The Doctor tries to get Tegan back to Heathrow Airport, but instead the TARDIS materializes on board an alien spacecraft. The Doctor puts on an atmospheric helmet and goes out to explore, telling the others to wait for him. Tegan worries that she'll be late and lose her job, and Adric is amused by what he perceives as her stupidity; even if it takes them weeks, the TARDIS can still get her back to work on time. The Doctor explores the room the TARDIS has arrived in, and is surprised by the advanced technology within; he eventually returns to the TARDIS and tells the others it's safe to come out as long as they wear atmospheric helmets. He gives Tegan a spare key to the TARDIS in case they get separated.

Their arrival has been noted by a hovering surveillance camera called a "monopticon", which transmits images of the new arrivals back to the ship's control room. The crew react with interest; could these new arrivals be Earthlings, and if so, does that mean that human science has progressed further than they expected? They are obviously from different cultures; have the humans learned the benefits of inter- cultural co-operation? And if so, how will that affect the aliens' reception when they arrive?

Nyssa finds an interferometer which could be used to recalibrate the TARDIS' shaky time-curve circuits. The Doctor tries to communicate with the monopticon, and a nearby door opens; he and Tegan follow the monopticon to a meeting with the crew, leaving Adric and Nyssa to match the interferometer readings to those of time-curve circuits. But while Adric is taking readings inside the TARDIS, a Greek philosopher without an atmospheric helmet enters the room and approaches Nyssa...

The Doctor and Tegan eventually reach the ship's bridge, which is more like a throne room. Three aliens with corrugated green skin greet them and introduce themselves as the Monarch of the planet Urbanka, and his Ministers for Enlightenment and Persuasion. They change the atmosphere so the Doctor and Tegan can breathe without helmets, and question the Doctor about his arrival. He tries to gloss over the details, claiming only that the ship's intense magnetic field caused a fluctuation in his artron energy and drew him off course. The aliens inquire about their clothing, and Tegan tries to describe current Earth fashions by drawing a picture of a man and woman in contemporary clothing.

Adric arrives to tell the others that Nyssa is missing, but the Doctor advises him not to worry. Monarch invites them to remain for refreshment, and as they leave, he hands Tegan's sketch to Enlightenment and sets off to investigate the TARDIS for himself. He is frustrated when he finds he can't even open the door; how can such an apparently primitive piece of equipment confound his advanced technology?

Tegan is terrified by this evidence of the Urbankans' almost magical technology, but Adric is fascinated. Enlightenment and Persuasion explain that their system's star, Inokshi, is an irregular variable and that they were forced to evacuate their homeworld; all three billion Urbankans are on board this one ship, which the Doctor finds hard to believe. Bigon shows the Doctor and his companions to their guest quarters, where he tells them that a hundred generations have passed since he was "rescued" from Earth; the Doctor assumes that they're on a generational ship, and that Bigon's ancestors were taken from ancient Athens. Before Bigon can say more, Monarch summons him away, unwilling to let the Doctor know too much too soon. The Doctor deactivates the monopticon in his quarters so he can speak with his companions privately. Tegan just wants to get away, but the Doctor is unwilling to leave just yet. The Urbankans have visited Earth at least four times in the past and now seem to be coming to stay -- but how can three billion Urbankans possibly co-exist on the same planet as the human race?

Monarch is amused by the Doctor's intelligence, and decides to arrange a "recreational" which will divert the Doctor's attention while Monarch tries to learn more about him through Nyssa and Adric. Monarch then chastises Bigon for telling the Doctor too much, but Bigon refuses to lie; as a philosopher he has been devoted to the truth for over two thousand years. And he and Monarch both know that if the Doctor learns of Monarch's plans before Monarch is ready, then he will oppose them...

The Doctor and his companions set off to explore the ship, but Adric and Nyssa are separated from the Doctor and Tegan and decide to explore on their own. The Doctor and Tegan are guided to a performance hall, where Persuasion observes them as they watch a demonstration of folk dancing and music from each of the cultures represented on the ship. Two gladiators arrive in the hall and begin fighting, and under cover of pretending to explain the fight, Bigon arranges to meet the Doctor back in his quarters and speak privately with him. The Doctor distracts Persuasion while Bigon slips away. Moments later, one of the gladiators drives a sword straight through the other's chest, and Tegan rushes from the hall in shock, followed by the Doctor.

