The play begins with the Smiths sitting around in their living room talking about a lot of nothing. Mrs. Smith recounts to her husband all the things that have happened that evening, even though he was there. Next they discuss a family in which everyone is named Bobby Watson. The Smiths seem to forget from moment to moment whether a certain Bobby Watson is alive or dead.
The Smith's maid, Mary, arrives and announces that the Martins are waiting outside. Mr. and Mrs. Smith hurry upstairs to change clothes. Mary shows the Martins into the living room, yells at them for being late, and then exits. It turns out that the Martins don't remember each other even though they apparently live in the same house, sleep in the same bed, and traveled on the same train together. Eventually, through an extended process of elimination they decide that they must be a married couple. Of course, Mary blows a hole in their theory. She tells the audience that, in fact, the Martins' reasoning is faulty, and that they aren't who they think they are at all.
The Smiths eventually rejoin their guests. The two couples sit around talking about unremarkable events, like the fact that Mrs. Martin saw a man tying his shoe. They all are amazed at this "fantastic" story. Eventually, the Fire Chief arrives. He's come to see if there is a fire in the house and is very depressed to find out there isn't one. Since he's apparently got nothing better to do, he settles in and shares some weird fables. Mary, the maid, busts in and tries to share some stories of her own. The Fire Chief suddenly recognizes Mary – she was his first love. The Smiths are very offended that Mary, the lowly maid, would want to share stories. They push her offstage as she recites a poem dedicated to the Fire Chief.
The Fire Chief takes his leave, saying that there's a fire across town that he must see to. After he leaves, the play goes totally haywire. The characters start spewing totally random non-sequiturs, clichés, and mutilated aphorisms. Eventually, the lights go out and we hear them screaming, "It's not that way, it's over here!" over and over again in the darkness (564). When the lights come back up, the Martins are in the same positions the Smiths were in at the beginning of the play. The curtain fall as the play begins again with the Martins saying the same lines that the Smiths did in the first scene.