Exhibit 5.1

Our ref

SMC/713299-000001/52437897v5

Ocean Rig UDW Inc.
PO Box 309, Ugland House
Grand Cayman
KY1-1104
Cayman Islands

27 September 2017

Dear Sirs

Ocean Rig UDW Inc.

We have acted as Cayman Islands counsel to Ocean Rig UDW Inc. (the "Company") to provide this legal opinion in connection with the Company's registration statement on Form F-1, including all amendments or supplements thereto, filed with the United States Securities and Exchange Commission (the "Commission") under the United States Securities Act of 1933, as amended (the "Act") (including its exhibits, the "Registration Statement") relating to, among other things, 35,260,089 common shares of the Company of par value US$0.01 per share (the "Common Shares") that have been issued to, and which may be offered by, the selling shareholders identified in the Registration Statement (together, the "Selling Shareholders"). This opinion is given in accordance with the terms of the Legal Matters section of the Registration Statement.

1	Documents Reviewed

We have reviewed originals, copies, drafts or conformed copies of the following documents:

1.1	The Certificate of Registration by Way of Continuation dated 14 April 2016 and the Memorandum and Articles of Association of the Company as adopted on 4 July 2016 as amended by special resolution dated 24 April 2017 (the "Memorandum and Articles").

1.2	The minutes of the meeting of the board of directors of the Company held on 18 September 2017 (the "Minutes") and the corporate records of the Company maintained at its registered office in the Cayman Islands.

1.3	The Register of Members of the Company dated 25 September 2017 as provided to us by the registrar and transfer agent of the Company.

1.4	A certificate of good standing with respect to the Company issued by the Registrar of Companies (the "Certificate of Good Standing").

1.5	A certificate from a director of the Company a copy of which is attached to this opinion letter (the "Director's Certificate").

1.6	The Registration Statement.

2	Assumptions

The following opinions are given only as to, and based on, circumstances and matters of fact existing and known to us on the date of this opinion letter. These opinions only relate to the laws of the Cayman Islands which are in force on the date of this opinion letter. In giving the following opinions, we have relied (without further verification) upon the completeness and accuracy, as at the date of this opinion letter, of the Director's Certificate and the Certificate of Good Standing. We have also relied upon the following assumptions, which we have not independently verified:

2.1	Copies of documents, conformed copies or drafts of documents provided to us are true and complete copies of, or in the final forms of, the originals.

2.2	All signatures, initials and seals are genuine.

2.3	No invitation has been made by or on behalf of the Company to the public in the Cayman Islands to subscribe for any of the Shares.

2.4	No monies paid to or for the account of any party under the Documents represent or will represent criminal property or terrorist property (as defined in the Proceeds of Crime Law (2017 Revision) and the Terrorism Law (2017 Revision), respectively).

Save as aforesaid we have not been instructed to undertake and have not undertaken any further enquiry or due diligence in relation to the transaction the subject of this opinion letter.

Opinions

Based upon, and subject to, the foregoing assumptions and the qualifications set out below, and having regard to such legal considerations as we deem relevant, we are of the opinion that, based solely of our inspection of the Register of Members, the Common Shares have been duly authorised, legally issued and are fully paid and non-assessable.

Under Cayman Islands law, the register of members (shareholders) is prima facie evidence of title to shares and this register would not record a third party interest in such shares. However, there are certain limited circumstances where an application may be made to a Cayman Islands court for a determination on whether the register of members reflects the correct legal position. Further, the Cayman Islands court has the power to order that the register of members maintained by a company should be rectified where it considers that the register of members does not reflect the correct legal position. As far as we are aware, such applications are rarely made in the Cayman Islands, but if such an application were made in respect of the Company's Common Shares, then the validity of such shares may be subject to re-examination by a Cayman Islands court.

Except as specifically stated herein, we make no comment with respect to any representations and warranties which may be made by or with respect to the Company in any of the documents or instruments cited in this opinion letter or otherwise with respect to the commercial terms of the transactions the subject of this opinion letter.

