The TARDIS materializes in Earth orbit in the year 2136 AD, and the Doctor picks up a distress call mentioning him by name. He nearly collides with another spaceship while following the call to its source, an orbiting hotel station which has been booked by a games enthusiast hosting a murder mystery weekend. Hornby's backers have pulled out at the last minute, cancelling the tour flight and sending only one representative, Alison Hayes; only a few guests have arrived, under their own power. The Doctor, uncertain who sent the call to him, pretends to be here for the game, and soon someone sends him an anonymous message via the hotel's electronic concierge, Thomas, asking to meet him privately after the game begins. While preparing for the initial briefing, the Doctor notices that the stars he can see are slightly out of position, indicating that a cloaked ship is lurking nearby. He sets the TARDIS scanners to observe the ship and takes a monitor to alert him should it begin to move.

Ben and Polly try to mingle with the other players; amateur thespian Henry Mace, the quiet Bryan Melrose, the uncommunicative Ted Matlock, and friends Daphne McAllister and Terri Willis. Neville and Dorothy Adler, two famed mystery authors, have also arrived for the game but fail to join the others for the preliminary meeting. Hornby hands out character bios to the players and the game begins. In character, Hornby invites Polly to meet him in the gymnasium, where he reveals that their characters have been having an affair and tells Polly to "kill" him. Unfortunately, Hayes hasn't prepared the room properly, and the javelin with which Polly was supposed to kill Hornby in a fit of rage is still locked up in the equipment room.

The Doctor interrupts a fight between Melrose, Matlock and Neville Adler, and in the scuffle somebody shoots and injures Melrose. The participants in the fight go their separate ways, and the Doctor suspects that what he's seen wasn't part of the game. Ben goes to speak with the Adlers, using the game as a pretext, and has a pleasant conversation with them while Dorothy uses her laptop to complete the latest draft of her forthcoming novel. As Ben leaves, the lights in the hotel flicker for a moment, and then somebody strikes him on the back of the head, knocking him out.

The Doctor finds nobody waiting for him at the arranged rendezvous, and when he leaves he stumbles across Matlock, who has been electrocuted while taking the lifts. Hayes finds the Doctor standing over the body but he convinces her that he is not responsible, and they summon the players to the lounge to tell them of the incident. Mace, all bluster and false bravado, panics at the thought of being trapped with a real killer and rushes to lock himself in his room. Ben, meanwhile, awakens in the medical bay to find he is being tended by Terri, who claims to have found him unconscious in the corridor. They set off for the lounge, but Polly and Daphne have gone to collect them and they miss each other on the way. Polly and Daphne see Neville Adler entering the docking bays, and follow him out of curiosity -- and hear the sounds of a scuffle, a shot and a scream. As Daphne flees in terror, Polly finds Neville's dead body and is taken prisoner by his killer, Alison Hayes.

The Doctor modifies Thomas to access government databases on Earth in order to learn more about the visitors to the station, and when inconsistencies surface in his own data records, he is forced to admit to the others that he and his friends are time-travellers. Thomas finds gaps in Terri Willis' recent history and can find no data on the Adlers, who booked into the hotel under their pen names. He can find no information on Hornby either, until Hornby admits that his real name is John Smith and that he changed it to be more interesting. Thomas also informs them that Polly is currently in the company of Ms Hayes, and the Doctor sets off after them. He is accompanied by Hornby, who is shaken by the effect of real death and vows never to make light of murder by using it as entertainment again.

The Doctor and Hornby find Hayes interrogating Polly to find out who she's working for, and demand answers. Hayes turns out to be a government agent, as was Matlock; Matlock must have found the Doctor's name in a government database and called upon him for help, although due to the vagaries of time-travel the Doctor hasn't worked for such an agency yet. Hayes reveals that someone on the station is attempting to strike a deal with the Selachians, a violent aquatic race. Centuries of abuse by the air-breathing species who hunted them for sport turned the Selachians into a race of vicious warriors, who are constantly seeking new weapons technology with which to meet their enemies -- the rest of the Universe -- from a position of strength. The human race used to trade with them until the Selachians destroyed the colony on Terra Alpha; and now they have come to the Hotel Galaxian in search of the ultimate weapon.

