Nye, born on October 14, 1936, in Greenwood, Mississippi, made her Broadway debut in 1960 in A Second String. In the early 1960s she also appeared on the Great White Way in the play Mary, Mary. In 1965 she received a Tony nomination for her featured work in Half a Sixpence. She was additionally featured on Broadway in A Very Rich Woman, Cop-Out and the 1980 revival of The Man Who Came to Dinner. Her off-Broadway credits include The Trojan Women, The White Devil and The Madwoman of Chaillot. Nye also made her mark on the stage outside of New York. She appeared in 24 Williamstown productions over 31 years, making her first appearance in 1958 as Margaret in Cat on a Hot Tin Roof and her last in 1989 as Zelda Fitzgerald in Clothes for a Summer Hotel.
She is survived by her husband, actor and television host Dick Cavett.