Sir Roger Moore and Sir Michael Caine play dual roles in this off-beat and highly silly caper, a pair of small time conmen, and a partnership of nuclear physicists. As conmen, they use their uncanny resemblance to the high-living scientists to con their way to the scientists' safe deposit boxes, but in doing so, become entangled in a shady world of spies and international intrigue.
- The film opens with narration from Sidney about how everyone in the world has doppelgänger. We see his doppelgänger, Daniel Hicklar, who is working on the formula for nuclear fusion. We are also introduced to Hicklar's partner, Sir John Bavistock. Hicklar successfully discovers nuclear fusion, and Hicklar and Bavistock begin scheming, planning to sell the formula on the black market. The film changes focus, and find Lipton just being let of prison, right when he is engaged in a game with "One-Arm" Alf, his cellmate. The audience is then introduced to Gerald Bradley-Scott/Smith, Lipton's old crime partner. He steals the luggage from an American politician outside a hotel. Next, Willie - Lipton's other crime partner - is at her husband's funeral, and it is implied that she only married him for money. At the reading of his will, his entire estate is given to his mistress, Donna Dultch, who was unknown to Willie.
Lipton goes back to his house, but it is demolished before he can enter. Wille finds him and takes him back to her home, as Dultch oversees the repossession of its contents. While Lipton is having a bath, he reminisces about the gang's glory days. Willie tells him to stay, as they will be having guests that night. The first guest is Inspector Grosse, a corrupt Chief Inspector, who Lipton believes sold him out. He begins to angrily choke Grosse, but Grosse reveals that it was Gerald who sold him out, which is why he was in prison for three years. Grosse explains that they arrested him for stealing luggage earlier that day. Gerald arrives, and Lipton starts to choke him. Willie then tells the pair that she wants them to do a caper, as she needs the money.
The plan is for Gerald and Lipton to impersonate Bavistock and Hicklar, as to steal the diamonds. Lipton is reluctant at first, as it would involve getting plastic surgery on his nose. However, he ultimately agrees. Willie explains that the diamonds are in a safety deposit box at Lacey's, and require keys to open them. To get them, Willie has to distract Hicklar and Bavistock during the day, so Lipton and Gerald can steal the keys. Gerald and Lipton are to steal Hicklar and Bavistock's keys, respectively. Gerald pretends to be a piano tuner, and Lipton pretends to be a window cleaner. Gerald is successful, but Lipton is not, as Bavistock's key is on the collar of his vicious dog. Gerald and Lipton circumvent this obstacle by getting Bavistock's to get really tired, so the key can be stolen.
In the following montage, Lipton gets blue-eye contacts, and Gerald gets a wig, so his hair now looks like Bavistock's. That night, Sidney challenges Gerald to fool someone into thinking he really is Bavistock. Gerald accepts, and goes to Bavistock's health club. However, it turns out to be a brothel. Sidney then goes to Hicklar's health club, in the hope that it is a brothel. However, it turns out to be a health club. While he is out, Gerald and Willie discuss Sidney's love life, and it is implied that either Gerald or Sidney were in a relationship with Willie when they lived together.
Later, Gerald and Sidney go out. Gerald wishes to use Bavistock's identity, as to impress women. They end up at a nuclear fusion conference, where they are accosted by Chesterton, a scientist who attempted to do an experiment of Bavistock's, which ended up damaging his garage roof. He aggressively challenges them, and Lipton punches him, and Lipton and Gerald are both arrested. In their cell, they discuss Willie, and they try to work out if the other was in a relationship with her. The next morning, Hicklar's sister, Chesterton, Willie and government scientist Sir Hugh - who scolds the two on their actions - arrive to pay the two thieves bail. The main three are able to escape by causing a small brawl.
Once out, Sidney and Gerald head straight for Lacey's, and Willie holds up Hicklar and Bavistock by causing a small car crash. Gerald and Lipton are able to steal the diamonds. Hicklar and Bavistock arrive just after they leave, but they are arrested by Inspector Grosse, who calls the "traitors." That night, the gang are gloating over their victory, but a horde of police arrive and arrest them. They are taken to meet Grosse, Daryll Hyde - the head of the CIA - and Nigel Holden - the head of MI5. The two spy bosses tell them that they invested half a billion into Hicklar's fusion project, and are deeply upset that they have gone freelance; selling the plans to the highest bidder. It is revealed that the diamonds that Sidney and Gerald stole were actually the deposit that the foreign powers paid. The gang is told that a series of auctions are to take place in Scotland, and Hyde and Holden wish for them to continue impersonating the two scientists, so that the two governments can make a return on their investment by keeping the money paid by the foreign powers, and giving them fake plans. The two thieves are introduced to Flo Fleming, a CIA agent who will accompany them, and work with Willie to try to find the location of the real formula. Gerald and Sidney ultimately agree.
