Exhibit 10.1

FIRST AMENDMENT TO REGISTRATION RIGHTS AGREEMENT

This FIRST AMENDMENT TO REGISTRATION RIGHTS AGREEMENT (this “Amendment”) is made and entered into as of May 23, 2013, by and between NEPHROS, INC., a Delaware corporation (the “Company”), and LAMBDA INVESTORS LLC (“Lambda”). Capitalized terms used herein but not defined herein shall have the meanings given to such terms in the Registration Rights Agreement (as defined herein).

WHEREAS, the Company and Lambda entered into that certain Registration Rights Agreement dated as of February 4, 2013 (the “Registration Rights Agreement”); and

WHEREAS, pursuant to Section 10(a) of the Registration Rights Agreement, the Company and Lambda desire to amend the Registration Rights Agreement as set forth in this Amendment.

NOW, THEREFORE, in consideration of the premises and mutual covenants and obligations hereinafter set forth, the Company and Lambda, intending legally to be bound, hereby agree as follows.

1.          Definitions. Section 1 of the Registration Rights Agreement is hereby amended to replace the following definition in its entirety:

“Filing Date” shall mean the thirtieth (30th) day after receipt by the Company of written notice from Lambda directing the Company to file the Resale Registration Statement; provided that, if the Filing Date falls on a Saturday, Sunday or any other day which shall be a legal holiday or a day on which the SEC is authorized or required by law or other government actions to close, the Filing Date shall be the following Business Day.

2.          Miscellaneous.

(a)        Ratification and Incorporation. Except as amended hereby, the Registration Rights Agreement is in all respects ratified and confirmed, and all of the terms thereof shall remain in full force and effect. This Amendment is executed and shall be construed as an amendment to the Registration Rights Agreement and, as provided in the Registration Rights Agreement, this Amendment forms a part thereof for all purposes. The Registration Rights Agreement and this Amendment shall be read, taken and construed as one and the same instrument, and each Holder shall be bound by the Registration Rights Agreement as amended hereby.

(b)        Counterparts. This Agreement may be executed in any number of counterparts and by the parties hereto in separate counterparts, each of which when so executed shall be deemed to be an original and all of which taken together shall constitute one and the same agreement.

(c)        Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE WITHOUT REGARD TO THE PRINCIPLES OF THE CONFLICT OF LAWS THEREOF.

(d)        Severability. In the event that any one or more of the provisions contained herein, or the application thereof in any circumstance, is held invalid, illegal or unenforceable, the validity, legality and enforceability of any such provision in every other respect and of the remaining provisions contained herein shall not be affected or impaired thereby.

IN WITNESS WHEREOF, the parties hereto have executed this Amendment as of the date first written above.