SECOND AMENDMENT TO THE DYNEGY INC. 2002 LONG TERM INCENTIVE PLAN

Exhibit 10.36

SECOND AMENDMENT TO THE DYNEGY INC.

2002 LONG TERM INCENTIVE PLAN

WHEREAS, Dynegy Inc., an Illinois corporation (“Dynegy Illinois”), has heretofore maintained the Dynegy Inc. 2002 Long Term Incentive Plan (the “Plan”), as amended;

WHEREAS, Dynegy Illinois entered into that certain Plan of Merger, Contribution and Sale Agreement by and among Dynegy Illinois, LSP GEN Investors, L.P., LS Power Partners, L.P., LS Power Equity Partners PIE I, L.P., LS Power Equity Partners, L.P., LS Power Associates, L.P., Falcon Merger Sub Co., and Dynegy Acquisition, Inc., executed September 14, 2006 (the “Merger Agreement”);

WHEREAS, pursuant to the transactions contemplated in the Merger Agreement, Dynegy Illinois became a wholly-owned subsidiary of a newly-formed Delaware corporation, named “Dynegy Inc.” (the “Company”), and Dynegy Illinois was renamed “Dynegy Illinois Inc.”, as of the Effective Time specified in the Merger Agreement (the “Effective Time”); and

WHEREAS, pursuant to the Merger Agreement, as of the Effective Time, Dynegy Illinois withdrew as sponsor of the Plan, and the Company assumed the Plan, the sponsorship thereof and all outstanding Dynegy Illinois stock options and stock-based awards (as described in the Merger Agreement), and such stock options and stock-based awards were converted into Company stock options and stock-based awards;

NOW THEREFORE, the Plan is hereby amended as follows, effective as of the Effective Time:

1. Section I of the Plan is amended by inserting the following paragraph to become the first paragraph thereof:

“I. PURPOSE

The DYNEGY INC. 2002 LONG TERM INCENTIVE PLAN (the ‘Plan’) was maintained by Dynegy Inc., an Illinois corporation (‘Dynegy Illinois’).

Dynegy Illinois entered into that certain Plan of Merger, Contribution and Sale Agreement by and among Dynegy Illinois, LSP GEN Investors, L.P., LS Power Partners, L.P., LS Power Equity Partners PIE I, L.P., LS Power Equity Partners, L.P., LS Power Associates, L.P., Falcon Merger Sub Co., and Dynegy Acquisition, Inc., executed September 14, 2006 (the ‘Merger Agreement’). Pursuant to the transactions contemplated in the Merger Agreement, Dynegy Illinois became a wholly-owned subsidiary of a newly-formed Delaware corporation, named ‘Dynegy Inc.’ (the ‘Company’), and Dynegy Illinois was renamed

‘Dynegy Illinois Inc.’, as of the Effective Time specified in the Merger Agreement (the ‘Effective Time’). Pursuant to the Merger Agreement, as of the Effective Time, Dynegy Illinois withdrew as sponsor of the Plan, and the Company assumed the Plan, the sponsorship hereof, and all outstanding Dynegy Illinois stock options and stock-based awards granted hereunder, and such stock options and stock-based awards were converted into Company stock options and stock-based awards hereunder.”

2. The definition of “Common Stock” in Section II(f) of the Plan is amended its entirety to provide as follows:

“(f) ‘Common Stock’ means the Class A common stock, $0.01 par value per share, of the Company, or any security into which such common stock may be changed by reason of any transaction or event of the type described in Paragraph XI.”

3. The definition of “Company” in Section II(g) of the Plan is amended its entirety to provide as follows:

“(g) ‘Company’ means Dynegy Inc., a Delaware corporation.”

4. As amended hereby, the Plan is specifically ratified and reaffirmed.

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IN WITNESS WHEREOF, the undersigned has caused this Amendment to the Plan to be executed on the date indicated below, to be effective as of the Effective Time.

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