If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of ss.240.13D-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box ☐.

The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

(1) George Economou, the Chairman, Chief Executive Officer and a Class A Director, of Ocean Rig UDW Inc. (the "Issuer") may be deemed to beneficially own 8,524,793 common shares of the Issuer through Prime Cap Shipping Inc., a Cayman Islands corporation controlled by Mr. Economou, as set forth below. Additionally, Mr. Economou may be deemed to beneficially own 803 common shares of the Issuer, as follows: (a) 704 common shares of the Issuer through Sphinx Investment Corp., a Marshall Islands corporation controlled by Mr. Economou; (b) 65 common shares of the Issuer through Azara Services S.A., a Marshall Islands corporation controlled by Mr. Economou; (c) 8 common shares of the Issuer through Elios Investments Inc., a wholly owned subsidiary of the Entrepreneurial Spirit Foundation, a Lichtenstein foundation, or the Foundation, the beneficiaries of which are Mr. Economou and members of Mr. Economou's family; (d) 15 of common shares of the Issuer through Entrepreneurial Spirit Holdings Inc., a Liberian corporation that is wholly owned by the Foundation; and (e) 11 common shares of the Issuer through Fabiana Services S.A., a Marshall Islands corporation, of which Mr. Economou is the controlling person.

(2) Based on 91,567,982 common shares outstanding as of September 7, 2018.

Item 1.  Security and Issuer.

This statement on Schedule 13D relates to the common shares, par value $0.01 per share (the "Common Shares") Ocean Rig UDW Inc., an exempted company incorporated with limited liability under the laws of the Cayman Islands (the "Issuer").  The address of the Issuer's principal executive office is c/o Ocean Rig Cayman Management Services SEZC Limited, 3rd Floor Flagship Building, Harbour Drive, Grand Cayman, Cayman Islands.

Item 2.  Identity and Background.

Item 4.  Purpose of Transaction.

Item 4 of the Schedule 13D is hereby amended and supplemented by the following:

On September 3, 2018, Transocean Ltd. ("Transocean"), Transocean Oceanus Holdings Limited, a direct, wholly owned subsidiary of Transocean ("HoldCo") and Transocean Oceanus Limited, an indirect, wholly owned subsidiary of Transocean ("Merger Sub"), entered into an agreement and plan of merger (the "Merger Agreement") with the Issuer.  The Merger Agreement provides that, upon the terms and subject to the conditions set forth therein, Merger Sub will merge with and into the Issuer, with the Issuer surviving the merger as an indirect, wholly owned subsidiary of Transocean (the "Merger").  Concurrent with the execution of the Merger Agreement, and as a condition to Transocean's willingness to enter into the Merger Agreement, the Reporting Persons entered into a voting and support agreement with Transocean (the "Voting Agreement").

Pursuant to the Voting Agreement, at any meeting of Ocean Rig shareholders during which a vote for the approval and adoption of the Merger Agreement and the other transactions contemplated by the Merger Agreement is to occur, the Reporting Persons have agreed to be present (in person or by proxy) and vote, or give written consent covering, all of its Ocean Rig shares as follows, among others:

(a) in favor of approval and adoption of the Merger Agreement and the transactions contemplated by the Merger Agreement;

(b) in favor of any other matter necessary or appropriate to consummate the transactions contemplated by the Merger Agreement;

(c) against any Acquisition Proposal (as defined in the Merger Agreement) or any other action, proposal, agreement or transaction made in opposition to or competition with, or inconsistent with, the Merger Agreement and the transactions contemplated by the Merger Agreement; and

(d) against any other action or agreement that would reasonably be expected to prevent, nullify, materially impede, interfere with, frustrate, delay, postpone, discourage or adversely affect the timely consummation of the transactions contemplated by the Merger Agreement or the performance by such shareholders of their obligations under such Voting Agreement.

In addition, the Reporting Persons agreed to vote all shares of Transocean that such shareholder beneficially owns in favor of the following proposals at any meeting of Transocean's shareholders held to approve the obtain the Transocean shareholder approvals necessary to consummate the Merger:

(a) the adoption of the Authorized Share Capital (as defined in the Merger Agreement);

(b) the Parent Share Issuance (as defined in the Merger Agreement);

(c) the related amendments to Transocean's articles of association in connection therewith;

(d) any other transactions contemplated by the Merger Agreement (as necessary); and

(e) any other "routine" matters presented at such meeting.

