Exhibit
10.51

FIRST AMENDMENT
 TO
LIMITED LIABILITY
COMPANY AGREEMENT

This First Amendment (the
‘‘Amendment’’) to the
Limited Liability Company Agreement of Nalco LLC (the
‘‘Company’’), dated as of
May  17,  2004 (the
‘‘Agreement’’), is made and
entered into as of December  30,  2005 by and among the
Sponsor Members named in the Agreement. Capitalized terms not otherwise
defined herein shall have the meanings ascribed to such terms in the
Agreement.

WHEREAS, pursuant to Section 3.14 of the Agreement, in
the event that the Company ceases to qualify as an
‘‘operating company’’ (as defined in 29
C.F.R. § 2510.3-101(c)), then the Company and each Member will
cooperate in good faith to take all reasonable action necessary to
provide that the investment (or at least 51% of the investment
valued at cost) of each Member that qualifies as a
‘‘venture capital operating company’’ (as
defined in 29 C.F.R. § 2510.3-101(d)) (a
‘‘VCOC Member’’) shall
continue to qualify as a ‘‘venture capital
investment’’ (as defined in 29 C.F.R. §
2510.3-101(d));

WHEREAS, upon the completion of the sale of
shares of common stock of Nalco Holding Company (the
‘‘Common Shares’’) by the
Company on the date hereof, the Company shall cease to qualify as an
‘‘operating company’’;

WHEREAS, in
connection with such event, the Company, pursuant to the stockholders
agreement dated as of November  16,  2004 by and among the
Company, the Sponsor Members and Nalco Holding Company, is obligated to
distribute to each VCOC Member, through a redemption of its Class A
Units, the Common Shares beneficially owned by such VCOC Member, as
determined by the Board and the pricing committee of the Board (such
redemption, the ‘‘VCOC
Redemption’’);

WHEREAS, in connection with
the VCOC Redemption and in accordance with Section 3.14 of the
Agreement, the parties desire to amend certain provisions of the
agreement to reflect the fact that the VCOC Members will hold Common
Shares directly and will no longer hold Class A Units;
and

WHEREAS, pursuant to Section 13.09 of thereof, the Agreement
may be amended by the agreement of two of the Investor
Groups;

NOW, THEREFORE, in consideration of the mutual covenants
and agreements contained herein and in the Agreement, and in
consideration of other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto,
intending to be legally bound, hereby agree to amend the Agreement as
follows:

1. Ownership Thresholds.    With
respect to any provision of the Agreement which provides for the
determination of an Investor Group’s beneficial ownership
percentage of Class A Units relative to such Investor Group’s
Initial Equity Stake, such Investor Group’s number of
‘‘Class A Units’’ shall be deemed to
include both (a) the number of Class A Units that such Investor Group
owns and (b)a number of Class A Units having a value equivalent to that
of the number of Common Shares owned by such Investor Group (calculated
based on the price per Class A Unit most recently determined by the
Board or the pricing committee of the
Board).

2. Entire Agreement.    The Agreement,
this Amendment, the Management Members Agreement and the Registration
Rights Agreement set forth the entire understanding and agreement of
the parties hereto and supersede any and all other understandings, term
sheets, negotiations or agreements between the parties hereto relating
to the subject matter of this Agreement and the Registration Rights
Agreement. In the event of any conflict between a provision of this
Agreement and a provision of the Management Members Agreement, the
relevant provision of this Agreement, as amended, shall be deemed to
control and shall supersede the conflicting provision of the Management
Members Agreement.

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3. Governing Law.    THIS
AGREEMENT SHALL BE CONSTRUED IN ACCORDANCE WITH, AND GOVERNED BY, THE
LAWS OF THE STATE OF DELAWARE WITHOUT REGARD TO CONFLICTS OF LAWS
PRINCIPLES WHICH WOULD RESULT IN THE APPLICATION OF THE LAWS OF ANOTHER
JURISDICTION.

4. Severability.    In the event
that any one or more of the provisions contained in this Agreement
shall for any reason be held to be invalid, illegal or unenforceable,
the same shall not affect any other provision of this Agreement, but
this Agreement shall be construed in a manner which, as nearly as
possible, reflects the original intent of the
parties.

5. Counterparts.    This Agreement may
be executed in counterparts, each of which shall be deemed an original,
and all of which together shall constitute a single
agreement.

