AEOLUS PHARMACEUTICALS, INC.

EXHIBIT 10.112

AEOLUS PHARMACEUTICALS, INC.

December 14, 2004

Dr. Shayne C. Gad

Aeolus Pharmaceuticals, Inc.

P.O. Box 14287

79 T.W. Alexander Drive

4401 Research Commons, Suite 200

Research Triangle Park, NC 27709

Dear Shayne:

This letter confirms our conversations regarding extending your consulting period with Aeolus Pharmaceuticals, Inc. (“Aeolus” or the “Company”) and sets forth the terms and conditions of that consulting.

The Company hereby offers to extend the term of your consulting agreement. During the period of your consulting, you shall devote yourself for two business days each week to work for or at the direction of the Company’s Chief Executive Officer, use your best efforts to complete all assignments, and adhere to the Company’s procedures and policies in place from time-to-time.

You will receive a monthly consulting fee of $19,500 for each full month of consulting. In addition, for each full month of consulting, the Company will grant you an option to purchase 2,500 shares of the Company’s stock at fair market value pursuant to the terms of the Company’s 2004 Stock Option Plan. The options will be fully vested upon grant.

Currently, we anticipate that you will continue as a consultant for an additional term of twelve months from January 1, 2005. However, the Company may terminate your consulting earlier for any reason at its sole discretion. In the event that the Company elects to terminate your consulting prior to the full term of this agreement, you will be given two (2) months notice before termination.

By executing this letter below, you agree that during the course of your consulting and thereafter that you shall not use or disclose, in whole or in part, any of the Company’s trade secrets, confidential and proprietary information, including customer lists and information, to any person, firm, corporation, or other entity for any reason or purpose whatsoever other than in the course of your employment with the Company or with the prior written permission of the Company. By signing this letter below, you further acknowledge that you have no claims against the Company up to the date of your signature and delivery of this letter.

All findings, conclusions and date and all methods, inventions, discoveries, trade secrets, techniques, processes and know-how, whether or not patentable, that are made by you, either alone or with others, in the performance of your services or which result, to any extent, from use of Aeolus’ materials, premises or other property (collectively, “Inventions”) shall become the exclusive property of Aeolus. You hereby assign, transfer and convey all of your rights, title and interest in and to any and all Inventions. Upon the request and at the expense of Aeolus, you will execute and deliver any and all instruments and documents and take such other acts as may be necessary or desirable to document Aeolus’ rights or to enable Aeolus to apply for, prosecute and enforce patents, trademark registrations or copyrights in any jurisdiction with respect to any Inventions or to obtain any extension, validation, re-issue, continuance or renewal of any such intellectual property right.

You are an independent contractor under this agreement and shall not be deemed an employee of Aeolus. You will not be entitled to participate in any benefit plan of an Aeolus employee.

Kindly sign your name at the end of this letter to signify your understanding and acceptance of these terms and that no one at the Company has made any other representation to you. We look forward to continuing our relationship with you.

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