Exhibit 5.1

‑6312 Steinhausen
To: Transocean Ltd. Turmstrasse 30 CH‑6312 Steinhausen Switzerland	Homburger AG Prime Tower Hardstrasse 201 | CH–8005 Zurich P.O. Box 314 | CH–8037 Zurich T  +41 43 222 10 00 F  +41 43 222 15 00 lawyers@homburger.ch
September 21, 2018

Transocean Ltd.

Ladies and Gentlemen:

We have acted as special Swiss counsel to Transocean Ltd., a Swiss corporation (the Company), in connection with the Registration Statement on Form S−4, as amended (the Registration Statement), filed with the Securities and Exchange Commission (the Commission) on September 21, 2018 under the Securities Act of 1933, as amended (the Act), relating to the registration with the Commission of registered shares, par value CHF 0.10 each, of the Company (each a Share and together the Shares), which will be newly issued (such newly issued Shares hereinafter referred to as the Consideration Shares) to shareholders of Ocean Rig UDW Inc.  (Ocean Rig) upon completion of the merger of Transocean Oceanus Limited, a newly-formed, indirect wholly-owned subsidiary of the Company (Merger Sub), with and into Ocean Rig in accordance with the laws of the Cayman Islands, with Ocean Rig being the surviving entity as a direct, wholly-owned subsidiary of Transocean Oceanus Holdings Limited, a newly-formed, direct, wholly-owned subsidiary of the Company (Holdco) and as an indirect wholly-owned subsidiary of the Company (the Merger)  in accordance with the terms and subject to the conditions set forth in the agreement and plan of merger by and among the Company, Holdco, Merger Sub and Ocean Rig, dated as of September 3, 2018 (the Merger Agreement). An exchange agent (the Exchange Agent) will be acting in its own name but on behalf and account of holders of shares of Ocean Rig (each an Ocean Rig Share) entitled to receive the consideration pursuant to the Merger Agreement (the Merger Consideration). In addition, Shares of the Company may be newly issued (such newly issued Shares hereinafter referred to as the Additional Shares, and, together with the Consideration Shares, the Registered Shares) to a third party, including a direct or indirect subsidiary of the Company (the Relevant Subsidiary), for (i) delivery of Shares to holders of Ocean Rig Shares who dissent from the Merger in accordance with the laws of the Cayman Islands (the Dissenting Shareholders) but who fail to perfect or effectively withdraw or otherwise lose the right to appraisal with respect to Ocean Rig Shares and are treated as if the Ocean Rig Shares held by them had been converted into the right to receive the Merger Consideration, or who otherwise may acquire a right to receive Shares, and/or (ii) the direct or indirect financing or re-financing of appraisal rights of Dissenting Shareholders.

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As such counsel, we have been requested to render an opinion as to certain Swiss legal matters relating to the Shares and the Registered Shares.

I.Basis of Opinion

This opinion is confined to and given on the basis of the laws of Switzerland in force at the date hereof. Such laws and the interpretation thereof are subject to change. In the absence of explicit statutory law, we base our opinion solely on our independent professional judgment. This opinion is also confined to the matters stated herein and the Documents (as defined below), and is not to be read as extending, by implication or otherwise, to any agreement or document referred to in any of the Documents (as defined below) (including in the case of the Registration Statement, any document incorporated by reference therein or exhibit thereto) or any other matter.

For purposes of this opinion we have not conducted any due diligence or similar investigation as to factual circumstances, which are or may be referred to in the Documents (as defined below), and we express no opinion as to the accuracy of representations and warranties of facts set out in the Documents (as defined below) or the factual background assumed therein.

