A comedy with spy overtones has David Wilson (Tony Curtis) as an assistant chemistry professor. His wife Ann (Janet Leigh) catches him in the act of kissing one of his female students. The desperate professor must come up with an excuse to avoid divorce procedure, and emplores television writer Michael Haney (Dean Martin) to concoct a plausible alibi. David must convince his wife he is a secret agent of the FBI and was only kissing the girl in the line of duty. This leads to humorous encounters with real foreign and FBI agents and cases of mistaken identity.