Exhibit 10.34

EXECUTION VERSION

AMENDMENT NO. 1 TO THE REGISTRATION RIGHTS AGREEMENT

THIS AMENDMENT NO. 1 (this “Amendment”) dated as of February 8, 2013, to the Amended and Restated Registration Rights Agreement dated as of October 7, 2009, as joined by Kosmos Energy Ltd. (the “Corporation”) pursuant to the Joinder Agreement dated as of May 10, 2011 (together, the “RRA”), is by and among the Corporation and Blackstone Capital Partners (Cayman) IV L.P., Blackstone Capital Partners (Cayman) IV-A L.P., Blackstone Family Investment Partnership (Cayman) IV-A L.P., Participation Partnership (Cayman) IV L.P., Blackstone Family Investment Partnership (Cayman) IV-A SMD L.P., Warburg Pincus International Partners, L.P., Warburg Pincus Private Equity VIII, L.P., Warburg Pincus Netherlands International Partners I, C.V., WP-WPIP Investors, L.P., Warburg Pincus Netherlands Private Equity VIII I, C.V. and WP-WPVIII Investors, L.P. (together, the “Qualified Holders”).

Capitalized terms used but not defined herein shall have the meanings given to such terms in the RRA.

WI T N E S S E T H:

WHEREAS, the parties hereto are parties to the RRA;

WHEREAS, the RRA grants the holders of Registrable Securities registration rights (the “Registration Rights”) as set forth therein;

WHEREAS, Section 12(a) of the RRA states that the provisions of the RRA may not be amended, modified or supplemented, and waivers or consents to departures from the provisions of the RRA may not be given without the written consent of the Supermajority Holders; provided, however, that in no event shall the obligations of any holder of Registrable Securities be materially increased or the rights of any Stockholder be adversely affected (without similarly adversely affecting the rights of all Stockholders), except upon the written consent of such holder.

WHEREAS, the Qualified Holders party hereto, as holders of at least 75% of the outstanding Registrable Securities currently held by holders of Registrable Securities, constitute Supermajority Holders (as such term is defined in the RRA).

WHEREAS, the parties hereto desire to amend certain provisions of the RRA on the terms and conditions hereinafter set forth.

NOW, THEREFORE, the parties hereto hereby agree as follows:

1. Amendment of Certain Registration Rights. (a) The fourth paragraph of Section 3(a) of the RRA is hereby deleted in its entirety, and is replaced by the following paragraph:

“Within one (1) day after receipt by the Corporation of a Demand Notice or a Pre-QPO Demand Notice, the Corporation shall give written notice (the “Notice”) of such Demand Notice or Pre-QPO Demand Notice to all other holders of Registrable Securities and shall, subject to the provisions of Section 3(b) hereof, include in such registration all Registrable Securities with respect to which the Corporation received written requests for inclusion therein within one (1) day after such Notice is given by the Corporation to such holders.”

(b) Section 4(a) of the RRA is hereby deleted in its entirety, and is replaced by the following:

“(a) Right to Piggyback. If the Corporation proposes to file a registration statement under the Securities Act (or, if applicable, a final prospectus supplement relating to a “shelf” registration pursuant to Rule 415 under the Securities Act) with respect to an offering of Common Stock by and for the account of the Corporation (other than a registration statement (i) on Form S-4, Form S-8 or any successor forms thereto or (ii) filed solely in connection with an exchange offer or any employee benefit or dividend reinvestment plan), whether or not for its own account, then, each such time, the Corporation shall give prompt written notice of such proposed filing at least one (1) day before the anticipated filing date (the “Piggyback Notice”) to all of the holders of Registrable Securities. The Piggyback Notice shall offer such holders the opportunity to include in such registration statement the number of Registrable Securities as each such holder may request (a “Piggyback Registration”). Subject to Section 4(b) hereof, the Corporation shall include in each such Piggyback Registration all Registrable Securities with respect to which the Corporation has received written requests for inclusion therein within one (1) day after notice has been given to the applicable holder. The eligible holders of Registrable Securities shall be permitted to withdraw all or part of the Registrable Securities from a Piggyback Registration at any time prior to the effective date of such Piggyback Registration. The Corporation shall not be required to maintain the effectiveness of the Registration Statement for a Piggyback Registration beyond the earlier to occur of (i) 180 days after the effective date thereof and (ii) consummation of the distribution by the holders of the Registrable Securities included in such Registration Statement; provided, however, that any Stockholder owning Common Stock that has been included on such shelf Registration Statement may request that such Common Stock be removed from such Registration Statement, in which event the Corporation shall promptly either withdraw such Registration Statement or file a post-effective amendment to such Registration Statement removing such Common Stock.”

