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An airplane from San Francisco to the Soviet Union has been hijacked by terrorists and is flying off the coast of Oregon, with several US fighters in escort. On board the terrorist Wesson worries that there may be plans being made to stop them, so his comrade Meryl reminds the passengers that Roger, the third terrorist, is terminally ill and has 50 pounds of plastic explosive strapped to his waist and a dead-man's switch in his hand that he will detonate if he has to. Also on board is the American Chess Team including young prodigy Carlisle Anderson.
At San Francisco International Airport, Hawk, Beach Head, Stalker, Flint and Lady Jaye discover how the terrorists murdered a news camera crew that was due to accompany the chess team and took their place. According to a broadcast by the terrorists they are the "Leon Trotsky Brigade of the Fourth International" seeking "to exact revenge upon the heirs of the murderer Stalin." Beach Head explains that although Stalin kicked Trotsky out of the Soviet Union, 13 years later Trotsky was killed in Mexico City with an icepick in the head, most likely on Soviet orders. Hawk orders the team to split in two, with Flint, Lady Jaye and Beach Head dispatched aboard an SST to intercept the airplane when it refuels at Anchorage, whilst Stalker and Hawk head into San Francisco to check leads - the Fourth International are listed in the phone book!
On the plane Carlisle tells the terrorists he has worked out every scenario in his head like a chess game and they come out losing every time. But Roger responds that nothing can stop him from detonating the trigger if attacked. In San Francisco Hawk and Stalker arrive at the Fourth International's headquarters to find it besieged by police. He pulls rank as a general and storms in with Stalker, who has a taser ready to capture one of the Trotskyites alive. At Anchorage Airport the other three Joes arrive before the airplane and demand schematics. The plane lands and the terrorists order it to stay on the runway with only refueling personnel allowed to come near. Wesson opens a hatch and stands with his gun at the head of a stewardess. In San Francisco Stalker and Hawk take cover as one women blasts away with a machine gun. During the rhetoric break they dive forward, shooting down several other Trotskyites and Stalker tasers the woman with the machine gun. Hawk explains that when tasered the electric shock causes the muscles to contract, hence the woman unconsciously triggering the gun.
In Anchorage the three Joes hide aboard a fuel tanker and then take advantage of the limited view from the hatch to run under the plane and climb into the three separate wheel housings. The plane has refueled and Wesson orders it to take off. Roger tells him to shoot the stewardess. Wesson is reluctant but the stewardess believes the terrorists always planned to kill the hostages and hits him. He shoots her dead. The plane takes off, with the three Joes slowly cutting their way onboard. Wesson orders the pilot to fly to Beringovskiy in eastern Siberia, a restricted secret military base, with the accompanying US fighters preventing the Soviets from shooting the jet down. In San Francisco Police Headquarters the captured Trotskyite is refusing to answer questions. Her file reveals her to be a girl from a rich background who found a cause to believe in. She is thrown in the holding pen, looking forward to the "honor to be incarcerated with my sisters of the oppressed proletariat" but the holding pen contains a rather different class.
On the plane the three Joes separately cut their way into unoccupied parts of the plane. Lady Jaye reaches the luggage compartment and disguises herself as a stewardess. Outside a pair of Mig 23S Flogger Ds approach the airplane and the fighter escorts and tell them to turn back, but the fighter pilots refuse because of the passengers onboard. In the passenger compartment Beach Head climbs up under Carlisle's chair, with the prodigy refusing to give him away. In San Francisco, Hawk radios Lady Jaye to tell her that the women talked and the terrorists' plan is to take the plane to a secret Soviet chemical warfare depot and crash the plane, releasing a gas cloud that will kill millions. In Beringovskiy, Colonel Koldunov, the nephew of the Soviet Deputy Minister of Defense, radios fighter command seeking an order for the plane to be shot down and the fighters ask for firing authorization. Aboard the plane, Flint has now cut his way into a toilet while Lady Jaye climbs into the passenger compartment and starts posing as a stewardess. When Meryl challenges her she claims her make-up needs touching up, hence her different appearance. Roger is now going insane at the impending destruction and Meryl tells him to relax. Beach Head attacks and subdues her as Lady Jaye tasers Roger, his hand contracting on the dead man's switch. Wesson rushes from the cockpit, only to be gunned down by Flint. Lady Jaye attaches her handbag containing a charge to the hatch and tells everyone to take refuge. The charge blows and Roger is sucked out of the plane, exploding in mid air. Beach Head captures Meryl while Flint tells the pilots to turn the airplane around. Soviet Fighter Command now gives authorization to shoot the plane down but the pilot reports it has altered course.
Later the plane lands in San Francisco and Meryl is taken away. However Lady Jaye has managed to get herself locked in the toilet!