Exhibit 5.1

June 17, 2010

Schlumberger Limited

5599 San Felipe

17th Floor

Houston, Texas 77056

Ladies and Gentlemen:

In connection with the Registration Statement on Form S-4 (the “Registration Statement”) being filed by Schlumberger N.V. (Schlumberger Limited), a corporation organized under the laws of the Netherlands Antilles (“Schlumberger”), with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of shares of common stock, par value $0.01 per share (“Common Stock”), of Schlumberger (the “Shares”) to be issued in connection with the merger of Turnberry Merger Sub Inc., a wholly owned subsidiary of Schlumberger, with and into Smith International, Inc. (“Smith”), pursuant to the Agreement and Plan of Merger dated as of February 21, 2010 among Schlumberger, Turnberry Merger Sub Inc., and Smith (the “Merger Agreement”), certain legal matters in connection with the Shares are being passed on for you by me. At your request, this opinion is being furnished for filing as Exhibit 5 to the Registration Statement.

I am a member of the bar of the State of Texas, and not of any other jurisdiction. I am not admitted to practice in, nor do I hold myself out as an expert on the laws of, the Netherlands Antilles. I have, however, consulted with the law firm of STvB, counsel qualified to practice in the Netherlands Antilles. Insofar as the opinions expressed below involve conclusions as to matters governed by the laws of the Netherlands Antilles, I am relying on the opinion of such counsel.

In my capacity as General Counsel and Secretary of Schlumberger, I am familiar with the Articles of Incorporation and Amended and Restated By-Laws of Schlumberger, each as amended to date; have familiarized myself with the matters discussed herein; and have examined all statutes and other records, instruments and documents pertaining to Schlumberger and the matters discussed herein that I deem necessary to examine for the purpose of this opinion. I have assumed that all signatures on all documents examined by me are genuine, that all documents submitted to me as originals are accurate and complete, that all documents submitted to me as copies are true and correct copies of the originals thereof and that all information submitted to me was accurate and complete.

In rendering this opinion, I have assumed that prior to the issuance of any of the Shares (i) the Registration Statement, as then amended, will have become effective under the Securities Act and such effectiveness shall not have been terminated or rescinded, (ii) the stockholders of Smith will have adopted the Merger Agreement, and (iii) the other conditions to consummating the transactions contemplated by the Merger Agreement will have been satisfied and such transactions are consummated.

Based on my examination as aforesaid, I am of the opinion that the Shares have been duly authorized by all necessary corporate action on the part of Schlumberger. Upon issuance and delivery in accordance with the terms and conditions of the Merger Agreement, such Shares will be validly issued, fully paid and nonassessable.

I consent to the filing of this opinion as an exhibit to the Registration Statement. In addition, I consent to the reference to me under the caption “Legal Matters” in the proxy statement/prospectus constituting a part of the Registration Statement. In giving such consent, I do not thereby concede that I am within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Alexander C. Juden, Esq.

Alexander C. Juden, Esq.