It is a parody of the Cold War and nuclear scares of the 1960s, although the actual play takes place in the early 1950s in New York City, namely in Central Park.
(The audience is told that, in light of recent military developments - the invention of the nuclear weapon - the cast may not make it to the end of the performance.)
The play begins when three Shakespearean witches who run the world, Zenobia, Ulga, and Luella, try to take the life of a young musician Dinny.
Finally, the witches manage to trick Dinny into agreeing to hand over the deed to the world while telling him that they will make his love, Amy, a perfect woman.
Finally, the witches retrieve the deed to the world and try to kill Dinny, but only succeed in turning back time to 100 years ago, the beginning of the play.