OPTION ASSUMPTION AGREEMENT

Exhibit 10.13

OPTION ASSUMPTION AGREEMENT

THIS OPTION ASSUMPTION AGREEMENT (this “Assumption Agreement”), dated July 29, 2005, is entered into by and between NCI, Inc., a Delaware corporation (“NCI Delaware”), and Linda Allan (the “Optionee”).

WHEREAS, NCI Information Systems, Inc., a Virginia corporation (“NCI Virginia”) and Optionee are party to that certain Non-Statutory Stock Option Agreement, dated May 4, 2001, a copy of which is attached hereto as Exhibit A, pursuant to which Optionee was granted an option to purchase 250 shares of NCI Virginia’s common stock, par value $0.01 per share (the “NCI Virginia Common Stock”), at an exercise price of $1.00 per share, which, by reason of a prior adjustment is currently an option to purchase 700,000 shares of NCI Virginia Common Stock at an exercise price of $0.00036 per share (the “Option Agreement”);

WHEREAS, NCI Delaware and NCI Virginia will consummate a series of transactions, as described on Exhibit B hereto (collectively referred to as the “Reincorporation Transaction”), pursuant to which NCI Virginia will become a wholly owned subsidiary of NCI Delaware;

WHEREAS, in connection with the Reincorporation Transaction, NCI Delaware has agreed to assume all of the issued and outstanding options of NCI Virginia; and

WHEREAS, each option to purchase one share of NCI Virginia Common Stock issued by NCI Virginia shall be converted into an option to purchase one share of Class A common stock of NCI Delaware (each, a “NCI Class A Share”) pursuant to NCI Delaware’s 2005 Performance Plan (the “NCI Delaware Plan”), substantially in the form attached hereto as Exhibit C;

NOW, THEREFORE, the parties agree that, in consideration of the mutual promises set forth in this Assumption Agreement, and as of the effective time of the Reincorporation Transaction:

1. Subject to the terms and conditions hereof, NCI Delaware hereby assumes all rights and obligations of NCI Virginia with respect to the Option Agreement, and Optionee acknowledges and accepts such assumption.

2. The NCI Virginia Option is hereby converted into an option to purchase 700,000 NCI Delaware Class A Shares, at an exercise price of $0.00036 per share, subject to adjustment in accordance with the last paragraph of Section 13(c) of the Option Agreement, on the terms and subject to the conditions set forth in the NCI Delaware Plan.

3. Optionee hereby waives, releases and forever discharges NCI Virginia and NCI Delaware from the obligation set forth in the last sentence of Section 2 of the Option Agreement regarding Optionee’s right to request NCI Delaware to purchase shares issuable upon exercise of the Option Agreement, as assumed by NCI Delaware.

Option Assumption Agreement

4. Optionee hereby waives, releases and forever discharges NCI Virginia and NCI Delaware from the obligation set forth in Section 10 of the Option Agreement regarding registration rights.

5. Optionee hereby waives, releases and forever discharges NCI Virginia and NCI Delaware from any obligation to provide additional shares or options pursuant to Sections 13(a) or (b) and the first paragraph of Section 13 (c) of the Option Agreement; provided, that, the wavier, release and discharge set forth in this paragraph 5 shall only become effective upon the closing of NCI Delaware’s initial public offering of Class A Shares under the Securities Act of 1933, as amended (the “NCI IPO”).

6. Except as otherwise provided herein, the terms of the Option Agreement shall remain in full force and effect; provided, that, to the extent any term or condition of the Option Agreement is inconsistent with or conflicts with any term or condition of this Assumption Agreement or the NCI Delaware Plan, the term or condition of this Assumption Agreement or the NCI Delaware Plan shall control. Notwithstanding any provision of this Assumption Agreement or the NCI Delaware Plan to the contrary, the parties acknowledge and agree that the provisions of Section 7 of the Option Agreement shall continue in full force and effect.

7. Simultaneously herewith, Optionee is delivering a fully-executed lock-up letter in the form attached hereto as Exhibit D, which letter shall only become effective on the closing of the NCI IPO. The parties acknowledge and agree that Optionee may exercise her rights under the Option Agreement to acquire Class A Shares immediately prior to the NCI IPO in order to include such shares in that offering, and that NCI Delaware, and not Optionee, will bear all of the fees, costs and expenses (including underwriting discounts and commissions, but expressly excluding any applicable taxes) in connection with the offer and sale of such shares. The parties further acknowledge and agree that Optionee may, subject to the terms and conditions of the lock-up letter, exercise her rights under the Option Agreement to acquire Class A Shares at any time after the NCI IPO.

8. The provisions of this Assumption Agreement are independent and severable. To the extent that any one provision is rendered inoperative, or is contrary to law, the parties agree that, to the extent possible, all other provisions of the Assumption Agreement shall be given full force and effect.

9. This Assumption Agreement shall be interpreted and construed under the laws of the Commonwealth of Virginia without regard to its conflicts of laws principles.

10. This Assumption Agreement may be executed in counterparts, each of which shall be deemed to be an original, but both of which together will constitute one and the same instrument.

[Signatures appear on following page.]

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Option Assumption Agreement

IN WITNESS WHEREOF, by signing below, the Optionee agrees to be bound by the terms of this Assumption Agreement.

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Option Assumption Agreement

EXHIBIT A

Option Agreement

(See attached.)

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Option Assumption Agreement

EXHIBIT B

Reincorporation Transaction

NCI Virginia will become a wholly owned subsidiary of NCI Delaware as a result of the following transactions (collectively referred to as the “Reincorporation Transaction”):

NCI Delaware will form Acquisition, LLC, a Virginia limited liability company (“Acquisition”), as a wholly owned subsidiary.

Charles Narang will contribute each of his shares of NCI Virginia Common Stock to Acquisition in exchange for one share of Class B common stock of NCI Delaware (each, a “NCI Delaware Class B Share”) pursuant to a Share Exchange Agreement.

Acquisition and NCI Delaware will become parties to an Agreement and Plan of Merger, pursuant to which (1) NCI Virginia will merge with Acquisition, with NCI Virginia being the surviving entity of such merger, and the existence of Acquisition terminating (the “Merger”), and (2) each share of NCI Virginia Common Stock issued and outstanding converting, by virtue of the Merger and without any action on the part of the holder thereof, into a right to receive, upon surrender of the certificate representing such NCI Virginia Common Stock, one share of Class A common stock of NCI Delaware (each, a “NCI Delaware Class A Share”), with all NCI Virginia Common Stock owned by NCI Virginia as treasury stock being no longer outstanding, and automatically cancelled and retired without payment of any consideration therefor.

Each NCI Delaware Class A Share will have the same rights and preferences as each NCI Delaware Class B Share, except that each NCI Delaware Class A Share will be entitled to one vote and each NCI Delaware Class B Share will be entitled to ten votes and will be convertible into one share of NCI Delaware Class A Share.

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Option Assumption Agreement

EXHIBIT C

NCI Delaware’s 2005 Performance Plan

(See attached.)

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Option Assumption Agreement

EXHIBIT D

Lock-Up Letter

(See attached.)

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Option Assumption Agreement