Exhibit 3.61

ENSCO DRILLING MEXICO LLC AMENDED LIMITED LIABILITY COMPANY AGREEMENT This Amended Limited Liability Company Agreement (the "Agreement"}, effective as of the 31 st day of March 2010, is made by Ensco Holdco Limited, an England and Wales Private Limited Company, having a registered office at 100 New Bridge Street (the "Sole Member''). WHEREAS, ENSCO Offshore Company caused ENSCO Drilling Mexico LLC (the "Company") to be formed under the Limited Liability Company Act of the State of Delaware (the "Act'') and any future amendments thereto, a copy of the Certificate of Formation (the "Certificate") being attached hereto as Exhibit A; and WHEREAS, ENSCO International Incorporated, and all of its direct and indirect subsidiaries, completed a series of redomestication and reorganization transactions including a contribution of the membership interest in the Company; and WHEREAS, Ensco Holdco Limited became the Sole Member of the Company on the 31 st day of March 2010 by way of a contribution of membership interest. NOW, THEREFORE, the Sole Member agrees as follows: Article I - Limited Liability Company Agreement Section 1.01 This Agreement is an Amended Limited Liability Company Agreement under and as provided in the Act. Section 1.02 Except as otherwise provided by the Act, the debts, obligations and liabilities of the Company, whether arising strictly at law, in contract, tort or otherwise, shall be the debts, obligations and liabilities solely of the Company, and the Member shall not be obligated personally for any such debts, obligations or liabilities solely by reason of being a Member. Article II - Organizational and Other Matters Section 2.01 The Company was formed as a limited liability company under the provisions of the Act by the filing of the Certificate with the Secretary of State of the State of Delaware on 22 June 2007. The rights and liabilities of the Member shall be as provided in the Act, except as otherwise expressly provided herein. F:\USERS\jengllsh\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

Section 2.02 The name of the Company is ENSCO Drilling Mexico LLC, and the business of the Company shall be conducted under such name. Section 2.03 The principal office of the Company shall be located at 500 N. Akard Street, Suite 4300, Dallas, Texas 75201, or such other place as the Sole Member may, from time to time, determine or designate. Section 2.04 The Company may, from time to time, apply for and qualify to do business in any state or territory of the United States or any foreign country, commonwealth, kingdom, sovereign state or territory. Article Ill - Members Section 3.01 Concurrent with the execution of this Agreement, Ensco Holdco Limited shall become and be the Sole Member of the Company. Article IV - Duration of the Company Section 4.01 The Company will have a perpetual existence. Article V - Purpose and Business of the Company Section 5.01 The Company may conduct any lawful business purpose or activity permitted by the Act. Section 5.02 The Company shall have the power to do any and all acts reasonably necessary, appropriate, proper, advisable, incidental or convenient to or for the furtherance of the purpose and business described herein and for the protection and benefit of the Company. 2 F:\USERS~english\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

Article VI - Capital Contributions Section 6.01 The Sole Member's capital contribution is US$100 in cash and the Sole Member shall own one hundred percent (100%) of the equity interest in the Company. Thereafter, unless otherwise determined by the Sole Member, the Sole Member shall have no further obligation to make any additional contributions to the Company. Section 6.02 The Sole Member's capital contributions to the Company may be increased by any additional amounts which the Sole Member deems appropriate and necessary and the Sole Member shall proportionally share in any profits of the Company. Likewise, the Sole Member's capital contributions may be decreased by any additional amounts which the Sole Member deems appropriate and necessary and the Sole Member shall proportionally share in any losses of the Company. Section 6.03 The Company shall not pay interest on the Sole Member's capital contribution(s) to the Company. Article VII - Management of the Company Section 7 .01 The business and affairs of the Company shall be managed by the Sole Member. The Sole Member shall have complete and exclusive discretion with regard to the management and control of the affairs and business of the Company, and shall posses all powers necessary, convenient or appropriate to carry out the purposes and business of the Company, including without limitation, doing all things and taking all actions necessary to carry out the terms and provisions of this Agreement and delegating any or all of its powers, right and obligations under this Agreement and appointing managers and/or officers of the Company to perform acts or services for and on behalf of the Company as the Sole Member shall deem appropriate in its sole discretion. Section 7 .02 The Sole Member shall have the power to appoint any person or persons as managers, officers and/or agents to act for and on behalf of the Company with such titles, if any, as the Sole Member, in its sole discretion, deems appropriate, and to 3 F:\USERS\jenglish\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

