New York's Odyssey Detective Agency is hired by two different clients to follow two women suspected of infidelity. Ladies' man John Russo (Ben Gazzara) trails Angela Niotes (Audrey Hepburn), the elegant wife of a wealthy Italian industrialist, while Charles Rutledge (John Ritter) and Arthur Brodsky follow Dolores Martin (Dorothy Stratten), the beautiful young wife of a jealous husband. Their respective cases are complicated when John falls for Angela, and Charles falls for Dolores.