In Croydon, England, seemingly grieving Stella Black (Lee Remick) has just returned home from her husband's funeral, he who died in a gliding accident when his rented glider crashed into the sea but his body was never recovered. In reality, she knows her husband Rex Black (Laurence Harvey) is still alive, he who has been in hiding at a seaside boarding house for the three months under the assumed name of Erskine, a shoe salesman on vacation, between the time of his "death" and the funeral. He has just clandestinely returned home following the funeral. They are perpetrating this ruse to collect on the £50,000 life insurance moneys from the Excelsior Insurance Company. They feel Excelsior owes them this money as, in the previous year, Excelsior did not pay out a £20,000 business insurance claim when his airplane, which he used to operate his own transport company, went down in bad weather on a flight to Hamburg, West Germany, and was destroyed. His insurance had lapsed by two days by his error in not paying the latest premium on time. Rex had the money and had never missed a payment.Rex at the house when Excelsior agent Stephen Maddux (Alan Bates) stops by unexpectedly to discuss details of the claim with Stella, most specifically confirmation from her that Rex's death was not a suicide.The next phase of the plan is for Rex to fly to Paris immediately. Stella, handling the finances, is to collect the insurance moneys, have it deposited in a bank account in Málaga, Spain, where she will be emigrating. She is then to take out a specific ad in The Daily Telegraph, which is code to advise Rex that all has been accomplished. Three days later, she is to fly to Málaga, where he will meet her.Rex accidentally acquires the passport of a drunken Jim Jerome, an Australian sheep farmer, and changes it to make it look as his own. Rex is now perpetrating the identity of Jerome, has grown a mustache, dyed his hair blond, and acquired an Australian accent, for his time in Málaga.Three days after placing the ad, Stella arrives in Málaga, and eventually meets up with Rex and his new group of international friends who only know him as sheep farmer Jim Jerome. They believe Stella is his casual widowed girlfriend, who he met while on a previous trip to London.At the bank, Rex and Stella go into the process of converting the insurance moneys into a bank draft which can be cashed anywhere in the world. This process will take one week.In the meantime, they are to pretend to be slowly moving into a more committed relationship, which Stella does not like if only because she feels the process is too slow, since she already has been without Rex for over three months, and is upset that Rex is staying with his international friends, which include some beautiful women. Stella also admits that she does not like "Jim" and by association what it looks Rex has become, a man doing anything for money, which he uses to buy a flashy new automobile, and expensive earrings for Stella. He also implies that he is in the process of another insurance scam where Jim Jerome has a bad heart and will die a premature death, which will allow them to collect further life insurance moneys.A British man who Stella recognizes but can't remember approaches her. He eventually divulges that he is Excelsior's agent, Stephen Maddux, and states he is in Málaga on vacation. He asks her out for dinner which she politely declines in a mild panic at his appearance. Stella and Rex later discuss the issue. Stella believes Stephen is a lonely man who just wanted company with someone he had previously met, albeit in less than pleasant circumstances, while Rex believes his arrival is too coincidental, and that he is looking for evidence as to their insurance fraud. After an argument, they agree to get away from Stephen by spending the week in a town down the coast until the bank draft is completed.Rex and Stella get settled in that small town, when Stephen arrives. Stephen notices Rex by the car he saw Stella previously drive. Rex does recognize who Stephen is until Stella arrives on the scene, she introduces Stephen to "Jim Jerome". Then, Rex believes a better tact to take, now that he knows Stephen knows that he and Stella are traveling together, is to keep Stephen close so that they can find out exactly how much he knows or suspects. If and when Stephen reveals that he knows too much, they will deal with him at that time in the appropriate manner. The immediate issue is for Stella to get another room, as they aren't supposed to be that close yet. Rex believes that in perpetrating only a casual relationship between the two of them, Stephen might be more willing to open up to her. Rex's plan places a further wedge between himself and Stella, who just wants to be with her husband.As Stella and Rex spend more time with Stephen this week, they find that he seems to ask a lot of questions about their lives, and that he secretly keeps writing things in a little notebook he carries around with him everywhere. Stephen takes a photograph of them, which