Exhibit 5.1

‑6312 Steinhausen Switzerland
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
October 9, 2018 OSD | ROG

Transocean Ltd.

Ladies and Gentlemen

We have acted as special Swiss counsel to Transocean Ltd., a company limited by shares incorporated under the laws of Switzerland (the Company), in connection with the Registration Statement on Form S‑8 (the Registration Statement) to be filed with the United States Securities and Exchange Commission (the SEC) on the date hereof under the Securities Act of 1933, as amended (the Act), with respect to the registration of an additional 12,000,000 registered shares of the Company, each with a par value of CHF 0.10 (the Registered Shares), that may be delivered pursuant to the Plan (as defined below). As such counsel, we have been requested to give our opinion as to certain legal matters under Swiss law.

Capitalized terms used herein shall have the meaning attributed to them in the Documents unless otherwise defined herein.

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 as currently applied by the Swiss courts. 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 is not to be read as extending, by implication or otherwise, to any document referred to in the Documents (other than listed below) or any other matter.

2 | 5

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, and we express no opinion as to the accuracy of representations and warranties of facts set out in the Documents or the factual background assumed therein.

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

(i) A copy of the resolution passed by the shareholders of the Company at the Company’s annual general meeting held on May 18, 2018 (the Shareholder Resolution), as reflected in the minutes of such meeting, dated May 18, 2018, regarding the approval by the Company’s shareholders of an increase of 12,000,000 shares in the aggregate amount of shares available for issuance pursuant to the Company’s 2015 Long-Term Incentive Plan (the Plan);

(ii) A copy of the minutes of the meeting of the Company’s board of directors, dated as of May 18, 2018 and February 8/9, 2018 (the Board Resolutions), including, among other things, a resolution approving the amendment and the restatement of the Plan and a resolution recommending that the Company’s shareholders approve at the 2018 annual general meeting an increase of 12,000,000 shares in the aggregate amount of shares available pursuant to the Plan;

(iii) A copy of the Plan, as amended and restated effective May 18, 2018;

(iv) A copy of the Articles of Association (Statuten) of the Company in the form as deposited with the Commercial Register of the Canton of Zug, Switzerland, dated as of May 18, 2018 (the Articles of Association);

(v) A copy of the Organizational Regulations (Organisationsreglement) of the Company, dated as of November 18, 2016 (the Organizational Regulations); and

(vi) A  copy of a certified excerpt from the Commercial Register of the Canton of Zug, Switzerland, for the Company, dated as of October 1, 2018 (the Excerpt).

No documents,  other than the Documents,  have been reviewed by us in connection with this opinion. 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.

II.Assumptions

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

(a) The filing of the Registration Statement with the SEC has been authorized by all necessary actions under all applicable laws other than Swiss law;

3 | 5

(b) all copies, fax copies or electronic versions of the documents produced to us conform to the respective original documents and the originals of such documents were executed in the manner and by the individuals appearing on the respective copies;

(c) all signatures appearing on all original documents or copies thereof which we have examined are genuine;

(d) all factual information contained in, or material statements given in connection with, the Documents are true and accurate;

(e) the Documents are within the capacity and power of, and have been validly authorized and executed by the Company;

(f) the Registration Statement has been filed by the Company;

(g) any Registered Shares issued out of the Conditional Share Capital (as defined below) will be listed on the New York Stock Exchange in accordance with applicable laws and regulations;

(h) all authorizations, approvals, consents, licenses, exemptions and other requirements for the filing of the Registration Statement or for any other activities carried on in view of, or in connection with, the performance of the obligations expressed to be undertaken by the Company in the Registration Statement have been duly obtained and are and will remain in full force and effect, and any related conditions to which the parties thereto are subject have been satisfied;

(i) the exercise notice with respect to Registered Shares issued out of Conditional Share Capital will be duly delivered in accordance with Swiss law and the Plan;

(j) to the extent the Company issues Registered Shares out of Conditional Share Capital, the performance of the contribution in money or by way of set-off shall be made at a banking institution subject to the Federal Law of November 8, 1934, Relating to Banks and Savings Banks, as amended;

(k) the Excerpt, the Articles of Association, Organizational Regulations and the other Documents are correct, complete and up-to-date; and

(l) each of the Shareholder Resolution and the Board Resolutions referred to under Section I.(i) and (ii), respectively, (x) has been duly resolved in a meeting duly convened and otherwise in the manner set forth therein, and (y) has not been rescinded or amended and is in full force and effect.

4 | 5

III.Opinion

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

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

2. 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 Registered Shares with a par value of CHF 0.10 each. Such Registered Shares have been validly issued, fully paid and are non-assessable.

3. The Registered Shares that may be issued from the conditional share capital of the Company (the Conditional Share Capital), if and when such Registered Shares are issued pursuant to the Plan, and after the nominal amount for such Registered Shares has been paid-in in cash or by way of set-off, will be validly issued, fully paid 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 thereto, or the effect thereon, of the laws of any other jurisdiction.

(b) We note that, under Swiss law, shares issued out of Conditional Share Capital cannot be paid-in by way of contribution in kind.

(c) The exercise of voting rights and rights related thereto with respect to any Registered 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 of Association.

(d) We express no opinion as to any commercial, accounting, tax, calculating, auditing or other non-legal matter.

(e) We have not investigated or verified the truth or accuracy of the information contained in the Registration Statement, nor have we been responsible for ensuring that no material information has been omitted from it;

(f) Any issuance of the Registered Shares out of Conditional Share Capital must be confirmed by the auditor of the Company, and amended Articles of Association of the Company reflecting the issuance of Registered Shares from Conditional Share Capital, together with said confirmation by the

5 | 5

Company’s auditor, must be filed with the competent commercial register no later than three months after the end of the Company’s fiscal year.

We have issued this opinion as of the date hereof and we assume no obligation to advise you of any changes that are made or brought to our attention hereafter.

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

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

Sincerely yours

/s/ Homburger AG

HOMBURGER AG