An automotive engineer who has been framed for murder is rescued from police custody by her husband; they flee to New Orleans, beginning a cross-country odyssey to elude the law and the real killers.
Jim and Kate meet a boy abandoned by his mother. Jim heals the lad's dog. Afterwards, while crossing through a small town, they're stopped by the sheriff. Jim covers Kate's retreat, but they're finally detained by the lawman.
Jim and Kate are sojourning in a horse farm, where they have found little solace from their pursuers. But this temporary peace is threatened by a news team that makes them appear on a coast-to-coast telecast. Meanwhile at the ranch the couple meets a female jockey hooked on stimulants.
Jim and Kate request assistance from an army buddy of Jim’s at an Army base, unknowingly, that the man still holds bad war memories which drive him insane. Another officer at the base distrusts Jim and begins to investigate him.
Jim's sister is convalescing in a hospital after suffering a stroke. The will to see her puts Jim’s life in jeopardy. Kate is told that she's pregnant and decides to run away.
Jim searches for the mysteriously vanished Kate while she tries to survive in a forest where Shaw is stalking her.
Jim and Kate help a young woman find her fiance while she aids them in tracking Kate's lookalike.
Jim and Kate abduct Mrs. Modrian by exhibiting a painting of Kate posing as her double. The couple use a drug to put the woman under hypnosis so they can draw out more details about the crime. But Shaw becomes suspicious and forces the painter woman to lead him to the couple's whereabouts.
Katy and Jim learn that Katy's double worked in a carny. Katy devises a scheme to extract some information from the owner. The woman worked there as a fortune teller using the alias Princess Lilly. However, the relationship between Katy's lookalike and the carny's owner was of more than friendship, which complicates the things further.
Jim and Katy arrive to a small town and play as singles in order to ward off suspicions. Some townspeople are suddenly falling sick because of the water poisoned by the toxic waste dumped from the chemical plant where Katy is working.
Jim and Kate are given lodgings in a home for the elderly. They discover that the old people who live there are being cheated off their pensions by a gang of well-dressed crooks.
Kate and Jim get jobs at a bar called "The Pony Espresso". Jim works as a barman while Kate serves as an electrician. They meet a duo, husband and wife, of country singers. But once they get along, Kate discovers that the woman undergoes grave sexual problems.