6. Full Force and Effect of
Agreement.    The Agreement, as modified by this Amendment, and
as this Amendment is made a part thereof, shall remain in full force
and effect.


[The remainder of this page
intentionally left blank]


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IN WITNESS WHEREOF, the parties
hereto have caused this Agreement to be duly executed as of the date
first written above.


		BLACKSTONE CAPITAL PARTNERS IV
L.P.








																			
	 		By:		Blackstone Management Associates IV L.L.C.,
 its General
Partner		 
	 		 		 		 		 
	 		 		By:		/s/ Chinh Chu                

Name:   Chinh
Chu
Title:       Member		 
	







		BLACKSTONE
CAPITAL PARTNERS IV-A
L.P.








																			
	 		By:
		Blackstone Management Associates IV L.L.C.,
 its
General Partner		 
	 		 		 		 		 
	 		 		By:		/s/ Chinh Chu                

Name:   Chinh
Chu
Title:       Member		 
	







		BLACKSTONE
FAMILY INVESTMENT
 PARTNERSHIP IV-A
L.P.








																			
	 		By:		Blackstone Management Associates IV L.L.C.,
 its General
Partner		 
	 		 		 		 		 
	 		 		By:		/s/ Chinh Chu                

Name:   Chinh
Chu
Title:       Member		 
	






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		APOLLO INVESTMENT
FUND V,
L.P.








																			
	 		By:		Apollo Advisors V, L.P.
Its general partner		 
	 		 		 		 		 
	 		By:		Apollo Capital Management V, Inc.
Its general
partner		 
	 		 		 		 		 
	 		By:		/s/ Joshua
Harris                

Name:    Josh
Harris
Title:       Vice
President
	







		APOLLO/NALCO
ACQUISITION
LLC








																			
	 		By:		Apollo Management V, L.P., its Manager		 
	 		 		 		 		 
	 		By:		AIF V Management, Inc.,
its General Partner		 
	 		 		 		 		 
	 		By:		/s/ Joshua
Harris                

Name:   Josh
Harris
Title:       Vice
President		 
	







		AP NALCO
LP








																			
	 		By:		Apollo Advisors V, L.P., its General Partner		 
	 		 		 		 		 
	 		By:		Apollo Capital Management V, Inc.,
its General
Partner		 
	 		 		 		 		 
	 		By:		/s/ Joshua
Harris                

Name:   Josh
Harris
Title:       Vice
President		 
	






4









		GOLDMAN SACHS DIRECT
INVESTMENT
 FUND 2000,
L.P.








																			
	 		By:		GS Employee Funds 2000 GP, L.L.C.,
its General
Partner		 
	 		 		 		 		 
	 		 		By:		/s/ Sanjeev K.
Mehra                

Name:
Title:		 
	







		GS
CAPITAL PARTNERS 2000,
L.P.








																			
	 		By:		GS Advisors 2000, L.L.C.,
its General Partner		 
	 		 		 		 		 
	 		 		By:		/s/ Sanjeev K.
Mehra                

Name:   Sanjeev K.
Mehra
Title:		 
	







		GS CAPITAL PARTNERS
2000 OFFSHORE, L.P.




				
		 	By:	GS Advisors
2000, L.L.C.,
 its General Partner


			
		 	By:
/s/ Sanjeev K.
Mehra                       

        Name:   Sanjeev
K. Mehra
        Title:



		GS CAPITAL
PARTNERS 2000 GmbH & CO. BETEILIGUNGS
KG








																			
	 		By:		Goldman Sachs Management GP GmbH,
 its General
Partner		 
	 		 		 		 		 
	 		 		By:		/s/ Sanjeev K.
Mehra                    

Name:   Sanjeev K.
Mehra
Title:		 
	







		GS CAPITAL PARTNERS
2000 EMPLOYEE 


FUND,
L.P.








															
	 		By:		GS Employee Funds 2000 GP, L.L.C.,
	 		 		its General
Partner
	 		 		 		 
	 		 		By:		/s/ Sanjeev K.
Mehra                

Name:   Sanjeev K.
Mehra
Title:
	







		NH ACQUISITION
LLC








																			
	 		By:		GS Advisors 2000, L.L.C.,
 its Manager		 
	 		 		 		 		 
	 		 		By:		/s/ Sanjeev K.
Mehra                

Name:   Sanjeev K.
Mehra
Title:		 
	






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