficially Owned
1.Title of Security
(Instr. 4)
2. Amount of Securities Beneficially Owned
(Instr. 4)
3. Ownership Form: Direct (D) or Indirect (I)
(Instr. 5)
4. Nature of Indirect Beneficial Ownership
(Instr. 5)
Common Shares, $.01 par value per share 61,171 (1)
D
 

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly. SEC 1473 (7-02)
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Table II - Derivative Securities Beneficially Owned (e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivative Security
(Instr. 4)
2. Date Exercisable and Expiration Date
(Month/Day/Year)
3. Title and Amount of Securities Underlying Derivative Security
(Instr. 4)
4. Conversion or Exercise Price of Derivative Security 5. Ownership Form of Derivative Security: Direct (D) or Indirect (I)
(Instr. 5)
6. Nature of Indirect Beneficial Ownership
(Instr. 5)
Date Exercisable Expiration Date Title Amount or Number of Shares
Stock Option (right to buy)   (2) 08/06/2012 Common Shares, $.01 par value per share 18,116 $ 26.31 D  
Stock Option (right to buy)   (3) 09/22/2014 Common Shares, $.01 par value per share 28,000 $ 39 D  
Stock Option (right to buy)   (4) 02/23/2016 Common Shares, $.01 par value per share 20,000 $ 56.27 D  
Stock Option (right to buy)   (5) 08/02/2016 Common Shares, $.01 par value per share 15,000 $ 59.65 D  
Stock Appreciation Right   (6) 05/11/2017 Common Shares, $.01 par value per share 8,350 $ 71.12 D  
Stock Appreciation Right   (7) 05/09/2018 Common Shares, $.01 par value per share 8,350 $ 69.3 D  

Reporting Owners

Reporting Owner Name / Address Relationships
Director 10% Owner Officer Other
Lyons Mark Donald
ONE LIBERTY PLAZA, 53RD FLOOR
NEW YORK, NY 10006
      Chairman & CEO Arch Insur Gr  

Signatures

/s/ Mark D. Lyons 07/07/2008
**Signature of Reporting Person Date

Explanation of Responses:

* If the form is filed by more than one reporting person, see Instruction 5(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) 1,000 of such shares are restricted and subject to vest on February 23, 2009; 15,000 of such shares are restricted and subject to vest on July 31, 2009; 5,566 of such shares are restricted and subject to vest in two equal annual installments on May 11, 2009 and May 11, 2010 and 8,350 of such shares are restricted share units that vest in three equal annual installments on May 9th in each of 2009, 2010 and 2011, subject to the applicable award agreements.
(2) The stock options became exerciable in three equal annual installments commencing on August 6, 2002, subject to the applicable award agreement.
(3) The stock options became exerciable in three equal annual installments commencing on September 22, 2004, subject to the applicable award agreement.
(4) The stock options became exercisable in three equal annual installments commencing on February 23, 2007, subject to the applicable award agreement.
(5) The stock options become exercisable on July 31, 2009, subject to the applicable award agreement.
(6) The stock appreciation rights became exercisable in three equal annual installments commencing on May 16, 2008, subject to the applicable award agreement.
(7) The stock appreciation right will become exercisable in three equal annual installments, with the first installment becoming exercisable on May 9, 2009 and the next two installments on May 9, 2010 and 2011, subject to the applicable award agreement.

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