Exhibit 5.1

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1735 Market Street, 51st Floor

Philadelphia, PA 19103-7599

TEL 215.665.8500

FAX 215.864.8999

www.ballardspahr.com

February 11, 2016

TransEnterix, Inc.

635 Davis Drive, Suite 300

Morrisville, NC 27713

RE: TransEnterix, Inc.

Ladies and Gentlemen:

We have acted as counsel to TransEnterix, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of the Company’s Registration Statement on Form S-3, dated the date hereof (the “Registration Statement”), under the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration of the resale of 42,759,127 shares of common stock, par value $0.001 per share of the Company (the “Shares”), which are held by certain selling stockholders (the “Selling Stockholders”) and that may be sold by the Selling Stockholders from time to time on a delayed or continuous basis pursuant to Rule 415 under the Securities Act.

In so acting, we have examined originals or copies (certified or otherwise identified to our satisfaction) of: (i) the Amended and Restated Certificate of Incorporation of the Company together with all amendments thereto; (ii) the Amended and Restated Bylaws of the Company; (iii) the Registration Statement and the exhibits thereto; (iv) the prospectus contained within the Registration Statement; (v) the Securities Purchase Agreement, dated as of August 13, 2013, by and among SafeStitch Medical, Inc. and the investors party thereto; (vi) the Registration Rights Agreement, dated as of September 3, 2013, by and among SafeStitch Medical, Inc. and the investors party thereto; (vii) such corporate records, agreements, documents and other instruments; and (viii) such certificates or comparable documents of public officials and other sources believed by us to be reliable, and of officers and representatives of the Company, and have made such inquiries of such officers and representatives, as we have deemed relevant and necessary as a basis for the opinions hereinafter set forth.

In such examination, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies and the authenticity of the originals of such latter documents. As to all questions of fact material to this opinion that have not been independently established, we have relied upon certificates or comparable documents of officers and representatives of the Company.

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TransEnterix, Inc.

February 11, 2016

Page 2

Based on the foregoing, and subject to the qualifications stated herein, we are of the opinion that the Shares have been duly authorized and are validly issued, fully paid and non-assessable.

We express no opinion as to the laws of any jurisdiction other than the federal laws of the United States of America and the laws of the State of Delaware.

We hereby consent to the use of this letter as an exhibit to the Registration Statement and to any references to our firm in the prospectus which is a part of the Registration Statement.

Sincerely yours,

/s/ Ballard Spahr LLP