Hague's Broadway Musicals include Plain and Fancy (1955), Redhead (1959), and The Fig Leaves Are Falling (1969, with lyrics by Allan Sherman). Famous songs he wrote include "Young and Foolish", "Look Who's in Love", and "Did I Ever Really Live?". He was the composer for the TV musical cartoon, How the Grinch Stole Christmas (1966).
He also was an actor, most notably on the TV series Fame.
His wife, Renee Orin, a singer, with whom he often collaborated, died, aged 73, in 2000 from lymphoma. They had been married since 1951. They had two children.
Albert Hague died at age 81 from cancer at a hospital in Marina del Rey, California in 2001. A widower, he was survived by his two children.