AGREEMENT REGARDING ONGOING SERVICES AS CHAIRMAN OF THE BOARD

Exhibit 10.19

AGREEMENT REGARDING ONGOING SERVICES

AS CHAIRMAN OF THE BOARD

This AGREEMENT REGARDING ONGOING SERVICES AS CHAIRMAN OF THE BOARD (the “Agreement”) is entered into as of the 28th day of October, 2004 (the “Effective Date”), by and between EXAR CORPORATION, a Delaware corporation (the “Company”), and DONALD L. CIFFONE, JR. (“Mr. Ciffone”).

WHEREAS, effective as of September 9, 2004, Mr. Ciffone retired as President and Chief Executive Officer of the Company;

WHEREAS, prior to his retirement, Mr. Ciffone had served as the Company’s President and Chief Executive Officer for over 7 years and has served as Chairman of the Board for over 2 years;

WHEREAS, while serving as the Company’s President and Chief Executive Officer and Chairman of the Board, Mr. Ciffone has developed a deep and unique understanding of the Company’s business and its industry;

WHEREAS, the Company believes that, as Chairman of the Board, Mr. Ciffone would continue to provide valuable services to the Company by assisting in strategic matters and in the transition to a new President and Chief Executive Officer, among other matters;

WHEREAS, the Company has determined that it is in the best interests of the Company and its stockholders that Mr. Ciffone continue to serve as Chairman of the Board on the terms set forth in this Agreement; and

WHEREAS, Mr. Ciffone wishes to continue to serve as Chairman of the Board on the terms set forth in this Agreement.

NOW, THEREFORE, in consideration of the mutual promises and covenants contained herein, it is hereby agreed by and between the parties hereto as follows:

ARTICLE 1

DEFINITIONS

For purposes of the Agreement, the following terms are defined as follows:

1.1 “Board” means the Board of Directors of the Company, and “Chairman of the Board” means Chairman of the Board of Directors of the Company.

1.2 “Common Stock” means the common stock of the Company.

1.3 “Executive Employment Agreement” means the Executive Employment Agreement, dated as of October 28, 2004, by and between the Company and Mr. Ciffone.

1.4 “Part-Time Employment Agreement” means the Part-Time Employment Agreement, dated as of October 28, 2004, by and between the Company and Mr. Ciffone.

1.5 “Second Part-Time Employment Agreement” means the Second Part-Time Employment Agreement substantially in the form attached to the Executive Employment Agreement as Exhibit A-2.

ARTICLE 2

DESCRIPTION OF SERVICES AND COMPENSATION

2.1 Description of Services. During the term of this Agreement, Mr. Ciffone shall comply with all laws, rules and regulations applicable to Mr. Ciffone as Chairman of the Board (including, without limitation, Mr. Ciffone’s fiduciary duties to the Company and its stockholders under state law), shall comply with all policies of the Company (as the same may be adopted or modified from time to time), shall act in the best interests of the Company and its stockholders and shall otherwise perform such duties and obligations as the Company and Mr. Ciffone shall agree.

2.2 Certain Benefits and Salary.

(a) Following the termination of the Part-Time Employment Agreement and for so long as Mr. Ciffone serves as Chairman of the Board, Mr. Ciffone shall be eligible under the terms and conditions of the Company’s medical, vision and dental benefit plans that may be in effect from time to time and are provided by the Company to its employees generally. This provision shall not apply at any time that Mr. Ciffone is employed by the Company pursuant to the Second Part-Time Employment Agreement or employed by any other company providing or offering to Executive substantially similar benefits, and this provision shall terminate upon the Company’s 2007 Annual Meeting of Stockholders. While this provision is in effect, Mr. Ciffone shall be obligated to pay fifty percent (50%) of the premiums associated with his participation in the aforementioned benefit plans.

(b) For so long as Mr. Ciffone serves as non-employee Chairman of the Board, Mr. Ciffone shall be entitled to such cash compensation as is provided for by Company policy (such amount currently being $60,000 per anum).

2.3 Stock Options. On April 1, 2005, Mr. Ciffone shall be granted an option to purchase fifty-four thousand (54,000) shares of Company common stock (as adjusted for stock combinations, splits and the like) pursuant to the Company’s 1997 Equity Incentive Plan (the “1997 Plan”); provided, that Mr. Ciffone is serving as Chairman of the Board and not as an employee on such date and that Mr. Ciffone is otherwise eligible to receive such grant under the 1997 Plan. Such option shall have substantially the same terms (e.g., vesting, term, etc.) as stock option grants made pursuant to Section 5(a) of the Company’s 1996 Non-Employee Directors’ Stock Option Plan (the

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“1996 Plan”), and it is intended that such grant shall be made in lieu of any stock option grant to which Mr. Ciffone might be entitled pursuant to Section 5(a) of the 1996 Plan in the future. For the purpose of clarity, such option grant shall vest ratably each year over a three-year period commencing with the date of grant (such that the option shall become one-third vested upon each anniversary of the date of grant). Mr. Ciffone acknowledges that, upon receipt of such grant, Mr. Ciffone shall not be entitled to a stock option grant pursuant to Section 5(a) of the 1996 Plan upon first being elected to the Company’s Board of Directors as a non-employee director, and Mr. Ciffone hereby waives any right with respect thereto. Other than a grant pursuant to Section 5(a) of the 1996 Plan, Mr. Ciffone shall receive any other stock option grant or grants to which he may be entitled as a non-employee director pursuant to the terms of the 1996 Plan (including a possible grant of an option to purchase forty-five thousand (45,000) shares upon the Company’s 2006 Annual Meeting of Stockholders pursuant to Section 5(b) of the 1996 Plan).

