Nye died Sunday at his home in Los Angeles after a long battle with lung cancer, his son, Peter Nye, told The Associated Press on Monday.
Nye had worked regularly in nightclubs and on television until just a couple of years ago, his son said. He had a recurring role from 2000 to 2002 in the HBO comedy "Curb Your Enthusiasm" as the father of Jeff Garlin's character.
When he joined Allen's show in 1956 he was already well established as one the era's hippest comics, appearing regularly on radio, in clubs and on early TV shows.
A master of voices and accents, he could go from being droll one moment to prissy the next. He could also switch effortlessly from comically evil Nazis to bumbling Russians.
"He has a great business card from that time that lists something like 15 accents that he could do," his son recalled with a chuckle.
On "The Steve Allen Show," which ran until 1961 under various names, he quickly endeared himself to audiences as Gordon Hathaway, the effete, country-club snob who would welcome Allen's arrival with the "Hi, ho, Steverino!" salutation.
Other regulars on the landmark show included comedians Don Knotts, Tom Poston and Bill Dana.
After the show's run ended, Nye appeared often on TV game shows, in films and as a regular on "The Ann Sothern Show." He was often cast as the second banana, never the lead.
Nye appeared as Sonny Drysdale, the prissy son of harried banker Milburn Drysdale, in the debut 1960-61 season of "The Beverly Hillbillies." He once said his character was dropped after one season because a CBS executive thought he was "too sissified." Nye returned as Sonny for the 1993 TV movie "The Legend of the Beverly Hillbillies."