In this opinion letter, the phrase "non-assessable" means, with respect to the Shares in the Company, that a shareholder shall not, solely by virtue of its status as a shareholder, be liable for additional assessments or calls on the Shares by the Company or its creditors (except in exceptional circumstances, such as involving fraud, the establishment of an agency relationship or an illegal or improper purpose or other circumstance in which a court may be prepared to pierce or lift the corporate veil).

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the reference to our firm under the heading "Legal Matters" in the prospectus included in the Registration Statement. In providing our consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the Rules and Regulations of the Commission thereunder.

This opinion letter is limited to the matters detailed herein and is not to be read as an opinion with respect to any other matter.

Yours faithfully

/s/ Maples and Calder

Maples and Calder

Ocean Rig UDW Inc.

PO Box 309, Ugland House

Grand Cayman

KY1-1104

Cayman Islands

27 September 2017

To:	Maples and Calder PO Box 309, Ugland House Grand Cayman KY1-1104 Cayman Islands

Dear Sirs

Ocean Rig UDW Inc. (the "Company")

I, being a director of the Company, am aware that you are being asked to provide a legal opinion (the "Opinion") in relation to certain aspects of Cayman Islands law. Capitalised terms used in this certificate have the meaning given to them in the Opinion. I hereby certify that:

1	The Current Memorandum and Articles remain in full force and effect and are unamended.

2	The Company has not entered into any mortgages or charges over its property or assets other than those entered in the register of mortgages and charges of the Company.

The Minutes are a true and correct record of the proceedings of such meeting, which was duly convened and held, and at which a quorum was present throughout. The resolutions contained in the Minutes were duly adopted, are in full force and effect at the date hereof and have not been amended, varied or revoked in any respect.

The authorised share capital of the Company is US$10,005,000,000 divided into 1,000,000,000,000 common shares of a par value of US$0.01 each and 500,000,000 preferred shares of a par value of US$0.01 each. The issued share capital of the Company is 86,262,278 common shares, which have been issued and are fully paid up.

The shareholders of the Company (the "Shareholders") have not restricted the powers of the directors of the Company in any way. There is no contractual or other prohibition or restriction (other than as arising under Cayman Islands law) binding on the Company prohibiting or restricting it from entering into and performing its obligations under the Registration Statement and any documents in connection therewith.

6	The directors of the Company at the date of the Resolutions and at the date of this certificate were and are as follows: George Economou, Chrysoula Kandylidis, Vassilis Karamitsanis, Georgios Kokkodis, John Liveris and Michael Pearson.

The minute book and corporate records of the Company as maintained at its registered office in the Cayman Islands and made available to you are complete and accurate in all material respects, and all minutes and resolutions filed therein represent a complete and accurate record of all meetings of the Shareholders and directors (or any committee thereof) of the Company (duly convened in accordance with the Memorandum and Articles) and all resolutions passed at the meetings or passed by written resolution or consent, as the case may be.

Prior to, at the time of, and immediately following the approval of the transactions the subject of the Registration Statement the Company was, or will be, able to pay its debts as they fell, or fall, due and has entered, or will enter, into the transactions the subject of the Registration Statement for proper value and not with an intention to defraud or wilfully defeat an obligation owed to any creditor or with a view to giving a creditor a preference.

Each director of the Company considers the transactions contemplated by the Registration Statement to be of commercial benefit to the Company and has acted in good faith in the best interests of the Company, and for a proper purpose of the Company, in relation to the transactions which are the subject of the Opinion.

10	To the best of my knowledge and belief, having made due inquiry, the Company is not the subject of legal, arbitral, administrative or other proceedings in any jurisdiction.

11	To the best of my knowledge and belief, having made due inquiry, there are no circumstances or matters of fact existing which may properly form the basis for an application for an order for rectification of the register of members of the Company.

12	The Registration Statement has been, or will be, authorised and duly executed and delivered by or on behalf of all relevant parties in accordance with all relevant laws.

13	The Common Shares to be issued pursuant to the Registration Statement have been, or will be, duly registered, and will continue to be registered, in the Company's register of members (shareholders).

I confirm that you may continue to rely on this certificate as being true and correct on the day that you issue the Opinion unless I shall have previously notified you in writing personally to the contrary.

Signature:	/s/ Michael Pearson
Name:	Michael Pearson
Title:	Director