delegate to such managers, officers and/or agents powers as it deems appropriate or necessary or such powers as granted to the Sole Member hereunder. Any decision or act of a manager, officer or agent appointed under this Section 7.02 within the scope of the manager's, officer's or agent's designated or delegated authority shall control and bind the Company. Unless the authority of the manager or agent designated as an officer in question is limited by the Sole Member, any manager or agent designated as an officer by the Sole Member shall have the same authority to act for and on behalf of the Company as the corresponding officer of a Delaware corporation would typically have to act for a Delaware corporation in the absence of a specific delegation of authority. The Sole Member, in its sole discretion, may by vote, resolution, or otherwise ratify any act previously taken by any manager, officer or agent acting on behalf of the Company. Section 7 .03 The Sole Member may fill any managerial vacancy, may remove a manager from office with or without cause, and may modify or terminate the responsibilities and authority of managers, agents or persons designated as officers. A manager, agent or designated officer may resign without liability to the Company. A manager, agent or officer removed from office by the Sole Member will have no claim against the Company by reason of such removal. Section 7 .04 The Sole Member shall have the power to establish a bank account or accounts in the name of the Company with such banking or financial institutions as the Sole Member shall deem advisable for the expeditious handling of the Company's funds. The Sole Member may grant authority to establish a bank account or accounts in the name of the Company to managers, agents or persons designated as officers. The Sole Member or any manager, agent or officer appointed by the Sole Member may designate signatories on bank accounts established in the name of the Company as the manager, agent or officer may deem appropriate. Article VIII - Distributions Section 8.01 The Company may distribute "Excess Cash" (as herein defined) to the Sole Member in the same percentage as the Sole Member's interest in the profits of the Company. For purposes hereof, "Excess Cash" shall mean cash in excess of the amount determined by the Sole Member required to pay current liabilities and other obligations of the Company as they may become due, including, without limitation, reserves for any contingencies. 4 F:\USERS\jenglish\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

Section 8.02 Distributions of Excess Cash shall be made, from time to time, as determined by the Sole Member. Article IX - Limitations on Acts by Managers and/or Officers Section 9.01 Sole Member written authorization and approval shall be required to: (i) purchase, lease or otherwise acquire any property, right or other asset having a value, either combined or separate, in excess of US$25,000, (ii) sell, lease or otherwise dispose of any property, right or other asset having a value of more than US$25,000, (iii) borrow, lend, issue a guarantee or encumber any property, right or other asset of the Company, or (iv) make an assignment for the benefit of creditors or seek relief under any bankruptcy, insolvency or similar law. Section 9.02 A manager, agent or officer of the Company may not and will not have the power to delegate any of his or her rights or powers to manage and control the business and affairs of the Company, except as otherwise authorized by the Sole Member. Article X - Dissolution and Liquidation Section 10.01 The Company may be dissolved and its affairs may be wound-up on the approval by the Sole Member. Section 10.02 Upon dissolution, the Company shall cease carrying on its business but shall not terminate until the winding-up of the affairs of the Company is completed, the assets of the Company shall have been distributed as provided below in the Section 10.03 of this Article X, and a Certificate of Cancellation of the Company pursuant to the Act has been filed with the Secretary of State of the State of Delaware. Section 10.03 Upon dissolution of the Company, sole and plenary authority to effectuate the liquidation of the assets of the Company shall be vested in the Sole Member, which shall have full power and authority to sell, assign and/or encumber any and all of the 5 F:\USERS\jenglish\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

Company's assets and to wind-up and liquidate the affairs of the Company in an orderly and business-like manner. The proceeds of the liquidation of the assets of the Company distributed upon dissolution and winding-up of the Company shall be applied in the following order of priority: (a) First, to the creditors of the Company in the order of priority by law, in satisfaction of all liabilities and obligations of the Company (of any nature whatsoever, including, without limitation, fixed or contingent, matured or unmatured, legal or equitable, secured or unsecured), whether by payment or the making of reasonable provision for payment thereof; and (b) Thereafter, to the Sole Member. Section 10.04 The winding-up of the Company shall be completed when all debts, liabilities and obligations of the Company have been paid and discharged, or reasonably adequate provision therefor has been made, and all of the remaining property and assets of the Company have been distributed to the Sole Member. Upon the completion of the winding-up of the Company, a Certificate of Cancellation of the Company shall be filed with the Secretary of State of the State of Delaware. Article XI - Indemnity Section 11.01 The Company shall indemnify the Sole Member, its managers, directors, officers, employees and agents, and each of the Company's managers, directors, officers, employees and agents against any claim, demand, liability, fine or expense (including, without limitation, reasonable legal fees and disbursements, court costs and costs of any appellate proceedings) arising out of any act or omission by the Sole Member, its managers, directors, officers, employees or agents or any manager, director, officer, employee or agent of the Company done in good faith and reasonably believed by the Sole Member, its managers, directors, officers, employees or agents or any manager, director, officer, employee or agent of the Company to be in the best interest of the Company, provided that in the case of any fine, the Sole Member, its managers, directors, officers, employees or agents or any manager, director, officer, employee or agent of the Company, had no reasonable cause to believe its conduct was unlawful. Section 11.02 The Company will, as authorized and approved by the Sole Member, pay the expense of any manager, officer, employee or agent of the Company seeking indemnity in advance of final disposition of any matter, subject to the receipt of any 6 F:\USERS~english\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

