A rich group of English youth, at the center of whom is the beautiful Iris Carr, frolic at a resort high in the Balkan mountains, earning the disapproval of fellow hotel guests. The Reverend and Mrs. Barnes try not to judge the drunken compatriots, but the elderly Flood Porter sisters are disgusted. When Iris is falsely accused of having an affair with one of her friends’ husbands, she decides to remain at the resort rather than travel home with her raucous companions.
But she is unnerved by gunfire she hears while hiking a remote trail. She arranges to depart for home after all, but while waiting at the train station, irritated at a booking error, the crowds and the unrelenting heat, she passes out. She awakens, disoriented and confused, and is rushed onto her train where she scrambles to settle down in a crowded car among a cold and haughty baroness and a middle-aged British tweed-clad spinster. That spinster, Miss Winifred Froy, rescues Iris from the oppressive atmosphere by inviting her to tea, where they encounter the nervous Mrs. Barnes and the overtly disapproving Flood Porters sisters.
Over tea, Miss Froy reveals that, prior to traveling, she had given notice as governess to the Baroness' family. Yet when there was confusion about her second-class ticket, the powerful Baroness paid the difference to secure her a first-class ticket in her carriage. Miss Froy chats on about the Baroness' brother, describing how she found him to be charming when she encountered him during a walk on their estate, a surprise because he supposedly was out of the country. En route back to their car, Miss Froy points out the Baroness' ill sister, bundled up and attached to an oxygen mask, who is being brought to Trieste. Her doctor is a sinister man who had entered the carriage and whispered in the Baroness' ear.
When Iris can tolerate Miss Froy's plucky chit-chat no longer, she accepts medicine for her headache from Miss Froy and falls asleep. When she awakens, Miss Froy is gone, and the Baroness coldly states that there never was another English woman in the carriage. Panicked, Iris seeks help from anyone who can speak the language and is rescued by Max Hare, a young Oxford academic, and his professor. Together, they interview all the travelers from her compartment, yet all maintain that Miss Froy never existed. The professor immediately believes the baroness and her entourage, and the doctor attributes her story to a vision induced by her sunstroke. Neither the gossipy sisters, nor the suspiciously private newlyweds, the Todhunters, remembers Miss Froy either, except for Mrs. Barnes.
Iris learns from the doctor that Miss Froy has returned and Iris happily rushes to greet her only to find an entirely different woman altogether: Frau Kummer. Kummer, wearing the very clothes that Iris remembered, insists that it was she who had tea with Iris. Panicked, she looks for confirmation from Mrs. Barnes, but she identifies Kummer as Miss Froy; she is anxious to return home so that she can be reunited with her sick child, and to confirm Miss Froy's disappearance and its attendant foul play would postpone her return.
Now, Max is Iris' only ally left. He encourages her to try to remember any clues, and when Iris mentions the Baroness' brother, Max describes an item from the British press about an intellectual murdered for opposing the king and notes rumors suggesting the Baroness' brother's involvement. But the brother was in Vienna at the time of the murder.
Meanwhile, the professor, in consultation with the doctor, suggests that Iris be detained overnight for psychiatric observation. Desperately, Iris tells Max her theory that she explicitly wasn't wanted in that train compartment. Max theorizes that no one would be able to trace when or where or in Europe Miss Froy had disappeared if they simply disguised her as the invalid, to be disposed of when they reach Trieste. But when Max admits he was just theorizing, Iris realizes she must take matters into her own hands. She finds an old English newspaper, its headlines featuring the murder, in the compartment. But the Baroness waylays her, calling on her nurse (a man, in a nun's disguise) to inject Iris with a sedative. Iris narrowly escapes.
Explaining to the professor that Miss Froy's encounter with the Baroness' brother invalidated his alibi for the murder, Iris declares that Miss Froy is disguised as the invalid sister. But when the doctor reluctantly reveals the patient, it is not Miss Froy. Iris threatens to go to the British embassy in Trieste and the doctor suggests to the professor that she be given a sedative by force. He convinces Max of her desperate need for sleep; to that end, Max brings her soup laced with a sedative, which she drinks and falls asleep. But when she awakens as they approach Trieste, she rushes, staggering, to rescue the patient she's convinced is Miss Froy. To escape Max, whom she now knows drugged her, and to save herself from the doctor, she hides in the goods compartment, but the doctor finds her. There, she finds Miss Froy, bound and gagged. But the doctor finds her and lunges as she screams.
At the station in Trieste, Mrs. Todhunter – who is actually a mistress finally weary of posing as the famous Sir Perceval Brown's wife – tells Max that they had lied: Miss Froy, had, in fact, existed. While Max rushes back onto the train to find Iris, Mrs. Barnes, overjoyed to have learned by telegram that their son is recovered, confirms Miss Froy's existence to the professor…all this as Iris, strapped to a gurney, is loaded into an ambulance. Max rescues her as the professor arrives with the police to arrest the Baroness. Max dashes to the goods car and interrupts Frau Kummer as she strangles Miss Froy. She is saved.