Exhibit 5.1

United States Securities and Exchange Commission

450 Fifth Street N.W.

Washington, DC 20549

United States of America

Date: April 13, 2015

Subject: Form S-8

Ladies and Gentlemen:

I refer to the Registration Statement on Form S-8 (the “Registration Statement”) of ASML Holding N.V., a Netherlands corporation (the “Company”), under the Securities Act of 1933 (the “Securities Act”). The Registration Statement relates to up to 1,266,753 ordinary shares, nominal value €0.09 per share, of the Company (the “Securities”), issuable and issued under the ASML Board of Management Umbrella Share Plan, ASML Employee Umbrella Share Plan and the ASML Share and Option Purchase Plan (collectively the “Plans”) and up to 177,000 options to acquire the Securities (the “Options”), issuable and issued under the ASML Employee Umbrella Share Plan and ASML Share and Purchase Plan.

I have examined and am familiar with (i) the Company’s Articles of Association, as amended, and (ii) the corporate proceedings relating to the Registration Statement. Upon the basis of the foregoing, and having satisfied myself as to such other matters of law and fact as I consider relevant for the purposes of this opinion, I advise you that, in my opinion, upon issuance in accordance with the terms and conditions of the Plans, the Securities and the Options will have been legally issued, fully paid and non-assessable.

I express no opinion herein, on or with respect to, any law other than the laws of The Netherlands, and I express no opinion on, or with respect to, the laws of the United States, any state thereof or any other laws, statutes, regulations or ordinances.

I hereby consent to the filing of this opinion as an exhibit to the Registration Statement and any reference to me therein. In giving such consent, I do not hereby admit that I am in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.