The Doctor plans to take Romana to Brighton, but misses the opening of the Pavilion for the second time and arrives in the off-season, when it's too cold for swimming or sun-bathing. K9 spouts off a list of all recreational facilities in the galaxy, and Romana, frustrated, tosses her beach ball into the surf for him to fetch. But the Doctor has forgotten to update K9's sea defenses and the robot explodes the moment he hits the water. Romana takes the damaged K9 back to the Doctor and demands to be taken somewhere else; following K9's lecture she's decided she likes the sound of the Leisure Hive of Argolis, built by the survivors of a devastating war with the reptilian Foamasi in the year 2250.

Forty years have passed since the war, and the Leisure Hive is now in dire financial trouble due to declining bookings and equipment failures. As far as their Earth agent, Brock, is concerned, the Argolins have frittered away their savings on pointless experiments in tachyonics while other Leisure Hives have been expanding to offer new and more attractive services. Brock turns down Chairman Morix's offer to join the Hive's board of directors, but shortly afterwards he arrives on Argolis in person. He and his lawyer Klout have a counter-offer from an alien species which wishes to buy the entire planet. Morix's son, Pangol, refuses point-blank; as the youngest of a species which was all but wiped out, he has developed a great mistrust of aliens. Morix -- who is reaching the end of his lifespan -- dismisses Pangol while he listens to Brock's offer, but is shocked to learn that the species which wishes to buy Argolis is the Foamasi. Ironically, due to the war, only the reptilian Foamasi can survive unprotected on the radioactive surface of Argolis. Morix dies, still refusing to sell his world, and with his death his consort Mena automatically becomes the new Chairman.

The TARDIS materializes in the observation hall of the Hive, where Pangol is demonstrating the Tachyon Recreation Generator to the visitors. The Doctor becomes intrigued when he realizes Pangol is manipulating a solid tachyonic image of himself, but he and Romana agree that despite the neat solutions the Argolins have developed to the problems of generating and manipulating tachyons, such images could only have a limited life span. Meanwhile, a reptilian creature breaks into the Hive in an empty corridor, and watches from hiding as Pangol invites a sceptical visitor to take part in a further demonstration -- but something goes terribly wrong, and instead of harmlessly manipulating the tachyon image, the generator tears the real Loman apart. The Doctor and Romana rush forward to offer assistance, and the Argolin, who have been expecting a scientist to arrive from Earth at Mena's request, assume that the Doctor is that scientist and take him and Romana to the boardroom to speak with Mena.

Pangol and Brock arrive too late to save the Doctor -- but fortunately he's already opened up the back of the generator and escaped. The tachyon image in the viewing bubble fades away as Argolin security guards take the Doctor and Romana back to the boardroom. There, Hardin has arrived on Argolis at last, although he and Mena both know that Mena's new duties mean that their relationship must be purely professional from now on. He is forced to admit that his experiments are not yet complete, and when the Doctor and Romana arrive, Mena offers to overlook their unconventional arrival in the Hive on condition that they help Hardin with his experiments.

As night falls over the Hive, the Doctor and Romana comment upon the beauty of the dust storms outside -- a legacy of the war which has rendered Argolis radioactive and uninhabitable. The Argolin will be unable to emerge from the Hive for at least three centuries, and thus devoted their shelter to the cause of cross-cultural understanding to prevent such genocidal wars from ever occurring again. One of the reptile creatures, meanwhile, sabotages a fibre-link connection, shutting down power to an experiential grid -- one of many faults which have plagued the Hive recently, Loman's death being the most prominent. While dealing with the crisis Mena suddenly collapses, aging years within seconds, just as Morix had done before her. The war has bequeathed the Argolin a metabolism which remains steady for years before suddenly collapsing -- and as well, all of the Argolin who survived the war are sterile.

Brock approaches Hardin about the investment potential of his experiments, and Hardin weakly tries to fob him off with vague promises. His partner, Stimson -- who had urged Hardin to fake the experiments in order to ensure continued funding from the Argolin -- fears that Hardin is about to blow it all, and his fears are confirmed when Mena brings the Doctor and Romana to the laboratory and Hardin sees that Mena is dying. The Doctor departs to investigate Loman's death, and Romana pushes past Stimson to examine the laboratory equipment. She obviously knows what she's doing, and when Hardin admits that the experiment doesn't really work, Stimson slips out of the lab and tries to book passage off Argolis as quickly as possible. All of the shuttles back to Earth are fully booked, however. Desperate to get away, he tries to contact Brock, but finds his quarters empty -- and when he opens Brock's closet to search it he finds the empty husk of Klout's skin hanging on the hook. Horrified, he flees from the cabin, but he has been observed by one of the reptile creatures, which follows him to the observation hall and kills him.

Hardin and Romana manage to solve many of the problems inherent in the time-reversal machinery, but although Hardin's theory is sound the hardware still won't work properly. Nevertheless, by increasing power they manage to halt the flow of Time over an hourglass, and a further increase of power causes the sand to flow upwards into the upper bell of the hourglass. Romana and Hardin depart to report success to Mena -- and moments later, there is a tachyon surge and the hourglass explodes.