undertaking from the manager, officer, employee or agent satisfactory to the Sole Member to repay the amount advanced if it is ultimately determined that the manager, officer, employee or agent seeking indemnity is not entitled to indemnification. Article XII - Accounting Section 12.01 The Company's fiscal year will be the calendar year and shall end on December 31. Article XIII - Amendment; Admission of New and Additional Members Section 13.01 This Agreement may be amended only by an instrument in writing signed by the Sole Member. Section 13.02 The Certificate of Formation of the Company may be amended only by an instrument in writing signed by the Sole Member. Section 13.03 A person or entity may not become a Member in the Company unless the person's or entity's admission is approved by the Sole Member, as evidenced by an amendment to this Agreement signed by the Sole Member and by the person or entity representative electing to become a Member. Article XIV - Severability Section 14.01 If any provision of this Agreement or the application of any such provision to any individual, corporation or other entity or to any circumstance is held to be invalid, the remainder of this Agreement, and the application of such provision other than to the extent it is held invalid, will not be invalidated or affected hereby. 7 F:\USERS~english\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

Article XV - Governing Law Section 15.01 This Agreement and the rights and obligations of the Sole Member of the Company shall be governed by and construed in accordance with the laws of the State of Delaware. For purposes of any proceeding involving this Agreement or any of the rights or obligations of the Sole Member of the Company, the Sole Member hereby submits to the non-exclusive jurisdiction of the courts of the State of Delaware, and agrees not to raise and waives any objection to or defense based upon the venue of any such court or based upon forum non conveniens. The Sole Member agrees not to bring action or other proceeding with respect to this Agreement in any other court unless such courts of the State of Delaware determine that they do not have jurisdiction in the matter. Section 15.02 The Sole Member hereby designates The Corporation Trust Company (CT Corporation System), with offices at 1209 N. Orange Street, Wilmington, Delaware 19801, its agent for service of process for purposes of any proceeding with respect to this Agreement or with respect to any of the rights or obligations of the Sole Member of the Company. At all times until the dissolution and completion of the winding-up of the Company and the filing of a Certificate of Cancellation of the Company's Certificate of Formation, the Sole Member will maintain an agent for service of process in the State of Delaware. The Company will pay the cost of maintaining the agent for service of process in Delaware, but if for any reason the Company fails to pay the cost, the Sole Member will pay such cost. Article XVI - Entire Agreement Section 16.01 This Agreement contains the entire understanding of the parties with respect to the subject matter of the Agreement, and it supersedes all prior understandings and agreements, if any, whether written or oral, and all prior dealings of the parties with respect to the subject matter hereof. Article XVII - Section Headings Section 17.01 Section headings are for reference purposes only and will not in any way affect the meaning or interpretation of any provision of this Agreement. 8 F:\USERS\jenglish\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

IN WITNESS WHEREOF, Ensco Holdco Limited, as the Sole Member, has executed this Agreement as of the day and year first above written. Ensco Holdco Limited, as the Sole Member By: ____ --L-___ _ Name: Title: By: __________ _ Name: Title: Dean Alan Kewish Secretary This Amended Limited Liability Company Agreement may be executed in multiple counterparts, all of which taken together shall constitute one document, and any signatory may sign any such counterpart. An executed counterpart transmitted by facsimile (fax) or email shall be deemed to be an original. 9 F:\USERS\jenglish\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

IN WITNESS WHEREOF, Ensco Holdco Limited, as the Sole Member, has executed this Agreement as of the day and year first above written. Ensco Holdco Limited, as the Sole Member By: ________ _ Name: John Mark Burns Title: Director Name: Title: Dean Alan Kewish Secretary This Amended Limited Liability Company Agreement may be executed in multiple counterparts, all of which taken together shall constitute one document, and any signatory may sign any such counterpart. An executed counterpart transmitted by facsimile (fax) or email shall be deemed to be an original. 9 F:\USERS\jenglish\Office\ENSCO Drilling Mexico LLC\Amended LLC Agreement

Exhibit 3.62

EXHIBIT A STATE OF DELAWARE LIMITED LIABILITY COMPANY CERTIFICATE OF FORMATION OF ENSCO DRILLING MEXICO LLC State o£ .De.lawa:re Seo,mtaJ:y o£ stat.a D:Lviaion of Corporation., Deliwred 06:41 PM 06/22/2001 FIL1lD 06:30 PN 06/22/2001 SRV 010143395 - 4316922 FILE 1. The name of the Umlted UabiBty Company Is ENSCO Drllllng Mexico LLC. 2. The name and address of Its registered agent In the State of Delaware Is: The Corporation Trust Corrc>any (CT Corporation System), 1209 N. Orange Street, Wilmington, Delaware 19801. 3. The Umited Liability Company shall have a perpetual exts1&nce. IN wrrNESS WHEREOF, the undersigned has executed this Certificate of Formation of ENSCO Drllllng Mexico LLC this 22"" day of June, 2007. Authorized Person F:\USERS\lllngllltl\Olflo9\ENSCO Df1lllng MtldCO Ll.C\CwUa:lle of Fonnauon.ot.azm