“(b) Notices. All notices required to be given hereunder shall be in writing and shall be deemed to be duly given if personally delivered, telecopied and confirmed, or mailed by certified mail, return receipt requested, or overnight delivery service with proof of receipt maintained, or e-mailed with read receipt requested, at the following address (or any other address that any such party may designate by written notice to the other parties):

If to the Corporation, to the address of its principal executive offices (and e-mail address set forth on the Corporation’s then-current website). If to any Stockholder, at such Stockholder’s address or email address, in each case as set forth on the records of the Corporation. Any such notice shall, if delivered personally, be deemed received upon delivery; shall, if delivered by telecopy, be deemed received on the first business day following confirmation; shall, if delivered by overnight delivery service, be deemed received the first business day after being sent; shall, if delivered by mail, be deemed received upon the earlier of actual receipt thereof or five business days after the date of deposit in the United States mail; and shall, if delivered by e-mail, be deemed received upon the earlier of actual receipt thereof, the receipt of a read receipt notice by the sender or the first business day after being sent.

2. Counterparts. This Amendment may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

3. Headings. The section and paragraph headings contained in this Amendment are for reference purposes only and shall not affect in any way the meaning or interpretation of this Amendment.

4. Governing Law. The provisions of this Amendment shall be governed by and construed in accordance with the laws of the State of New York (without giving effect to the choice of law principles thereof).

5. Severability. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction to be invalid, illegal, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions set forth herein shall remain in full force and effect and shall in no way be affected, impaired or invalidated, and the parties hereto shall use their best efforts to find and employ an alternative means to achieve the same or substantially the same result as that contemplated by such term, provision, covenant or restriction. It is hereby stipulated and declared to be the intention of the parties that they would have executed the remaining terms, provisions,

covenants and restrictions without including any of such that may be hereafter declared invalid, illegal, void or unenforceable.

6. Entire Agreement. This Amendment is intended by the parties as a final expression of their agreement, and is intended to be a complete and exclusive statement of the agreement and understanding of the parties hereto in respect of the subject matter contained herein. This Amendment supersedes all prior agreements and understandings between the parties with respect to such subject matter.

7. Consent to Jurisdiction. The parties hereto hereby irrevocably submit to the exclusive jurisdiction of the courts of the State of New York and the federal courts of the United States of America located in New York, and appropriate appellate courts therefrom, over any dispute arising out of or relating to this Amendment or any of the transactions contemplated hereby, and each party hereby irrevocably agrees that all claims in respect of such dispute or proceeding may be heard and determined in such courts. The parties hereby irrevocably waive, to the fullest extent permitted by applicable law, any objection which they may now or hereafter have to the laying of venue of any dispute arising out of or relating to this Amendment or any of the transactions contemplated hereby brought in such court or any defense of inconvenient forum for the maintenance of such dispute. Each of the parties hereto agrees that a judgment in any such dispute may be enforced in other jurisdictions by suit on the judgment or in any other manner provided by law. This consent to jurisdiction is being given solely for purposes of this Amendment and is not intended to, and shall not, confer consent to jurisdiction with respect to any other dispute in which a party to this Agreement may become involved.

Each of the parties hereto hereby consents to process being served by any party to this Agreement in any suit, action, or proceeding of the nature specified in the paragraph above by the mailing of a copy thereof in the manner specified by the notice provisions of the RRA, as hereby amended.