Ben gets lost in the hotel while searching for Polly, and stumbles across Melrose, who seems to be priming a bomb. Ben tries to stop him, and learns too late that Melrose had in fact planted the bomb earlier and is now trying to defuse it. The bomb goes off, breaching the hull, and although Ben and Melrose manage to get to safety before the bulkheads close, the Galaxian begins to drop out of orbit. The Doctor gets to the engineering deck and manages to stabilise the hotel, but its orbit is still decaying, and within a few hours it will burn up in the atmosphere. The Selachians, detecting this disruption to their plans, approach the hotel and attempt to dock with the erratically moving airlock.

Hayes finally explains that the "Adlers" are not the mystery writers after all, but government scientists who developed a fantastic new weapon -- and intended to sell it to the Selachians via their human agent, Melrose. The hand-off was supposed to take place under cover of the murder game, but Hayes' organisation put pressure on World Corps to cancel it, thus making it more difficult for them to meet secretly. Realizing that the weapon is now their only bargaining chip, the Doctor sends the others to search for the disks containing its blueprint while he tries to bluff the Selachians into holding off. Unfortunately, he has underestimated their current level of technology, and a group of Selachians spacewalks from their ship to the hotel airlock, breaking in before he can warn the others.

Polly and Hayes manage to convince Dorothy Adler that the Selachians will grant no mercy for failure, pointing out that their agent Melrose had been ordered to destroy the hotel once he left with the disks. Dorothy hands over her disk, but Neville hid his before Hayes killed him, and they have no idea where it is. The Selachians hunt down the hotel's occupants and take them to the lounge for questioning. Melrose is killed for his failure, and the Selachians take Polly back to their ship, intending to force her to act as their new agent. Under threat of torture, Dorothy admits that Hayes has the first disk, and the Selachians kill her and take it. Mace turns out to have found the second disk, and he tries to use it to bargain for his life; the Selachians, however, unable to operate human computer keyboards, force him to activate the programme on the disks in order to test it, and then kill him.

The Selachians lock the survivors in the lounge and return to their ship to await the destruction of the Galaxian. Dorothy admits that the disks don't contain blueprints, but the weapon itself -- an AI programme which targets a single victim and turns every computer system in the vicinity into a weapon until its victim, and that one victim alone, is dead. Ben turns out to be the test subject, but the programme must find a way to kill him without harming the others around him. The Doctor builds a sonic device to open the lounge's lock, musing that he should really build himself a portable one, and evacuates the others to the TARDIS. The assassination programme tries to divert Ben away from the others, but Terri remains close by him, saving his life and getting him to the TARDIS. The Doctor deactivates the temporal circuits, ensuring that the TARDIS remains in Earth orbit when he takes it away from the disintegrating hotel.

Polly, left alone to familiarise herself with the Selachian computer system, manages to access the communications mode and sends a distress call to the Terran Security Forces. The Doctor, meanwhile, successfully makes a short hop to the Selachian warcraft, materializing in the underwater areas. Ben and Terri accompany him, intending both to rescue Polly and install a virus which will corrupt the assassination programme if the Selachians attempt to run it on their computers. The Selachians detect their presence and pursue them through the ship, and they emerge from the water in the guest quarters where the Selachians deal with air-breathing species. The Selachians have allowed the TSF officers to board the ship and then killed them, but have left Polly alive in order to test the assassination programme on her. At the last moment, Terri grabs the programme disks and tries to flee, but the Selachians shoot and kill her.

Ben gets the disks from Terri's body and follows the Doctor and Polly to the TSF ship, but it unexpectedly seals him out and tries to strand him in the opening airlock; the assassination programme has transferred itself from the Hotel Galaxian to the Selachian craft. The Selachians pull him out of the airlock to recover the disks, but their entire ship suddenly starts to break up around them, and in the confusion Ben gets back underwater and boards the TARDIS. The xenophobic Adlers had programmed their weapon to preserve the lives of other humans, but not aliens -- and it causes the entire Selachian ship to self-destruct in order to get Ben. Unable to transfer itself into the TARDIS and unable to detect Ben anywhere in the vicinity, the programme then presumably shuts itself down, its mission complete. The Doctor docks the TSF ship with the TARDIS, which has survived the explosion, and sets about trying to return the survivors home. Ben realizes that Terri, who had seemed to care for him, was really using him to get to the disks; she must have knocked him out after he left the Adlers, assuming that they'd handed the disks over to him, which was why she stayed close to him for so long. He and Polly must now come to terms with the feelings they realize they've developed for each other.