For purposes of giving this opinion, we have only examined originals or copies of the following documents available to us (collectively the Documents):

(i) an electronic copy of the executed Merger Agreement, filed as Appendix A to the Registration Statement;

(ii) the Registration Statement, as filed with the Commission on September 21, 2018, constituting a prospectus of the Company for purposes of the Act with respect to the Registered Shares to be issued to holders of Ocean Rig Shares in exchange for their Ocean Rig Shares pursuant to the Merger Agreement, and constituting a proxy statement of each of the Company and Ocean Rig (the Proxy Statement) for purposes of the Act, which contains, among other things, an invitation to and a notice of meeting with respect to an extraordinary general meeting of the Company (the EGM)  for approval by the Company’s shareholders of, inter alia, the creation of additional authorized share capital of the Company (the Additional Authorized Capital), the respective amendments to the Articles (as defined below) and the issuance of the Registered Shares against a contribution in kind of newly issued shares, par value USD 0.0001 each, of Holdco, such contribution constituting a mixed contribution in kind and acquisition of assets (together, the Contribution) by virtue of the Merger Consideration consisting of a mix of Shares and cash, whereby the preferential subscription rights (Bezugsrechte) of the Company’s shareholders will be withdrawn (the EGM Matters);

(iii) an electronic copy of the articles of association of the Company, in their version dated May 18, 2018 (the Articles);

(iv) an electronic copy of the organizational regulations (Organisationsreglement) of the Company, dated as of November 18, 2016 (the Organizational Regulations);

(v) an electronic copy of an  excerpt from the Commercial Register of the Canton of Zug for the Company, dated September 21, 2018 (the Excerpt);

(vi) an electronic copy of the minutes of the meeting of the Board of Directors of the Company, dated August 9/10, 2018, and an electronic copy of the resolutions adopted by the Company’s transaction committee, dated August 31, 2018, regarding, among other things, the authorization of the Merger and the actions to be taken in connection therewith (the Resolutions); and

(vii) an electronic copy of a certificate provided by the secretary of the Company’s board of directors, dated as of September 21, 2018 (the Certificate).

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No documents have been reviewed by us in connection with this opinion other than the Documents. Accordingly, we shall limit our opinion to the Documents and their legal implications under Swiss law.

In this opinion, Swiss legal concepts are expressed in English terms and not in their original language. These concepts may not be identical to the concepts described by the same English terms as they exist under the laws of other jurisdictions. With respect to Documents governed by laws other than the laws of Switzerland, for purposes of this opinion we have relied on the plain meaning of the words and expressions contained therein without regard to any import they may have under the relevant governing law.

II.Assumptions

In rendering the opinion below, we have assumed the following:

(a) all documents produced to us as originals are authentic and complete, and all documents produced to us as copies (including, without limitation, fax and electronic copies) are accurate and conform to the original;

(b) all documents produced to us as originals and the originals of all documents produced to us as copies were duly executed and certified, as applicable, by the individuals purported to have executed or certified, as the case may be, such documents;

(c) no laws other than those of Switzerland will affect any of the conclusions stated in this opinion;

(d) the Merger Agreement, which is governed by the laws of the State of New York, is valid, binding and enforceable under the laws of the State of New York and will have been completed no later than concurrently with the registration of the Registered Shares in the competent Commercial Register in Switzerland;

(e) the Company’s EGM will (i) have been duly invited and convened to resolve, among other things, on the EGM Matters, and (ii) have approved the EGM Matters with the necessary majorities, as described in the Proxy Statement and in accordance with Swiss law and the Articles then in effect;

(f) following the EGM and receipt of the approvals set forth in paragraph (e) above, the Company’s board of directors will (i) have adopted all resolutions, including execution resolutions (Durchführungsbeschluss) authorizing the issuance of the Registered Shares from the Additional Authorized Capital and potentially from existing authorized share capital of the Company, (ii) have established the report (the Board Report) pursuant to Article 652e of the Swiss Code of Obligations (CO) regarding, among other things, the nature and condition of the Contribution and the appropriateness of the valuation thereof, (iii) have made all determinations and ascertainments and adopted respective resolutions on amendments to the Articles, including the necessary ascertainments regarding the issuance of the Registered Shares and resolutions on the respective amendments to the Articles (Feststellungs- und Statutenänderungsbeschluss), and (iv) have entered, or caused authorized signatories to enter, on behalf of the Company, into one or more contribution in kind and acquisition of assets agreement(s) regarding the Contribution with the Exchange Agent, acting on behalf and account of the holders of Ocean Rig Shares entitled to receive the Merger Consideration, and the Relevant Subsidiary, respectively, in each case together with all corporate and other documents and public deeds, as required to effect and implement the issuance of the Registered Shares and as described in the Proxy Statement and in accordance with Swiss law and the Articles then in effect;

