In a fictional country in a highly mountainous region of Europe, a motley group of travelers is delayed by an avalanche that has blocked the railway tracks. The passengers cram into a small village hotel for the night. Among the hotel guests eager to return to England are two British gentlemen, Caldicot and Charters, who are worried about missing the upcoming cricket Test match and much concerned about getting international news, as the events takes place about the time of the 1938 Munich conference. Other Britons are Iris (Margaret Lockwood), a young woman of independent means who has spent a holiday with some friends, now returning home to be married, Miss Froy (May Whitty), an elderly lady who has worked some years abroad as a governess and music teacher, Gilbert (Michael Redgrave), a young musicologist who has been studying the folk songs of the region, and a secretive couple Mr. and Mrs. Todhunter who are having a clandestine affair. Folk musicians play music late into the night. Miss Froy seems to particularly enjoy a certain ballad, and she throws a coin out her window. The music stops, as a murderous hand is seen to strangle the balladeer, but no one seems to notice anything wrong.
The next morning, as the passengers are leaving the hotel to board the train, Miss Froy asks Iris for help in finding her luggage. They huddle around a pile of baggage, and just then a flowerpot is pushed off a window ledge from an upper floor. The pot appears meant for Miss Froy, but it knocks Iris on the head, instead. She says she is all right and gets on the train, but drops unconscious once aboard. When she recovers, she finds herself seated in a compartment across from Miss Froy, who has evidently helped her. In the compartment are other passengers who appear not to understand English.
Iris and Miss Froy strike up a conversation. They leave the compartment together to go to the dining car for tea . On route to the dining car, Miss Froy stumbles into the compartment of the English couple the Todhunters and proffers her excuses. In the dining car, the pair are seated by a waiter and Miss Froy provides a supply of her own tea, Herriman's Herbal Tea. While in the dining car, Miss Froy writes her name in the dust of the window after Iris mishears it as Freud when the noise of another train drowns out their conversation. During tea, Miss Froy annoys the two English gentlemen returning to England for the test match by asking to borrow their sugar cubes which are being used to illustrate a cricket match. Miss Froy tells Iris about her job as a children's governess and music teacher. They reserve two places for the first sitting of lunch. After returning to the compartment, encouraged by Miss Froy, Iris drops off into a heavy nap.
When she reawakens, the governess has vanished. Iris is shocked to learn that the other passengers in the compartment, the Baroness and her Italian manservant, claim Miss Froy never existed. Even the other English travelers deny ever seeing her, for their own reasons, the Todhunters for fear of drawing attention to their affair and the cricket fans Caldicot and Charters because they are worried about missing the cricket Test match if confirming the disappearance causes delays.
A psychiatrist on the train, Dr. Egon Hartz (Paul Lukas), suggests that Miss Froy never existed: Iris was bumped on the head before boarding, and the conversation may have only taken place in her mind. Dr. Hartz, declares that she must be hallucinating due to her accident. However, Iris is certain that something more sinister is going on and continues to investigate,.
As she searches the second class carriages looking for Miss Froy, Iris meets Gilbert. Their earlier interactions back at the hotel had not been good, but he believes she is sincerely distressed and offers to help. Since the train had not stopped anywhere during Iris nap, she is convinced Miss Froy is somewhere in the train.
At the first stop the train picks up a heavily bandaged brain tumor patient, carried on a gurney, a patient of Dr. Hartz who is being transported to a hospital for surgery. Iris watches carefully on one side of the train, Gilbert on the other, and they see no one get off the train.
After the train starts off again, Gilbert and Iris question all the people who should have seen Miss Froy, but they draw a blank until Mrs. Todhunter comes forward to say she has seen Miss Froy, hoping that having her name made public would trigger a scandal, which would result in divorces for herself and her paramour. After this, the manservant from Iris's compartment appears to say that Miss Froy has returned. Iris and Gilbert return to the compartment to find someone dressed like Miss Froy seated there, however when her face is seen it is not Miss Froy. This lady is Frau Kummer. The Baroness says she did not equate Iris's English nanny with her German friend. Gilbert announces that he can dispel the confusion as there is someone else on the train who has seen Miss Froy/Frau Kummer. Unfortunately while this has been going on, Mrs. Todhunter has told her lover what she has done. Mr. Todhunter says that while her husband would divorce her, he would not leave his wife . With this in her mind, Mrs. Todhunter identifies Frau Kummer as the same woman she saw wearing oatmeal tweeds early on.
Feeling dejected, Iris takes Gilbert to the dining car. Gilbert tells Iris bits about his life. During this conversation, Iris notices Miss Froy's name fingered on the dust of the window just as they enter a tunnel. By the time they come out into the open, the name has disappeared. Iris becomes annoyed and frustrated at Gilbert's disbelief as she tells him about the Herriman's Herbal Tea package. Iris storms off the dining car and pulls the emergency cord in desperation.
