Tertuliano Máximo Afonso is a divorced high school history teacher who spends his nights reading about Mesopotamian civilizations. One day Tertuliano rents a movie recommended by a colleague and sees a bit actor who looks exactly like him. Tertuliano becomes obsessed with meeting the actor and spends weeks discovering the actor's name. Posing as a film student and using his girlfriend's address, he sends a letter to the production company asking to be put in contact with the actor. His relationship with his girlfriend, Maria da Paz, suffers because he refuses to disclose his motives to her. After acquiring the actor's phone number and address, Tertuliano stalks his double, António Claro, and eventually telephones him. António's wife answers and mistakes Tertuliano's voice for her husband's. Initially, António dismisses Tertuliano and refuses to meet, but later contacts him and agrees. They decide to meet at António's country home in a week.
Tertuliano buys a fake beard and goes to meet António. Upon arrival, the men strip down and find that they are indeed physically identical. They have the same birth date. Their voices are identical and they share the same scars and moles. António asks Tertuliano to clarify one more thing: the exact time he was born. He wants to know which of them is the "original" and which the copy. Tertuliano says that he was born at two in the afternoon. António smugly informs Tertuliano that he was born a half-hour earlier, making him the original. Tertuliano gets up to leave, saying that he at least has the compensation of knowing that António will be the first to die, and that he will become the original in turn. To this António responds, "Well, I hope you enjoy those thirty-one minutes of personal, absolute, and exclusive identity, because that is all you will enjoy from now on." The men agree that they have no reason to ever meet again, and Tertuliano leaves.
Tertuliano sends the fake beard to António, who has not been able to stop thinking about their encounter. Meanwhile, Tertuliano and Maria get engaged to be married. António wonders how Tertuliano acquired his phone number and address. He visits the production company office and retrieves the letter Tertuliano authored and sent in Maria's name. Donning the fake beard, António stakes out Maria's apartment and, finding her very attractive, he follows her to work. António realizes that Tertuliano has not told Maria about his double.
Soon after, António pays Tertuliano a visit at home. He shows Tertuliano the letter with Maria's signature. Threatened, Tertuliano tells him to leave, saying he will call the police. António says that he will call Maria and tell her of Tertuliano's forgery. Tertuliano asks what he wants, and António says he intends to spend the night with Maria. António has already contacted her while pretending to be Tertuliano and invited her to look at a country home with him, his country home. António wants revenge for Tertuliano's intrusion into his stable married life. Furious and ashamed, Tertuliano gives António his clothes, identification, and the keys to his.
After António leaves, Tertuliano exchanges his clothes for some in António's closet. He drives in António's car to António's house, where he makes love to António's wife Helena that night. In the morning, she makes him breakfast while he reads the paper without ever suspecting that he is not her husband.
Meanwhile, Maria and António have spent the night together. In the morning, Maria wakes first and notices the indentation on António's finger from his wedding ring. She deduces that he is not Tertuliano and demands she be allowed to leave.
Tertuliano had hoped that António would return to find him in bed with Helena. As time passes without António returning home, he becomes anxious about Maria, leaves António and Helena's home, and rushes to a pay phone to call Maria's house. A colleague of Maria's answers the phone and tells him that Maria died earlier that morning in a car accident.