Exhibit10.51

FIRST AMENDMENT TOLIMITED LIABILITYCOMPANY AGREEMENT

This First Amendment (the‘‘**Amendment**’’) to theLimited Liability Company Agreement of Nalco LLC (the‘‘**Company**’’), dated as ofMay  17,  2004 (the‘‘**Agreement**’’), is made andentered into as of December  30,  2005 by and among theSponsor Members named in the Agreement. Capitalized terms not otherwisedefined herein shall have the meanings ascribed to such terms in theAgreement.

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

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

WHEREAS, inconnection with such event, the Company, pursuant to the stockholdersagreement dated as of November  16,  2004 by and among theCompany, the Sponsor Members and Nalco Holding Company, is obligated todistribute to each VCOC Member, through a redemption of its Class AUnits, the Common Shares beneficially owned by such VCOC Member, asdetermined by the Board and the pricing committee of the Board (suchredemption, the ‘‘**VCOCRedemption**’’);

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

WHEREAS, pursuant to Section 13.09 of thereof, the Agreementmay be amended by the agreement of two of the InvestorGroups;

NOW, THEREFORE, in consideration of the mutual covenantsand agreements contained herein and in the Agreement, and inconsideration of other good and valuable consideration, the receipt andsufficiency of which are hereby acknowledged, the parties hereto,intending to be legally bound, hereby agree to amend the Agreement asfollows:

1. Ownership Thresholds.    Withrespect to any provision of the Agreement which provides for thedetermination of an Investor Group’s beneficial ownershippercentage of Class A Units relative to such Investor Group’sInitial Equity Stake, such Investor Group’s number of‘‘Class A Units’’ shall be deemed toinclude both (a) the number of Class A Units that such Investor Groupowns and (b)a number of Class A Units having a value equivalent to thatof the number of Common Shares owned by such Investor Group (calculatedbased on the price per Class A Unit most recently determined by theBoard or the pricing committee of theBoard).

2. Entire Agreement.    The Agreement,this Amendment, the Management Members Agreement and the RegistrationRights Agreement set forth the entire understanding and agreement ofthe parties hereto and supersede any and all other understandings, termsheets, negotiations or agreements between the parties hereto relatingto the subject matter of this Agreement and the Registration RightsAgreement. In the event of any conflict between a provision of thisAgreement and a provision of the Management Members Agreement, therelevant provision of this Agreement, as amended, shall be deemed tocontrol and shall supersede the conflicting provision of the ManagementMembers Agreement.

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3. Governing Law.    THISAGREEMENT SHALL BE CONSTRUED IN ACCORDANCE WITH, AND GOVERNED BY, THELAWS OF THE STATE OF DELAWARE WITHOUT REGARD TO CONFLICTS OF LAWSPRINCIPLES WHICH WOULD RESULT IN THE APPLICATION OF THE LAWS OF ANOTHERJURISDICTION.

4. Severability.    In the eventthat any one or more of the provisions contained in this Agreementshall for any reason be held to be invalid, illegal or unenforceable,the same shall not affect any other provision of this Agreement, butthis Agreement shall be construed in a manner which, as nearly aspossible, reflects the original intent of theparties.

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

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

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**IN WITNESS WHEREOF,** the partieshereto have caused this Agreement to be duly executed as of the datefirst written above.

|  | **BLACKSTONE CAPITAL PARTNERS IVL.P.** |
|--|----------------------------------------|

|        |  |        |  |                                                                |  |                                                                                                                                                                                                    |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|----------------------------------------------------------------|--|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | Blackstone Management Associates IV L.L.C., its GeneralPartner |  |                                                                                                                                                                                               |
|   |  |   |  |                                                           |  |                                                                                                                                                                                               |  |   |
|   |  |   |  | By:                                                            |  | /s/ Chinh Chu                Name:   ChinhChuTitle:       Member |  |   |
|        |

|  | **BLACKSTONECAPITAL PARTNERS IV-AL.P.** |
|--|-----------------------------------------|

|        |  |        |  |                                                                |  |                                                                                                                                                                                                    |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|----------------------------------------------------------------|--|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | Blackstone Management Associates IV L.L.C., itsGeneral Partner |  |                                                                                                                                                                                               |
|   |  |   |  |                                                           |  |                                                                                                                                                                                               |  |   |
|   |  |   |  | By:                                                            |  | /s/ Chinh Chu                Name:   ChinhChuTitle:       Member |  |   |
|        |

|  | **BLACKSTONEFAMILY INVESTMENT PARTNERSHIP IV-AL.P.** |
|--|------------------------------------------------------|

|        |  |        |  |                                                                |  |                                                                                                                                                                                                    |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|----------------------------------------------------------------|--|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | Blackstone Management Associates IV L.L.C., its GeneralPartner |  |                                                                                                                                                                                               |
|   |  |   |  |                                                           |  |                                                                                                                                                                                               |  |   |
|   |  |   |  | By:                                                            |  | /s/ Chinh Chu                Name:   ChinhChuTitle:       Member |  |   |
|        |