After the train has restarted and under the threat of being put off the train at the next stop, Iris returns to her compartment alone. Meanwhile, some rubbish has been thrown out of the dining car and a gaudy tea label for Herriman's Herbal sticks briefly to the window in front of Gilbert. This is enough to make him believe Iris and he rushes back to her They embrace in the corridor. After this, they search the train and end up in the baggage car, where they find the broken glasses of Miss Froy among items that identify the Baroness' Italian manservant as a professional touring magician, adept at making people disappear. The manservant of the Baroness appears and he takes the glasses from Gilbert. A struggle ensues and with some help from Iris they knock the manservant unconscious and put him in a trunk, and tie a rope around it. Unbeknownst to them, the trunk is a magicians trick trunk and the Italian makes his escape.
After this, they head off to tell all of this to the one person they think they can trust, Dr Hartz. They open the door of his compartment but he is not there, only the heavily bandaged patient and the nun nurse.
Iris notices that the nun with the patient is wearing high heels, which means she is in disguise. Iris surmises that Miss Froy was lured to the baggage car and held captive. Frau Kummer, who wasnt seen boarding the train, must have come aboard disguised as the patient, then dressed in Miss Froy's clothes, with Miss Froy becoming the bandaged patient. Dr. Hartz returns and tells them to wait in the next compartment while he orders some drinks. Dr. Hartz arranges for the drinks to be drugged, as one waiter is an accomplice. He returns to the compartment where Iris and Robert are waiting. He tells them the patient is Miss Froy and she will be taken off the train at the next station. He also tells them that the drinks they have just had have been drugged. Iris and Gilbert then seem to go to sleep due to the drug.
Dr. Hartz leaves the compartment to get ready to get off at the next station. But the drug hasn't taken full effect yet, and Gilbert and Iris have heard that they can fight this particular drug's drowsiness by a lot of physical activity. Gilbert climbs out of the window and into the compartment where the nun and Miss Froy are. The nun speaks perfect English and tells Gilbert that she was hired to play a part but is unwilling to help in a murder. They unwrap Miss Froy from her constraining bandages. At this point Frau Kummer enters so they bandage her up in Miss Froy's place against her will. Gilbert and Miss Froy return to the next compartment and pretend to be still asleep because of the drug.
At the following stop, Dr Hartz, the patient, the nun and the Baroness with her servants leave the train and board a waiting ambulance. With the train still at the station, the identity of the patient is discovered. Dr Hartz bribes a station worker to decouple the rear cars, so when the engine starts off again, only the first class car and the dining car are pulled out and they are diverted away from the border. After the train pulls off, pleased that they will soon be over an international border. Gilbert notices that the back of the train has been uncoupled and goes back to tell the others. They agree that there is only the carriage they are in and the dining car between them and the engine but that there wouldn't be anyone there right now. Gilbert points out that it is teatime so all the English people will be there. The three of them go to the dining car. At first no one believes that the train has been uncoupled. Just as they confirm this, the train stops in a wood, and they see cars waiting, uniformed people in them. Dr. Hartz is seen with the cars. A military officer approaches the train and politely tells the English group to get off the train so they can be escorted to safety. Gilbert smells a trap and refuses. The nun is able to sneak away and clobber the officer and he falls unconscious. It turns out that Gilbert and Mr. Todhunter have revolvers, which Gilbert and Charters start firing, in response to attacking shots. Mr. Todhunter goes outside waiving a white handkerchief in truce and is shot by the attackers. While this is going on, Miss Froy reveals to Iris and Gilbert that she is taking a message: a tune to take to a Mr. Callender at the Foreign Office. Gilbert promises that he can memorize Miss Froy's tune quickly because of his musical training. Miss Froy leaves and is seen in the distance dropping to the ground after a shot is fired towards her.
Gilbert decides that they need to get the train started, head back to the divert junction, switch the points and ram it across the next border. He and Caldicot head to the engine while Charters will, at the right moment, jump down and switch the points. They start the train and head back to the station. However Charters has been mildly wounded in the gunfire so the nun jumps down to change the points. After she throws the switch, and is scooped up by Gilbert in the nick of time, she is shot in the leg by Dr. Hartz, who has pursued them in one of the cars back from the woods.
On arrival at a train station London, they all go their separate ways. Sadly for Caldicot and Charters, the Test match has been postponed due to flooding. On seeing her fiancé coming to greet her, Iris hides in a cab, pulls Gilbert in with her, and says she wants to marry Gilbert instead. They continue on to the Foreign Office. On arriving there, in the excitement of their feelings for each other, Gilbert forgets the tune. After a few unsuccessful attempts to refresh his memory they hear the tune being played on a piano, and walk into the next room to see Miss Froy playing it. It is the same tune the balladeer strangled at the hotel had been playing. Iris and Gilbert approach Miss Froy, she turns round to see them both and they all embrace joyfully.