As he's observing other voyagers aboard a German passenger freighter bound for Bremerhaven in 1933, a puckish dwarf named Glocken (Michael Dunn) warns that it is "a ship of fools," whose passengers are all deeply involved with one folly or another. As Virginia divorcee Mary Treadwell (Vivien Leigh) vainly flees middle age, the drug-dependent Spanish noblewoman, La Condesa (Simone Signoret) and the ship's doctor, Schumann (Oskar Werner) are falling in love. Unmarried young Americans Jenny and David (Elizabeth Ashley and George Segal) risk staying in separate cabins to see if they have a life beyond sex, while the Jewish Lowenthal (Heinz Ruehmann) is returning to Germany, a country which he still strongly believes in despite "extremists" like his cabin-mate, Rieber (Jose Ferrer), an anti-Semitic publisher. With a wife at home, Rieber is carrying on a shipboard romance with the Brunhildean Lizzi Spockenkieker (Barbara Luna). A baseball player who's past his prime, Bill Denny (Lee Marvin) is pursuing one of the Spanish dancers, while Elsa (Olga Fabian), a young Swiss girl, awaits only a spark to incite her to rebellion against her puritanical parents. One by one, their problems unfold during the voyage. Yet, upon disembarking, each goes their own way, leaving the bemused Glocken behind.