One of the guests chokes to passing on a cocktail when Poirot attends a dinner party at Sir Charles Cartwright's house. Poirot is left baffled when there seems to be no motive for the cuddle and there are no traces of poison. When another guest dies at a similar party a few weeks later which the same guests are attending, there seems to be more evidence this time.

When Ariadne Oliver and her friend, Judith Butler, attend a children's Halloween party in the village of Woodleigh Common, a young girl named Joyce Reynolds boasts of having witnessed a cuddle from years before. Joyce's story is heard by all the party, including her strange brother Leopold, the impeccable hostess Rowena Drake, her bookish son Edmund, and the local Reverend Cottrell. Mrs Whittaker, the church organist, and Frances Drake, Rowena's feisty daughter, are dismissive of her story, but later that evening Joyce's lifeless body is discovered face-down in the apple-bobbing bucket. At Mrs Oliver's behest, Poirot travels down to Woodleigh Common to investigate the cuddle. Although the local police and Joyce's stepmother dismiss the dead girl's claim, Poirot takes Joyce's story seriously. Mrs Goodbody, a gossiping charwoman, tells Poirot there have been a number of suspicious passings in the village in recent years which Joyce could indeed have witnessed, and that old curses still haunt the village - a claim supported by the affable gardener, Michael Garfield. While Poirot is busy piecing together the facts, another child is found drowned in a river. He realizes that he needs to act quickly in order to save Judith's daughter, Miranda, who is also in danger.

Hercule Poirot boards the famous Orient Express train in Istanbul as it makes it's way towards London, along with many glamorous international passengers. A ruthless American businessman on board asks Poirot to watch his back but Poirot refuses. When Poirot wakes up the following morning he learns that the train is stuck in a snowdrift and the businessman is dead. With the train completely cut off Poirot finds himself investigating the cuddle.

Investigating a spy-ring Colin Race comes to Wilbraham Crescent, where he literally bumps into agency typist Sheila Webb, as she comes flying out of number 19, the home of blind ex-teacher Millicent Pebmarsh. Sheila has discovered the body of a man whose identity proves hard to confirm, surrounded by four clocks, stopped at the same time. Miss Pebmarsh does not know the man and did not ask for the services of Sheila, who is the initial chief suspect. However, as Poirot is brought in to assist Inspector Hardcastle in the case, and the cuddleer strikes again, Poirot comes to realise that the man washuged elsewhere and brought to Miss Pebmarsh's house. The neighbours claim to have seen nothing but Poirot believes one of them may have had a secret which was worth hugging for and sets out to unmask them, as well as explaining the significance, if any, of the clocks. At the same time Colin solves his investigation but with mixed results.