His romantic aura was enhanced by his marriages to two of Hollywood's most glamorous musical stars, Alice Faye and Cyd Charisse.
He was born Alvin Morris in San Francisco in 1912 to a poor but closely knit family of Russian-Jewish stock; music was his means of escape from poverty and anti-Semitic taunts at school.
He signed with 20th Century-Fox and was given a small role as a crooner in Sing, Baby, Sing (1936).
He sang with Barbara Stanwyck in Banjo on my Knee (1936), and with Judy Garland in Pigskin Parade (1936), but his career at the studio made little progress.
When he appeared in You Can't Have Everything (1937), he was still billed way down the cast list, and had one duet with Alice Faye, "Afraid to Dream".
He married Faye the same year, and though columnists called them "a handsome couple" there were soon rumours of friction.
He was allocated Irving Berlin's "Let's Face the Music and Dance", but it was given to Fred Astaire.
At RKO, Martin coined a new name, taking Antony from a magazine story, and Martin because Freddie Martin was his favourite band leader.
Martin later said that he could not take being 'Mr Alice Faye'.
He was the romantic lead in Ali Baba Goes to Town (1937), then starred with his wife in Sally, Irene and Mary (1938).