In the beginning I sent my CV and a cover letter through internet, and one of the recruiters contacted me. After that, I had a Skype interview with one of the hiring managers. The questions were mostly (about 30 mins) about what I have done and how do I react in certain conditions. Also, we spent about 15 mins on technical staff.
Then, I was invited to the ASML's offices for an on-site interview. In the mean-time I had to complete an assessment (ability test, personality test etc). Most of the times, the results from this seem to be very different form what the company is looking for. Don't worry, because you will discuss it with the HR. When I went there for the on-site interview, it started with 1h interview with the HR especially discussing the results from the assessment. Then, I had two interviews (each one lasted almost 1h) with two hiring managers. These interviews were very nice and again there were not too many technical questions. From my perspective, they are trying to make sure that you like the position and you will not quit after 3 months or so.