(g) the Company’s existing authorized share capital pursuant to Article 5 of the Articles is in full force and effect and has not been amended;

(h) the Exchange Agent, acting on behalf and account of the holders of Ocean Rig Shares entitled to receive the Merger Consideration, and the Relevant Subsidiary will (i) have subscribed to the

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Registered Shares, and (ii) have paid in the issuance price (Ausgabebetrag) of the Registered Shares by effecting the Contribution, as described in the Proxy Statement and in accordance with Swiss law and the Articles then in effect; and

(i) the Company’s statutory auditor will have issued its written confirmation pursuant to Article 652e CO that the Board Report is complete and accurate.

III.Opinion

Based on the foregoing and subject to the qualifications set out below, we are of the opinion as of the date hereof:

1. The Company has been duly incorporated and is validly existing as a corporation (Aktiengesellschaft) under the laws of Switzerland with all requisite corporate power and authority to conduct its business as described in the Articles.

2. The statements set forth in the Registration Statement under the caption "Material Swiss Tax Consequences," insofar as they purport to describe the provisions of the Swiss tax laws referred to therein, constitute a fair summary of such provisions in all material respects.

3. The Company’s share capital registered in the Commercial Register of the Canton of Zug amounts to CHF 46,285,269.50, divided into 462,852,695 Shares. Such Shares have been validly issued, fully paid as to their nominal value and are non-assessable.

4. The Registered Shares, if and when issued by the Company pursuant to and in the manner described in the Registration Statement, in accordance with Swiss law and the Articles, and registered in the competent Commercial Register in Switzerland and the Company’s uncertificated securities book (Wertrechtebuch), will be validly issued, fully paid as to their nominal value and non-assessable.

IV.Qualifications

The above opinions are subject to the following qualifications:

(a) The lawyers of our firm are members of the Zurich bar and do not hold themselves out to be experts in any laws other than the laws of Switzerland. Accordingly, we are opining herein as to Swiss law only and we express no opinion with respect to the applicability, or the effect, of the laws of any other jurisdiction.

(b) We express no opinion as to any commercial, accounting, calculating, auditing or other non-legal matter. Except as expressed in the opinion set forth in Section III.3 above, we express no opinion as to tax matters.

(c) We express no opinion as regards compliance with Swiss law and the Articles of the withdrawal of the preferential subscription rights (Bezugsrechte) of the Company’s shareholders in connection with the creation of the Additional Authorized Capital or existing authorized share capital of the Company or in connection with the issuance of the Registered Shares.

(d) The resolutions of the Company’s EGM regarding the EGM Matters, including but not limited to, the withdrawal of the preferential subscription rights (Bezugsrechte) of the Company’s shareholders, may be challenged by shareholders in court or otherwise.

(e) The registration of the Additional Authorized Capital, the respective amendments to the Articles and the Registered Shares with the competent Commercial Register and thus the issuance of the Registered Shares may be prevented by any person in accordance with article 162 of the Ordinance Regarding the Commercial Register (Handelsregisterverordnung).

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(f) The exercise of voting rights and rights related thereto with respect to any Shares is only permissible after registration in the Company’s share register as a shareholder with voting rights in accordance with the provisions of, and subject to the limitations provided in, the Articles.

(g) Any Registered Shares to be issued by the Company will not be fully fungible and will not rank pari passu with the Company’s existing and outstanding Shares until such Registered Shares have been duly entered into the Company’s register of uncertificated securities (Wertrechtebuch) and all steps have been taken in order for such Registered Shares to constitute intermediated securities (Bucheffekten) in accordance with the Swiss Federal Act on Intermediated Securities.

(h) We express no opinion as to any Shares issued out of the Company’s conditional share capital not yet registered in the Commercial Register of the Canton of Zug.

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We have rendered this opinion as of the date hereof and we assume no obligation to advise you on changes relevant to this opinion that may thereafter be brought to our attention.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to us under the heading "Legal Matters" in the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required pursuant to Section 7 of the Act.

This opinion shall be governed by and construed in accordance with the laws of Switzerland.

Sincerely yours,

/s/ Homburger AG

Homburger AG