Exhibit 10.1

AGREEMENT

This Agreement (the “Agreement”) is entered into on this 4th day of August, 2003, between Arch Capital Group Ltd. and its affiliates (collectively, the “Company”) and Peter Appel (the “Executive”).

The Executive and the Company agree as follows:

1.                                  The employment relationship between the Executive and the Company terminated on July 31, 2003 (the “Termination Date”).  Effective on the Termination Date, the Executive has resigned all officer and employee positions with the Company and its subsidiaries.

2.                                  The Executive will continue to serve on the Board of Directors of Arch Capital Group Ltd. (the “Board”); provided, however, that the Executive’s continued service on the Board shall not be a condition to any payments provided for in this Agreement or in the Non-Core Business Payment Agreement between the Company and the Executive of even date herewith (the “Non-Core Business Payment Agreement”).  The Executive hereby acknowledges that, if he becomes employed by, or otherwise related to, an insurance business in competition with the Company, conflicts with his position on the Board may arise.  In the event the Board determines that such a conflict has arisen, the Executive will enter into discussions with the Board in order to resolve the conflict.

3.                                  Following the completion of the 7-day revocation period referred to in paragraph 22 below, the Executive will receive a payment from the Company in the amount

of $2,263,166, less required tax withholding.  The Executive will also receive an aggregate of $16,000 (less required tax withholding) from the Company, payable over the two year period following the Termination Date in equal semimonthly installments.

4.                                  The Compensation Committee of the Board (the “Compensation Committee”) shall determine a prorated annual bonus for the Executive for the period from January 1, 2003 through the Termination Date.  The amount of any such bonus shall be determined by the Compensation Committee in accordance with past practice and paid (less required tax withholding) in cash in a single lump sum as soon as practicable following the next regularly scheduled Compensation Committee meeting after the Termination Date.

5.                                  Medical, dental, and vision benefits will remain in effect for the Executive and his covered dependents until the earlier of (i) the second anniversary of the Termination Date or (ii) the date the Executive obtains other employment or engagement, whether as a proprietor, partner or otherwise, in which he is eligible for such insurance coverage.  The insurance coverage shall be provided on the same basis as provided to active U.S.-based employees of the Company in accordance with the terms and provisions of each applicable plan as in effect from time to time, including any contribution required to be made by the Executive toward such coverage in excess of $145 per month.

6.                                  For the avoidance of doubt, (i) all options to purchase common stock of Arch Capital Group Ltd. (“ACGL”) held by the Executive (all of which are listed on Annex I hereto and are referred to herein as the “Stock Option Agreements”) shall continue to be

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exercisable for their respective full option terms, notwithstanding the Executive’s termination of employment, and (ii) the restricted shares of common stock of ACGL set forth in the Restricted Share Agreement between the Executive and ACGL dated February 20, 2003 shall vest in full on the Termination Date.

7.                                  Except as set forth in paragraph 5 above, the Executive will cease participation in all employee benefit plans and arrangements of the Company as of the Termination Date.  The Executive’s rights with respect to his accrued benefits as of the Termination Date under the Company’s Savings Plan, the Company’s Pension Plan, the Company’s Executive Supplemental Non-Qualified Savings and Retirement Plan and the Company’s 1995 Employee Stock Purchase Plan are as set forth in the applicable plan documents.  Other than as expressly set forth in this Agreement, the Executive will have no continuing rights under any employee benefit plan or arrangement of the Company following the Termination Date.

8.                                  In consideration of the above, the sufficiency of which the Executive hereby acknowledges, the Executive, on behalf of the Executive and the Executive’s heirs, executors and assigns hereby releases and forever discharges the Company and its members, shareholders, parents, affiliates, subsidiaries, divisions, any and all current and former directors, officers, employees, agents, and contractors and their heirs and assigns, and any and all employee pension benefit or welfare benefit plans of the Company, including current and former trustees and administrators of such employee pension benefit and welfare benefit

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plans, from all claims, charges, or demands, in law or in equity, whether known or unknown, which may have existed or which may now exist from the beginning of time to the date of this Agreement, including, without limitation, any claims the Executive may have arising from or relating to the Executive’s employment or termination from employment with the Company, including a release of any rights or claims the Executive may have under Title VII of the Civil Rights Act of 1964, as amended, and the Civil Rights Act of 1991 (which prohibit discrimination in employment based upon race, color, sex, religion and national origin); the Americans with Disabilities Act of 1990, as amended, and the Rehabilitation Act of 1973 (which prohibit discrimination based upon disability); the Family and Medical Leave Act of 1993 (which prohibits discrimination based on requesting or taking a family or medical leave); the Equal Pay Act, as amended, 29 U.S.C. §206(d)(1); the Fair Labor Standards Act of 1938, as amended; Section 1981 of the Civil Rights Act of 1866 (which prohibits discrimination based upon race); Section 1985(3) of the Civil Rights Act of 1871 (which prohibits conspiracies to discriminate); the Employee Retirement Income Security Act of 1974, as amended; any other federal, state or local laws against discrimination; or any other federal, state, or local statute, or common law relating to employment, wages, hours, or any other terms and conditions of employment.  This includes a release by the Executive of any claims for wrongful discharge, breach of contract, torts or any other claims in any way related to the Executive’s employment with or termination from the Company.  This release also includes a release of any claims for age discrimination under the Age Discrimination in Employment Act, as amended (“ADEA”).  The ADEA requires that the Executive be advised

