A woman wakes up one morning in a strange bed; beside her is a stranger. He swears he's her husband Bill Clayton, and her name is Norma. She gets hysterical, says her name is not Norma; she must be having another nightmare, and she starts to pack The Overnight Case, which is always a part of this bad dream. She is taken to a psychiatrist.
She meets with Dr. Sandham, but when she sees the man she knows is her husband, he doesn't recognize her. Again, she grabs the overnight case and starts to run. One morning, she finally wakens in her own bed. But the man who says he is her husband is a stranger. She grabs her overnight case to run again, swearing she must still be dreaming.
[this ""loss of identity"" was used in a few Twilight Zone episodes, such as ""A World of Difference"" (3/11/1960) a year before this ""Way Out"" episode, and ""Person or Persons Unknown"" (3/23/1962) broadcast a year after this episode.]