AMENDMENT NO. 2 TO AGREEMENT AND PLAN OF MERGER

Exhibit 10.2

AMENDMENT NO. 2 TO AGREEMENT AND PLAN OF MERGER

THIS AMENDMENT NO. 2 TO AGREEMENT AND PLAN OF MERGER (this “Amendment”) is made and entered into as of November 2, 2009, by and among LIGAND PHARMACEUTICALS INCORPORATED, a Delaware corporation (“Parent”); NEON SIGNAL, LLC, a Delaware limited liability company and a wholly-owned Subsidiary of Parent (“Merger Sub”); and NEUROGEN CORPORATION, a Delaware corporation (the “Company”). This Amendment is made with regard to the Agreement and Plan of Merger dated August 23, 2009, by and among Parent, Merger Sub and the Company (as previously amended, the “Agreement”).

1. The Agreement is hereby amended by changing Section 7.01(c) of the Agreement to read in full as follows:

by Parent or the Company at any time after December 24, 2009 (the “Outside Date”) if the Effective Time shall not have occurred on or before the Outside Date (provided that the right to terminate this Agreement pursuant to this Section 7.01(c) shall not be available to any party where the failure of such party (or any Affiliate or Representative of such party) to fulfill any obligation under this Agreement or any voting agreement has resulted in the failure of the Effective Time to have occurred on or before the Outside Date;

2. Except as expressly set forth herein, the Agreement remains unchanged and in full force and effect.

3. This Amendment may be executed in counterparts, each of which shall be deemed to be an original, and all of which taken together shall be deemed to constitute one and the same instrument. The parties agree that delivery of an executed counterpart of a signature page of this Amendment electronically or by facsimile shall be effective as delivery of a manually executed counterpart of this Amendment.

IN WITNESS WHEREOF, Parent, Merger Sub and the Company have caused this Amendment No. 2 to be executed as of the date first written above.