During his service in the United States Army in World War II, Nelson debuted on the Broadway stage in Moss Hart's play "Winged Victory" (1943) in the role of Bobby Grills. His next Broadway appearance was as Peter Sloan, playwright, in Hart's "Light Up the Sky" (1948). He appeared on Broadway with Barbara Bel Geddes in the original Broadway production of "The Moon Is Blue". During the play's run, he also starred in a CBS half-hour drama called "The Hunter", premiering in July 1952. He played Bart Adams, a wealthy young American whose business activities involved him in a series of adventures. He also appeared with Lauren Bacall in the Abe Burrows comedy "Cactus Flower" in 1965 and with Dorothy Loudon in "The Fig Leaves Are Falling" in 1969. Nelson performed another Broadway role, that of Gus Hammer in "The Rat Race" (1949).