Nelson was the original Boy in the popular Off-Broadway musical The Fantasticks but he made his mark as Michael, the self-hating homosexual in play The Boys in the Band.

After reprising the role for the 1971 London production of The Boys in the Band, he decided to stay in England, and went on to appear in West End productions of such American musicals as Show Boat, Annie and 42nd Street.

Nelson spent much of the later part of his career in small roles on television and in movies.

Nelson died in 1993 of AIDS-related complications in London.