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|  | **APOLLO INVESTMENTFUND V,L.P.** |
|--|----------------------------------|

|        |  |        |  |                                                                                                                                                                                                                 |  |        |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | Apollo Advisors V, L.P.Its general partner                                                                                                                                                                      |  |   |
|   |  |   |  |                                                                                                                                                                                                            |  |   |  |   |
|   |  | By:    |  | Apollo Capital Management V, Inc.Its generalpartner                                                                                                                                                             |  |   |
|   |  |   |  |                                                                                                                                                                                                            |  |   |  |   |
|   |  | By:    |  | /s/ JoshuaHarris                Name:    JoshHarrisTitle:       VicePresident |
|        |

|  | **APOLLO/NALCOACQUISITIONLLC** |
|--|--------------------------------|

|        |  |        |  |                                                                                                                                                                                                                |  |        |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | Apollo Management V, L.P., its Manager                                                                                                                                                                         |  |   |
|   |  |   |  |                                                                                                                                                                                                           |  |   |  |   |
|   |  | By:    |  | AIF V Management, Inc.,its General Partner                                                                                                                                                                     |  |   |
|   |  |   |  |                                                                                                                                                                                                           |  |   |  |   |
|   |  | By:    |  | /s/ JoshuaHarris                Name:   JoshHarrisTitle:       VicePresident |  |   |
|        |

|  | **AP NALCOLP** |
|--|----------------|

|        |  |        |  |                                                                                                                                                                                                                |  |        |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | Apollo Advisors V, L.P., its General Partner                                                                                                                                                                   |  |   |
|   |  |   |  |                                                                                                                                                                                                           |  |   |  |   |
|   |  | By:    |  | Apollo Capital Management V, Inc.,its GeneralPartner                                                                                                                                                           |  |   |
|   |  |   |  |                                                                                                                                                                                                           |  |   |  |   |
|   |  | By:    |  | /s/ JoshuaHarris                Name:   JoshHarrisTitle:       VicePresident |  |   |
|        |

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|  | **GOLDMAN SACHS DIRECTINVESTMENT FUND 2000,L.P.** |
|--|---------------------------------------------------|

|        |  |        |  |                                                      |  |                                                                                                                                |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|------------------------------------------------------|--|--------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | GS Employee Funds 2000 GP, L.L.C.,its GeneralPartner |  |                                                                                                                           |
|   |  |   |  |                                                 |  |                                                                                                                           |  |   |
|   |  |   |  | By:                                                  |  | /s/ Sanjeev K.Mehra                Name:Title: |  |   |
|        |

|  | **GSCAPITAL PARTNERS 2000,L.P.** |
|--|----------------------------------|

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

|  | **GS CAPITAL PARTNERS2000 OFFSHORE, L.P.** |
|--|--------------------------------------------|

|  |        |     |                                              |
|--|--------|-----|----------------------------------------------|
|  |   | By: | GS Advisors2000, L.L.C., its General Partner |

|  |        |                                                                                                                                                                                                                                                                                                              |
|--|--------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|  |   | By:/s/ Sanjeev K.Mehra                               Name:   SanjeevK. Mehra        Title: |

|  | **GS CAPITALPARTNERS 2000 GmbH & CO. BETEILIGUNGSKG** |
|--|-----------------------------------------------------------|

|        |  |        |  |                                                      |  |                                                                                                                                                                                         |  |        |  |  |  |  |  |  |  |  |  |  |
|--------|--|--------|--|------------------------------------------------------|--|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--------|--|--|--|--|--|--|--|--|--|--|
|   |  | By:    |  | Goldman Sachs Management GP GmbH, its GeneralPartner |  |                                                                                                                                                                                    |
|   |  |   |  |                                                 |  |                                                                                                                                                                                    |  |   |
|   |  |   |  | By:                                                  |  | /s/ Sanjeev K.Mehra                    Name:   Sanjeev K.MehraTitle: |  |   |
|        |

|  | **GS CAPITAL PARTNERS2000 EMPLOYEE****FUND,L.P.** |
|--|---------------------------------------------------|

|        |  |        |  |                                    |  |                                                                                                                                                                 |  |  |  |  |  |  |  |  |
|--------|--|--------|--|------------------------------------|--|-----------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--|--|--|--|--|--|--|
|   |  | By:    |  | GS Employee Funds 2000 GP, L.L.C., |
|   |  |   |  | its GeneralPartner                 |
|   |  |   |  |                               |  |                                                                                                                                                            |
|   |  |   |  | By:                                |  | /s/ Sanjeev K.Mehra                Name:   Sanjeev K.MehraTitle: |
|        |

|  | **NH ACQUISITIONLLC** |
|--|-----------------------|

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

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