At the train station, Sidney runs into Alf, who recognises him. This depletes some of his confidence in the plan. In the dining car, Sidney acts out hugely and does things Hicklar would never do, like ordering alcohol. This depletes some of Flo and Willie's confidence in the plan. Later that night, the two women work on finding out where the plans are. Afterwards, Flo goes to Sidney's compartment and prepares him for the auction that night. She gives him an earpiece, so she will be able to tell him what to say. Outside the train, Willie runs into Hicklar. Willie believe he is Sidney, and tells him to get changed. Hicklar finds Sidney getting ready in his apartment, and holds him up with a gun. However, Sidney is able to overpower him and tie him up.
Sidney arrives at Heperton Hall, which is where the auction is taking place. He tries to tell Gerald and Willie about Hicklar, but they send him away to perform the auction. The earpiece begins malfunctioning, and Sidney is forced to complete the auction on his own. He is successful, however, and a buyer called Death's Head - representing some European country - is to bid in the final auction. Hicklar, who has escaped, tries to kill Sidney, but he is knocked out by someone else. When Sidney is trying to tie Hicklar back in his cabin, Hicklar overpowers Sidney and ties him up. Willie and Flo go to a village called Knap-Hurst, where they suspect the plans are held. The next morning, Sidney begins formulating his escape plan, while Hicklar gets some sleep. Willie and Flo arrive in the village, and they find the bank where the fusion plans might be held. However, they return to the train without investigating. Just as they leave, Bavistock arrives at the bank. Back on the train, Sidney successful escapes his bindings and overpowers Hicklar. Before he can tell Gerald, Gerald leaves on a bus for Whittingham Moat, the castle where the second auction will be taking place. Sidney takes a second bus to catch up to him. Sidney tries to tell Gerald again, but the buyers arrive before he can. Gerald successfully runs the auction, with Francesca - a bidder from a European country - set to bid in the final auction.
Back on the train, Sidney takes Gerald to his compartment, but they find that Hicklar has escaped. Gerald is unconcerned. Willie and Flo arrive back just before the train leaves, and they run into Hicklar. Thinking he is Sidney, Flo starts to talking to him about their progress in finding the plans. The other three realise what's going on and rush to Flo's aid. Hicklar is successfully defeated. Later, Gerald and Sidney learn that Flo is Willie's daughter, and one of them is the father. They also learn that Willie has been working for the CIA, and she got them into this on purpose. Darryl arrives with a force of men, yet Hicklar still manages to escape. Hyde promises them a lot of cash if they continue. Flo and Willie return to Knap-Hurst, as to try to find the plans. It is revealed that Bavistock is on the train.
Later, three members of the train's staff are killed in traps presumable set by Bavistock. Worried, Gerald and Sidney head to the dining car and start having dinner. It is shown that Bavistock has poisoned the dinner. However, Sidney doesn't eat any, and he is one of the only two passengers who is not violently ill. Despite Bavistock's efforts to kill the two thieves, he is re-captured. Gerald and Sidney arrive at the final castle, and are prepared for the final auction, which is taking place during a highland gathering the next day. Hyde promises them that they will be surrounded by CIA agents who will protect them, which they are.
Hyde and Holden then release Bavistock, in the hope that he and Hicklar will kill Gerald and Sidney. Flo and Willie are able to get the real fusion plans. After surviving a further attempt on their life, Gerald and Sidney head for the final auction. During the final auction, Bavistock and Hicklar arrive, and steal the diamonds. After a furious chase, Gerald and Sidney are able to overcome Bavistock and Hicklar, and they are arrested. Hyde and Holden tell Gerald and Sidney that they can only give them immunity from prosecution, and no diamonds. Flo is about to leave with the two spy bosses, but she overhears them discussing their plan to kill Gerald, Sidney, Bavistock and Hicklar, as to avoid embarrassment. Flo returns to the dejected three, and gives them the real plans. They use to extort lots of money from the British government, and they move to Barbados. Bavistock and Hicklar are sent to jail; Flo moves to New Mexico; and Willie marries a senator.
Three years later, the British have completed a plant, based on Hicklar's plans. However, the plant blows up, due to Hicklar's plans not being entirely finished. Meanwhile, Gerald and Sidney are broke again, because they gave all their money to someone who looked like John Cleese.