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to consult with an attorney before the Executive waives any claim under ADEA.  In addition, the ADEA provides the Executive with at least 21 days to decide whether to waive claims under ADEA and seven days after the Executive signs the Agreement to revoke that waiver.  This release does not release the Company from any obligations due to the Executive (i) under this Agreement, (ii) under the Non-Core Business Payment Agreement, (iii) under the Executive’s Stock Option Agreements, or (iv) for indemnification in accordance with the Company’s By-Laws.

9.                                  In consideration of the above, the sufficiency of which the Company hereby acknowledges, the Company hereby releases and forever discharges the Executive and his heirs, executors and assigns, from all claims, charges or demands, in law or in equity, whether known or unknown, which may have existed or which may now exist from the beginning of time to the date of this Agreement, including, but not limited to, any claims, related to the Executive’s employment with the Company.  This release does not release the Executive from any obligations due to the Company under this Agreement, the Non-Core Business Payment Agreement or the Executive’s Stock Option Agreements.  The Executive acknowledges, and hereby confirms, that his agreements relating to noncompetition and nonsolicitation set forth in the Non-Qualified Stock Option Agreement between ACGL and the Executive dated as of October 23, 2001 shall continue in effect in accordance with their terms and shall survive the exercise of the option set forth in such Non-Qualified Stock Option Agreement and continue through the second anniversary of the Termination Date.

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10.                            This Agreement is not an admission by either the Executive or the Company of any wrongdoing or liability.

11.                            The Executive understands and agrees that the consideration provided for herein is more than the Executive would otherwise be entitled to under the Company’s existing plans.

12.                            The Executive waives any right to reinstatement or future employment with the Company following the Executive’s separation from the Company on the Termination Date.

13.                            (a)  The Executive recognizes and acknowledges that the Company’s and its subsidiaries’ and their affiliates’ trade secrets and confidential or proprietary information, are valuable, special and unique assets of the Company’s business.  For purposes of this Agreement, a trade secret or confidential or proprietary information shall mean and include information treated as confidential or as a trade secret by the Company, any of its subsidiaries or their affiliates, including but not limited to information regarding contemplated products, models, compilations, business and financial methods or practices, marketing, merchandising and selling techniques, customers, vendors, suppliers, trade secrets, training programs, manuals or materials, technical information, contracts, systems, procedures, mailing lists, know-how, trade names, improvements, pricing, price lists, financial or other data (including the revenues, costs or profits associated with any of the Company’s or its subsidiaries, products or services), business plans, strategy, code books, invoices and other

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financial statements, computer programs, software systems, databases, discs and printouts, other plans (technical or otherwise), customer and industry lists, supplier lists, correspondence, internal reports, personnel files, sales and advertising material, telephone numbers, names, addresses, or any other compilation of information, written or unwritten, which is or was used in the business of the Company, any of its subsidiaries or their affiliates.  In addition, without in any way limiting the foregoing, confidential or proprietary information includes any and all information in the Executive’s possession or of which the Executive has knowledge relating to or arising out of any actual or threatened regulatory investigation or proceeding or settlement or any other litigation, claim, investigation, suit, action or other proceeding involving or relating to the Company or any of its subsidiaries or affiliates, so long as such investigation, proceeding, settlement, claim, litigation, suit, action or other proceeding or the Executive’s knowledge thereof occurred or was obtained during or prior to the term of the Executive’s employment by the Company or his directorship with the Company.

(b)  Except as may be required by the lawful order of a court or agency of competent jurisdiction or required by applicable law, the Executive will not, at any time during or after the termination of his employment by the Company, in whole or in part, disclose such trade secrets or confidential or proprietary information to any person, firm, corporation, association or other entity for any reason or purpose whatsoever, or make use of any such property for his own purposes or for the benefit of any person, firm, corporation or other entity (except the Company) under any circumstances.  The Executive’s obligation under this paragraph 13 shall not apply to any information which is generally available to the public or

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hereafter becomes available to the public without the fault of the Executive.  The Executive agrees and acknowledges that all of such information, in any form, and copies and extracts thereof, are and shall remain the sole and exclusive property of the Company and the Executive shall return to the Company the originals and all copies of any such information provided to or acquired by the Executive in connection with the performance of his duties for the Company, and shall return to the Company all files, correspondence and/or other communications received, maintained and/or originated by the Executive during the course of his employment, and no copy of any such information shall be retained by him.

(c)  It is the desire and intent of the parties that the provisions of this paragraph 13 shall be enforced to the fullest extent permissible under the laws and public policies applied in each jurisdiction in which enforcement is sought.  Accordingly, if any particular portion of this paragraph 13 shall be adjudicated to be invalid or unenforceable, this paragraph 13 shall be deemed amended to delete therefrom the portion thus adjudicated to be invalid or unenforceable, such deletion to apply only with respect to the operation of this paragraph 13 in the particular jurisdiction in which such adjudication is made.

