Railway director and fellow Belgian Monsieur Bouc secures Poirot a last minute berth on the Orient Express, returning to England from Istanbul. Ratchett, an abrasive American businessman, traveling with his valet and male secretary, tries to secure Poirots services as he fears that his life is in danger. Poirot turns him down, but the next morning, whilst the train is stuck in a snowdrift in Serbia, Ratchett is found stabbed to death. There is vague talk of a man seen fleeing the train, but many of the passengers in Poirots compartment do not appear to know either Ratchett or each other, so what could the motive be* Poirot, assisted by Bouc and Dr. Constantine, attempts to find out.

While driving through the New Mexico Desert during a rainy night, the college students Jim Halsey and his girlfriend Grace Andrews give a ride to the hitchhiker John Ryder. While in their car, the stranger proves to be a psychopath threatening the young couple with a knife, but Jim succeeds to throw him out of the car on the road. On the next morning, the young couple sees John in another car with a family, and while trying to advise the driver that the man is dangerous, they have an accident. While walking on the road, they find the whole family stabbed in the car, and John sees that the driver is still alive. He drives to a restaurant seeking for help, but the police blame Jim and Grace to the murder and send them to the police station. However, John kills the policemen and pursues the couple, playing a tragic and violent mouse and cat game with Grace and Jim.