I applied through a recruiter. The process took 10 months. I interviewed at US Navy (Washington, DC) in Aug 2014
Interview
Two hour long technical interviews in Washington DC then a 5 minute interview with a 4 star admiral. The interview process is to ensure that you can pass nuclear power school and make sure you have what it takes to become a nuclear propulsion officer.
Interview questions [1]
Question 1
How to calculate various physics and electrical problems.