In the Broadway musical Kiss Me, Kate, which Shakespeare play are the actors performing?

In the Broadway musical Kiss Me, Kate, the actors are performing The Taming of the Shrew.

The musical uses a play-within-a-play structure: its backstage story follows a touring company preparing a musical version of Shakespeare’s comedy. The onstage roles of Petruchio and Katherine mirror the conflicts between the performers Fred Graham and Lilli Vanessi, who are also divorced former spouses.

Cole Porter wrote the music and lyrics, while Bella and Samuel Spewack wrote the book. The original production opened at the New Century Theatre in New York on December 30, 1948, and starred Alfred Drake as Fred and Patricia Morison as Lilli.

Songs such as “Wunderbar,” “So in Love,” and “Brush Up Your Shakespeare” helped make the show a major success. Kiss Me, Kate won the first Tony Award for Best Musical in 1949, when the award was known as the Best Musical prize. Its Shakespearean source is sometimes mistaken for another comedy, but The Taming of the Shrew is the play explicitly staged within the musical.