Rex believes he wants as evidence and Rex then "accidentally" falls in the ocean with the camera.As Rex heads to Málaga one day to pick up the bank draft and to insure the earrings he bought Stella, he gives Stella the task of trying to get a look at Stephen's notebook. During their day together, Stella almost lets slip to Stephen that Rex and Jerome are indeed one and the same person. In turn, Stephen starts to tell her something - what she believes will be that he knows their ruse as he talks about her spending the insurance moneys and traveling aimlessly around the world - when she stops him. Seeing Stephen's room door ajar and knowing he is not inside, Stella sneaks in and tries to find his notebook. Stephen catching her in his room before she could read the notebook's contents, Stella implies that she was in his room to seduce him. They make love. After their lovemaking session, Stephen tells her among other things that he no longer works for the insurance company, and that what he writes in his notebook are musings about his travels, which he shows her. She now realizes that he knows nothing about their scam and that his interest in them is purely in her alone. She is so relieved that once again, with her guard down, she lets slip that Jerome is Rex, but she is able to cover up her mistake.When Rex returns from Málaga, he first runs into Stephen, who talks as if he knows what's going on with their scam without actually saying it. As such, Rex later tells Stella that their new plan, no more scams, is to ditch Stephen by leaving first thing in the morning before he awakens, and cross the border into Gibraltar. Relieved that there will be no more scams, Stella does not tell Rex what she has found out about Stephen.Catching Stella alone later that night, Stephen implies that he sees a future for the two of them. Stella responds in turn that he should not count on anything concerning her.The next morning, Stephen, awake and alone in his bed, finds one of Stella's expensive earrings in the bed. Hearing a noise outside, he gets up and sees Rex and Stella driving off in their car. He rushes off to catch up with them if only to return Stella's earring. He is able to catch up to them because they are caught behind a temporary roadblock in a town. Rex is standing at the roadblock seeing what is going on while Stephen approaches Stella in the car. Stella initially believes Stephen has come for her, but Stephen shows Stella the earring, Stephen having that earring which could get Stella into trouble with Rex. Stephen is unable to return the earring as Rex returns. Rex, seeing Stephen, is angry under the surface as he still believes Stephen is after them. On the surface however, Rex is cordial, telling Stephen to meet him and Stella for a drink further up the mountain. With Stephen following the pair in his own car along the winding mountain road, Rex tries to run Stephen off the road and over the cliff. Rex believes he is successful seeing Stephen's car go off the road. Stella is horrified. Two road workers witnessed the event, and are able to save Stephen, whose car, albeit in a precarious position, only slid a small distance down the hill. Stephen believes Rex tried to run him off the road out of jealousy, since he thinks Stella told him about their tryst.Rex, with a hysterical Stella as his passenger, drives off toward the Gilbraltar border. Reaching the border, they are stopped behind a long line of cars. Once they reach border patrol, they are questioned. The telephone rings. It is the police, who have reached Stephen in the mountain. They alert border patrol to stop Rex and Stella. When Rex figures out what is going on, he notices that Stella has run off into the crowd with the bank draft. He jumps back into the car and drives off into the crowd chasing after Stella. Rex eventually catches up with Stella in a crowded church. Angry, he tries quietly to get the bank draft from her. She replies that he will never be able to cash the draft as the authorities everywhere will know he killed Stephen as Stephen has her insured earring his possession, the earring which she lost while in his bed. Incensed, Rex tries to strangle Stella out of jealousy. He is stopped when a policeman arrives. Rex runs off to his car and drives off while the police take Stella into custody. At the police station, Stella is surprised to see a still alive Stephen there. Stephen refuses to press charge against either Rex or Stella, Stephen still believing Rex's actions were purely out of jealousy. Stella continues the ruse as she tells Stephen that she told "Jerome" about their tryst.Meanwhile, Rex drives to an airfield and steals a plane. However, he is unaware of a leak in the fuel line. The plane runs out of fuel mid-air and crashes into the ocean. Rex's just barely alive body is pulled out of the water and returned to the Spanish dock, where Stella, with the police, are waiting. As Rex dies, Stella still continues the ruse, stating to the police that he is a man she met on vacation and barely knew.