The Voting Agreement also contains certain restrictions on the transfer of Ocean Rig shares.  In particular, the Voting Agreement prohibits the Reporting Persons from transferring any Ocean Rig shares, subject to certain limited exceptions, prior to the time when the Ocean Rig shareholder approvals necessary to consummate the Merger have been obtained.

The Voting Agreement and all obligations thereunder terminate, if, among other things, the Merger Agreement is terminated in accordance with its terms, or if the board of directors of Ocean Rig fails to make, withdraws or modifies in a manner adverse to Transocean its recommendation (or recommends an Alternative Acquisition Proposal (as defined in the Merger Agreement) or takes any action or makes any statement inconsistent with its recommendation) following the receipt of a Superior Proposal (as defined in the Merger Agreement).

The foregoing summary of the Voting Agreement is not complete and is qualified in its entirety by the full text of the Voting Agreement, which is included as Exhibit A hereto and is incorporated herein by reference. In addition, the foregoing description of the Merger Agreement does not purport to be complete and is qualified in its entirety by reference to the full text of the Merger Agreement, which is attached as Exhibit 2.1 to the Form 6-K filed by the Issuer on September 4, 2018.

Item 5.  Interest in Securities of the Issuer.

Items 5(a) and (b) of the Schedule 13D is hereby amended and restated in its entirety by the following:

(a), (b)  Based on the foregoing and unless otherwise disclosed, the Reporting Persons report beneficial ownership of the following Common Shares:

As of September 7, 2018, Mr. Economou may be deemed to beneficially own 8,525,596 Common Shares representing approximately 9.3% of the total outstanding Common Shares.  Mr. Economou has the sole power to vote or direct the vote of 0 Common Shares and the shared power to vote or direct the vote of 8,525,596 Common Shares. Mr. Economou has the sole power to dispose or direct the disposition of 0 Common Shares and has shared power to dispose or direct the disposition of 8,525,596 Common Shares.

As of September 7, 2018, Prime Cap may be deemed to beneficially own 8,524,793 Common Shares representing 9.3% of the total outstanding Common Shares.  Prime Cap has the sole power to vote or direct the vote of 0 Shares and has the shared power to vote or direct the vote of 8,524,793 Common Shares. Prime Cap has the sole power to dispose or direct the disposition of 0 Common Shares and has the shared power to dispose or direct the disposition of 8,524,793 Common Shares.

(c)  Other than as described herein, no transactions in the Common Shares were effected by the persons enumerated in Item 2 during the past 60 days.

(d)  No person other than the Reporting Persons is known to have the right to receive, or the power to direct the receipt of, dividends from, or proceeds from the sale of, the Common Shares reported in this Schedule 13D.

(e)  Not Applicable.

Item 6.  Contracts, Arrangements, Understandings or Relationships with Respect to Securities of the Issuer.

Item 6 of Schedule 13D is hereby amended and supplemented by the addition of the following:

The response of the Reporting Persons in Item 4 is incorporated by reference into this Item 6.

Item 7.  Material to be Filed as Exhibits.

Item 7 of the Schedule 13D is hereby amended and supplemented by the addition of the following:

Exhibit A: Joint Filing Agreement

Exhibit B: Voting and Support Agreement, dated September 3, 2018 (incorporated by reference to Exhibit 99.1 to the Issuer's Form 6-K filed with the SEC on September 4, 2018).

SIGNATURE

After reasonable inquiry and to the best of our knowledge and belief, the undersigned certify that the information set forth in this statement is true, complete and correct.

Dated: September 7, 2018

EXHIBIT A

The undersigned, being duly authorized thereunto, hereby executes this agreement as an exhibit to this Schedule 13D with respect to the shares of common stock of Ocean Rig UDW Inc. to evidence the agreement of the below-named parties, in accordance with the rules promulgated pursuant to the Securities Exchange Act of 1934, as amended, to file this Schedule 13D jointly on behalf of each such party.

Dated: September 7, 2018