He was a regular attendee of the Darmstadt International Summer Courses for New Music, and he was particularly affected by the twelve-tone classes of René Leibowitz (1948) and Ernst Krenek (1951), which helped him move from free atonality to serialism.
A brief marriage took him to Iceland from 1953-4, before returning to Darmstadt to work as the music adviser and composer for the Hessisches Landestheater for the next seven years.
In the early 60's, Engelmann began to incorporate techniques like electronic sound generation, graphic notation, jazz and collage into his music.
By the end of the decade, he had assembled a pluralistic style which he showcased in large multimedia works such as Ophelia (1969).
A recipient of many scholarships and awards throughout his career, some of Engelmann's most notable honors include scholarships from Harvard and the Villa Massimo (1960, 1967, 1983), the Lidice Prize of Radio Prague (1960), the Stereo Prize of the German broadcasting industry (1969), the Johann Heinrich Merck Award (1971), the Goethe Medal (1986), the Order of the BRD (1991) and the Hessian Order pour le merite (1997).