ARTICLE 3

GENERAL PROVISIONS

3.1 Term and Termination.

(a) Either party may, at its option, terminate this Agreement if the other party: (i) defaults in the performance of a material obligation hereunder, provided such default has not been corrected within thirty (30)—days after receipt of notice describing such default; (ii) becomes a party to any proceeding involving his or its bankruptcy or other insolvency; or (iii) ceases to be actively engaged in business or financially incapable of fulfilling its obligations under this Agreement.

(b) This Agreement shall terminate automatically upon the termination of Mr. Ciffone’s services as Chairman of the Board or the date of the Company’s 2007 Annual Meeting of Stockholders, whichever shall first occur.

(c) Nothing contained herein shall limit any remedies that either party may have for the default of the other party under this Agreement.

3.2 Notices. Any notices provided hereunder must be in writing and shall be deemed effective upon the earlier of personal delivery (including personal delivery by telex) or the third day after mailing by first class mail, to the Company at its primary office location and to Mr. Ciffone at Mr. Ciffone’s address as listed on the Company payroll.

3.3 Severability. Whenever possible, each provision of this Agreement will be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be invalid, illegal or unenforceable in any respect under any applicable law or rule in any jurisdiction, such invalidity, illegality or unenforceability will not affect any other provision or any other jurisdiction, but this Agreement will be reformed, construed and enforced in such jurisdiction as if such invalid, illegal or unenforceable provisions had never been contained herein.

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3.4 Waiver. If either party should waive any breach of any provisions of this Agreement, they shall not thereby be deemed to have waived any preceding or succeeding breach of the same or any other provision of this Agreement, unless such waiver is agreed to in writing by both parties.

3.5 Complete Agreement. This Agreement constitutes the entire agreement between Mr. Ciffone and the Company and is the complete, final, and exclusive embodiment of their agreement with regard to this subject matter. This Agreement is entered into without reliance on any promise or representation other than those expressly contained herein or therein, and it cannot be modified or amended except in a writing signed by Mr. Ciffone and by an officer of the Company.

3.6 Counterparts. This Agreement may be executed in separate counterparts, any one of which need not contain signatures of more than one party, but all of which taken together will constitute one and the same Agreement.

3.7 Headings. The headings of the sections hereof are inserted for convenience only and shall not be deemed to constitute a part hereof nor to affect the meaning thereof.

3.8 Successors and Assigns. This Agreement is intended to bind and inure to the benefit of and be enforceable by Mr. Ciffone and the Company, and their respective successors, assigns, heirs, executors and administrators, except that (i) Mr. Ciffone may not assign any of Mr. Ciffone’s duties hereunder and Mr. Ciffone may not assign any of Mr. Ciffone’s rights hereunder, without the written consent of the Company, which shall not be withheld unreasonably and (ii) the Company may assign its rights and duties hereunder only to a parent or subsidiary of the Company or to a corporation or other entity that will become the Company’s successor in interest due to a merger, consolidation, acquisition or similar transaction.

3.9 Arbitration. Unless otherwise prohibited by law or specified below, all disputes, claims and causes of action, in law or equity, arising from or relating to this Agreement or its enforcement, performance, breach, or interpretation shall be resolved solely and exclusively by final and binding arbitration held in Santa Clara County, California through Judicial Arbitration & Mediation Services/Endispute (“JAMS”) under the then existing JAMS arbitration rules. However, nothing in this Section is intended to prevent either party from obtaining injunctive relief in court to prevent irreparable harm pending the conclusion of any such arbitration. Each party in any such arbitration shall be responsible for its own attorneys’ fees, costs and necessary disbursement; provided, however, that if one party refuses to arbitrate and the other party seeks to compel arbitration by court order, if such other party prevails, it shall be entitled to recover reasonable attorneys’ fees, costs and necessary disbursements. Pursuant to California Civil Code Section 1717, each party warrants that it was represented by counsel in the negotiation and execution of this Agreement, including the attorneys’ fees provision herein.

3.10 Attorneys’ Fees. If either party hereto brings any action to enforce rights hereunder, each party in any such action shall be responsible for its own attorneys’ fees and costs incurred in connection with such action.

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3.11 Choice of Law. All questions concerning the construction, validity and interpretation of this Agreement will be governed by the law of the State of California without regard to its principles of conflicts of law.

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IN WITNESS WHEREOF, the parties have executed this Agreement as of the day and year first above written.

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