The Doctor checks the generator controls and finds them set to eliminate intruders, but before he can investigate further, he is arrested by Argolin guards who have found Stimson's body with the Doctor's scarf wound tightly about his neck. The Doctor is taken back to the boardroom to stand trial, and swears his innocence before the Helmet of Theron, the symbol of the Argolin who led the war against the Foamasi. Mena insists upon a civilised trial, but Pangol would prefer the more traditional trial by ordeal. At that moment Hardin and Romana arrive to announce their experiment's success, but before risking Mena to the time-reversal process Hardin needs to conduct an experiment on another living organism. And this gives Pangol an idea.

The outcome of the trial by ordeal seems obvious. The Doctor and Romana are taken back to the guest quarters and fitted with limiting collars; if they attempt to enter a prohibited area or remove the collars, the collars will administer electrical shocks. The Doctor and Romana, left alone, try to figure out why the experiment went wrong, and although the Doctor's memory is failing he recalls seeing a second baryon shield in the generator. He didn't have time to see what was behind it, but it seems clear that there must be a second circuit in the generator, with a purpose which they don't yet understand.

Hardin supports the ailing Mena back in the boardroom, until Pangol arrives to announce that the guards sorting Stimson's effects have found proof that the experiments were faked. Hardin admits the truth but insists that he was close to a genuine breakthrough, which he achieved with Romana's help. Mena is bitterly disappointed in him but nevertheless agrees, despite Pangol's objections, to let Hardin continue his work -- alone. Hardin, knowing that he can't possibly succeed without Romana's help, releases her and the Doctor from their collars. The Doctor is beginning to suspect that the recreation generator isn't all that it seems -- what exactly is it meant to re-create?

Pangol discovers that Hardin's experiment has destabilised the generator, and works through the night to repair the damage. He then returns to the boardroom to find Brock presenting Mena with the Foamasi contracts, which Pangol tears to pieces. The contract appears to have come from a private group named the West Lodge, but Pangol knows that the Foamasi have outlawed private enterprise and concludes that the "offer" is an attempt to foist unwanted restitution for the war upon his people. Pangol's own plans to rebuild the New Argolis are near completion, and Mena is too weak to stop him from revealing the Argolin's greatest secret to Brock. He, Pangol, is the first of the new Argolin, a product of cloning experiments conducted in the recreation generator. The technology was outlawed when most of his brethren emerged stillborn or disfigured; only Pangol survived, whole in body and mind, to come of age as a fully proficient tachyon engineer. And now he is ready to conduct the next phase of the experiment...

The Doctor, Romana and Hardin arrive in the observation hall to see Vargos and the other guides conducting repairs to the generator. Somebody needs to find out what the second circuit is for, and Romana is the only one who can survive if exposed to another tachyon surge. The Doctor and Hardin distract Vargos while Romana slips into the imaging chamber; once there, she removes the second baryon shield to expose the circuitry beyond it, but is then confronted by one of the reptile creatures. Pangol spots the Doctor on the surveillance monitors and rushes to the hall to stop him. The Doctor and Hardin have gone by the time he arrives, but the generator controls are registering an intruder; certain that it's the Doctor, Pangol programmes the generator to age him a further two thousand years.

The Foamasi who rescued Romana takes Brock's voice synthesizer and explains that the real Brock never left Earth; both he and "Klout" were replaced by criminal Foamasi, the leaders of the local branch of the West Lodge. Since the West Lodge has been outlawed on the Foamasi homeworld they intended to move their base of operations to Argolis, and they and their agents are responsible for the acts of sabotage and murder which have nearly driven Argolis into bankruptcy in order to make their offer seem more attractive. The criminals are placed under restraint to be taken back to the Foamasi homeworld for trial, but the Doctor isn't convinced that the troubles are over. Indeed, Pangol seems to have gone completely over the edge by now, and as dawn breaks over Argolis he shuts down the Hive completely, refusing to let the Foamasi leave -- even though this could be considered an act of war against their government. Pangol seems convinced that the Foamasi and the Doctor are collaborating in an alien plot to infiltrate the Hive and conquer the Argolin, but he can stop them now. Mena is too weak to prevent him from seizing the Helmet of Theron and preparing to usher in the dawn of the new Argolis. "We, Pangol, will be the army..."

The Doctor, Romana and Hardin return to the laboratory, to find that Pangol has already recovered the control circuitry from the generator. They need another random field frame to stop him and protect against the generator's tachyon surges; the Doctor suggests using the Randomiser from the TARDIS, but Romana isn't convinced it will work and instead she and Hardin begin to build a new one. Pangol, meanwhile, orders the Argolin to assemble in the great hall to witness the dawn of the new Argolis, and Romana and Hardin fear that he has taken power due to Mena's death; but Hardin sees on the monitors that Mena is still alive, barely, and rushes to the boardroom to help her. Romana then realizes that the Doctor has gone and sees him on the surveillance monitors, taking the Randomiser into the imaging cubicle.

Romana rushes to the observation hall, but finds the Argolin unwilling to stop Pangol. The Foamasi shuttle attempts to leave without permission, and Pangol has it shot down -- a deliberate act of war. Pangol then enters the imaging cubicle, wearing the Helmet of Theron, and Romana watches in horror as an army of tachyon-duplicated Pangols begins to march out of the cubicle. The Pangols grab Romana and begin to drag her out of the Hive, and Pangol orders that Mena's body be disposed of outside as well. But once they're out of the hall, the clones drop Romana and remove their helmets to reveal that beneath they are all images of the Doctor, restored to youth. Moments later the army vanishes, as all of the tachyon images were fundamentally unstable; only the original Pangol and the original Doctor remain.