EACH OF THE PARTIES HERETO HEREBY IRREVOCABLY WAIVES ALL RIGHT TO TRIAL BY JURY IN ANY ACTION, PROCEEDING OR COUNTERCLAIM ARISING OUT OF OR RELATING TO THIS AMENDMENT.

8. RRA Affirmed. Except to the extent expressly provided herein, the RRA is not affected hereby and continues in full force and effect in accordance with its original terms.

[signature pages follow]

WARBURG PINCUS INTERNATIONAL PARTNERS, L.P.

By:	Warburg Pincus Partners LLC, its General Partner
By:	Warburg Pincus & Co., its Managing Member

By:	/s/ David Krieger
	Name:	David Krieger
	Title:	Partner


WARBURG PINCUS NETHERLANDS INTERNATIONAL PARTNERS I, C.V.

By:	Warburg Pincus Partners LLC, its General Partner
By:	Warburg Pincus & Co., its Managing Member

By:	/s/ David Krieger
	Name:	David Krieger
	Title:	Partner


WP-WPIP INVESTORS, L.P.

By:	WP-WPIP Investors LLC, its General Partner
By:	Warburg Pincus Partners LLC, its Sole Member
By:	Warburg Pincus & Co., its Managing Member

By:	/s/ David Krieger
	Name:	David Krieger
	Title:	Partner


WARBURG PINCUS PRIVATE EQUITY VIII, L.P.

By:	Warburg Pincus Partners LLC, its General Partner
By:	Warburg Pincus & Co., its Managing Member

By:	/s/ David Krieger
	Name:	David Krieger
	Title:	Partner


WARBURG PINCUS NETHERLANDS PRIVATE EQUITY VIII I, C.V.

By:	Warburg Pincus Partners LLC, its General Partner
By:	Warburg Pincus & Co., its Managing Member

By:	/s/ David Krieger
	Name:	David Krieger
	Title:	Partner

[Signature Page to Amendment No.1 to the RRA]

BLACKSTONE CAPITAL PARTNERS (CAYMAN) IV L.P.

By:	BLACKSTONE MANAGEMENT ASSOCIATES (CAYMAN) IV L.P., its general partner
By:	BCP IV GP L.L.C., its general partner

By:	/s/ David I. Foley
	Name:	David I. Foley
	Title:	Senior Managing Director


BLACKSTONE CAPITAL PARTNERS (CAYMAN) IV-A L.P.

By:	BLACKSTONE MANAGEMENT ASSOCIATES (CAYMAN) IV L.P., its general partner
By:	BCP IV GP L.L.C., its general partner

By:	/s/ David I. Foley
	Name:	David I. Foley
	Title:	Senior Managing Director


BLACKSTONE FAMILY INVESTMENT PARTNERSHIP (CAYMAN) IV-A L.P.

By:	BCP IV GP L.L.C., its general partner

By:	/s/ David I. Foley
	Name:	David I. Foley
	Title:	Senior Managing Director

[Signature Page to Amendment No.1 to the RRA]

BLACKSTONE PARTICIPATION PARTNERSHIP (CAYMAN) IV L.P.

By:	BCP IV GP L.L.C., its general partner

By:	/s/ David I. Foley
	Name:	David I. Foley
	Title:	Senior Managing Director


BLACKSTONE FAMILY INVESTMENT PARTNERSHIP (CAYMAN) IV-A SMD L.P.

By:	BLACKSTONE FAMILY GP L.L.C., its general partner

By:	/s/ David I. Foley
	Name:	David I. Foley
	Title:	Senior Managing Director

[Signature Page to Amendment No.1 to the RRA]

KOSMOS ENERGY LTD.


By:	/s/ W. Greg Dunlevy
	Name:	W. Greg Dunlevy
	Title:	Executive Vice President and Chief Financial Officer

WP-WPVIII INVESTORS, L.P.

By:	WP-WPVIII Investors LLC, its General Partner
By:	Warburg Pincus & Co., its Managing Member

By:	/s/ David Krieger
	Name:	David Krieger
	Title:	Partner