In this Gershwin musical a rumor gets out that two dancers are married; she is ambivalent about it, but they like to dance together.
In France ballet company owner Jeffrey Baird (Edward Everett Horton) objects to Peter P. Peters (Fred Astaire) tap dancing. Peter says he wants to marry Linda Keene (Ginger Rogers), who complains to Arthur Miller (Jerome Cowan) about hand-kissers and heel-clickers. Peter appears as Petrov and clicks his heels. Denise Tarrington (Ketti Gallian) tells Jeffrey that she wants to return to ballet; but Peter says to get rid of her and promises to sail for New York. Peter tells Denise that he is married. Linda finds Peter on the boat. Peter joins black workers singing "Slap That Bass" and dances. Arthur objects to Linda getting married. Peter sways to make Jeffrey sea-sick. Peter finds Linda on deck and explains he wanted to meet her. Arthur and Jeffrey get drunk. Jeffrey throws his breakfast overboard. Peter walks with Linda and her dog and sings "Beginner's Luck." A rumor spreads that Peter is secretly married to Linda. Jeffrey tells her that Peter wanted to get rid of a woman. Linda leaves the boat on a plane.
Arthur tells Peter that Linda is going to marry in New York. Cecil (Eric Blore) welcomes Linda with children's toys and puts Peter in an adjoining room; but Jeffrey says they are not married. Linda sings "They All Laughed." She is asked to dance with Peter. Arthur uses a figure of Linda and gets photos with Peter in bed. Linda sees them in the paper. Arthur complains and says he'll handle it. Linda's fiancé Jim complains, finds Peter in her room, and suggests they not announce their engagement. Peter and Linda go to the park, sing "Let's Call the Whole Thing Off," and dance on skates. Linda tells Peter to marry her so that she can divorce him, and they wed.
Denise learns from Jeffrey that Peter is not married. On the ferry Peter sings "They Can't Take That Away from Me." Peter says good-night. Cecil learns that Linda is married and gives her the key back. Denise comes in to Peter's room, and he says he is married. Linda opens the door and sees them, saying she won't divorce him. Linda packs and leaves before Peter can tell her he is happy about that; but Arthur tells Peter that Linda is divorcing him. Arthur shows Peter how the pictures were made. Jeffrey tells Peter that he was fired, but Arthur hires Peter. Cecil is arrested for battery of a man trying serve Peter with divorce papers. Peter dances in a ballet. Linda brings the summons and sees Peter dance with images of her. Peter sings "Shall We Dance." He sees Linda on stage and removes the masks to find her.
This musical offers the public the entertainment they love. The dancing stars pretend to be married to each other so as not to be bothered by others.