Remembered best as the composer of the 1950s and 1960s Broadway musicals Redhead, Plain and Fancy, The Fig Leaves Are Falling, and Cafe Crown, Hague also had an acting career, starring as Benjamin Shorofsky in the 1982 NBC series Fame.
After graduating from the University of Cincinnati, he served during the World War II years in the United States Army Air Forces.
He wrote the music for the How the Grinch Stole Christmas holiday cartoon special.
Born Albert Marcuse, he grew up in Berlin, Germany as the son of psychiatrist and musician Harry Marcuse and renowned chess player Mimi Heller Marcuse. His five-decade marriage to vocalist Renee Orin resulted in two children.
Stage performer Cady Huffman starred in a 2006 New York revival of Hague's 1955 musical comedy Plain and Fancy.