(d)  If there is a breach or threatened breach of the provisions of paragraph 13 of this Agreement, the Company or its affiliates shall be entitled to an injunction restraining the Executive from such breach.  Nothing herein shall be construed as prohibiting the Company from pursuing any other remedies for such breach or threatened breach.

14.                 The Company agrees that if the Executive is made a party, or is threatened to be made a party, to any pending or threatened action, suit or proceeding, whether civil, criminal, administrative or investigative (each, a “Proceeding”), by reason of the fact that he is or was a director, officer or employee of the Company or is or was serving

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at the request of the Company as a director, officer, member, employee or agent of another corporation, partnership, joint venture, trust or other enterprise, including service with respect to employee benefit plans, the Executive shall be indemnified and held harmless by the Company to the fullest extent permitted or authorized by applicable law and the Company’s certificate of incorporation or bylaws, against all liability, loss and reasonable costs and expenses incurred or suffered by the Executive in connection therewith, including, without limitation, judgments and reasonable attorney’s fees and disbursements, and the Company shall advance expenses in connection therewith, to the fullest extent permitted or authorized by applicable law and the Company’s certificate of incorporation or bylaws.  Such indemnification shall continue as to the Executive even if he has ceased to be a director, member, employee or agent of the Company or other entity and shall inure to the benefit of the Executive’s heirs, executors and administrators.  The Company agrees to continue and maintain a directors’ and officers’ liability insurance policy covering the Executive to the extent the Company provides such coverage for its other directors and executive officers.

15.                 Except as otherwise provided in paragraph 5 of the Non-Core Business Payment Agreement, the Executive shall promptly return all the Company’s property in the Executive’s possession, including, but not limited to, the Company’s keys, credit cards, cellular phones, computer equipment, software and peripherals and originals or copies of books, records, or other information pertaining to the Company’s business.

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16.                 The Executive shall, at the request of the Company, assist the Company in effecting the transition in management of the Company.

17.                 The Executive shall, at the reasonable request of the Company, reasonably assist and cooperate with the Company in the defense and/or investigation of any third party claim or any investigation or proceeding, whether actual or threatened, including, without limitation, participating as a witness in any litigation, arbitration, hearing or other proceeding between the Company and a third party or any government body.  The Company shall reimburse the Executive for all reasonable out-of-pocket expenses incurred by him in connection with such assistance, including, without limitation, travel and lodging expenses.

18.                 This Agreement shall be governed by and construed in accordance with the laws of the State of New York, without reference to the principles of conflict of laws thereof.

19.                 All payments to be made hereunder shall be net of all applicable income, employment, social security or other taxes required to be withheld therefrom.

20.                 This Agreement and the Non-Core Business Payment Agreement represent the complete agreement between the Executive and the Company concerning the subject matter in this Agreement and the Non-Core Business Payment Agreement, and they supersede all prior agreements or understandings, written or oral.  This Agreement may not be amended or modified otherwise than by a written agreement executed by the parties hereto or their respective successors and legal representatives.

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21.                 Each of the paragraphs contained in this Agreement shall be enforceable independently of every other paragraph in this Agreement, and the invalidity or unenforceability of any paragraph shall not invalidate or render unenforceable any other paragraph contained in this Agreement.

22.                 It is further understood that, for a period of 7 days following the execution of this Agreement, the Executive may revoke this Agreement.  Any such revocation must be effected by delivery of a written notification of revocation of the Agreement to the Chief Financial Officer of ACGL prior to the end of such 7 day revocation period.  In the event that the Agreement is revoked by the Executive, the Company shall have no obligations under the Agreement or under the Non-Core Business Payment Agreement, no amounts will be payable under either agreement, and this Agreement and the Non-Core Business Payment Agreement shall each be deemed to be void ab initio and of no force or effect.

23.                 This Agreement has been entered into voluntarily and not as a result of coercion, duress, or undue influence.  The Executive acknowledges that the Executive has read and fully understands the terms of this Agreement and has been advised to consult with an attorney before executing this Agreement.  Additionally, the Executive acknowledges that the Executive has been afforded the opportunity of at least 21 days to consider this Agreement.

24.                 The Company will require any successor or assignee, whether direct or indirect, by purchase, merger, consolidation or otherwise, of all, or substantially all, of the

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business and/or assets of the Company to assume and agree to perform this Agreement in the same manner and to the same extent that the Company would be required to perform it if such succession or assignment had not taken place.

25.                 This Agreement shall inure to the benefit of and be enforceable by the Executive’s personal and legal representatives, executors, administrators, heirs, distributees, devisees and legatees.  If the Executive dies while any amounts are still payable to him hereunder, all such amounts, unless otherwise provided herein, shall be paid in accordance with the terms of this Agreement to the Executive’s devisee, legatee, or other designee or, if there be no such designee, to the Executive’s estate.

The parties to this Agreement have executed this Agreement on the day and year first written above.

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ANNEX I

Schedule of the Executive’s Stock Options

(1)                                  Includes 1,780 stock options with an expiration date of November 17, 2008.

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