Adric and Nyssa, exploring the ship, find an arboretum filled with Earth plant life and small Earth frogs. Exploring further, they find a room full of Greek scholars working on banks of computers, but none of the humans they've met apart from the four Representatives will speak to them. Nyssa notices that the silent humans all have metal implants on their hands. They explore further and find the "Mobiliary", what appears to be a type of surgery -- and the dead Greek soldier from the recreational walks in under his own power and is instantly healed by a glowing cabinet. Monarch decides that Nyssa and Adric have seen enough and orders that they be brought to him immediately.

The Doctor and Tegan listen, respectively fascinated and horrified, as Bigon explains that all aboard the ship are androids. Those with metal implants in their hands are servitors with no personality circuits, the android equivalent of a slave class. Monarch intends to approach Earth with a message of peace and goodwill, and then release a toxin which will cause all organic matter on the planet to collapse in upon itself. Urbanka was not destroyed by solar activity, but by Monarch's ambition; he strip-mined the planet of all its resources and destroyed its ozone layer with his technology. Now he intends to do the same to Earth, all to support his mad quest to travel faster than the speed of light and thus travel backwards in Time. He believes that if he goes back beyond the Big Bang he will meet God -- whom he believes to be himself. Bigon is unable to act against him due to fail-safe protocols programmed into his new body, but he knows that Monarch must be stopped...

Monarch tells Adric and Nyssa about the android nature of the Urbankans and the wonders of his technology. Adric, enraptured by Monarch's vision, gladly volunteers information about the Doctor, the TARDIS, and Gallifrey. Nyssa, however, is appalled; her father was murdered by a tyrant and she recognizes Monarch's megalomania for what it is. Monarch sends Adric to fetch the Doctor, but stops Nyssa from accompanying him; instead, he has Enlightenment hypnotise her and send her to the Mobiliary. There, Lin Futu scans her memories into a computer data bank, preparing for her transformation into an android.

Tegan, terrified, wants to leave immediately and warn Earth of the danger, but the Doctor knows he would never be believed and instead plans to stay and defeat Monarch aboard the ship. Tegan has no choice but to wait in the guest quarters while Bigon leads the Doctor about the ship, revealing more of its secrets. The Floral Chamber has been fertilised with the organic remains of those who didn't meet Monarch's exacting standards, and the frogs kept there are hosts for the toxin which will destroy all life on Earth. Adric, meanwhile, finds Tegan alone in the guest quarters, and when she realizes he's fallen under Monarch's charm she decides to pilot the TARDIS back to Earth herself, using the spare key the Doctor gave her. When Adric tries to stop her, she pushes him out of the way and flees, unaware that he's hit his head and knocked himself out.

Nyssa uses the lead pencil to conduct power from the sonic screwdriver into the metal implant on the servitor's hand, causing the android to short-circuit. Adric stops Persuasion from shooting the Doctor and begs Monarch to spare his life. Monarch agrees to do so, but has the sonic screwdriver confiscated and Nyssa held hostage to ensure the Doctor's future good behaviour; Monarch believes that this demonstration of his benevolence will win Adric over completely. Bigon is decircuited, and the empty android shell is taken to the recreational, where it sits placidly watching the entertainment. Tegan, meanwhile, finds the TARDIS floating in space outside the Urbankan ship, and nothing she does makes a difference -- even the TARDIS instruction manual can't help her escape.

The Doctor repairs the monopticon in the guest quarters and publicly tells Adric that he's misjudged Monarch and now regrets opposing him. He and Adric then go to the recreational, where, under cover of the music, the Doctor angrily reveals Monarch's true motives to Adric and tells him about the toxin. Monarch's human servants are all androids; he needs the organic Adric to convince the people of Earth of his good intentions until it's too late. Now Adric must choose whom to trust, and after some initial uncertaintly he decides to trust the Doctor.

Adric and the Doctor return to the Mobiliary, where the Doctor speaks privately with Lin Futu and convinces him that Monarch has no intention of keeping his promise; the Chinese are the most populous of peoples on Earth, and would Monarch really give up control of such a population? Lin Futu agrees to recircuit Bigon and help convince Villagra and Kurkutji of the truth. The Doctor and Adric manage to smuggle Bigon out of the recreational under cover of a dancing Chinese dragon, and get him back to the Mobiliary, where Lin Futu recircuits him. The Doctor now intends to spacewalk to the TARDIS with Adric's help; although there is only one spacesuit available, the Doctor is able to resist the intense cold of space for up to six minutes, and thus needs only one breathing helmet.

In order to distract Monarch's attention, Lin Futu and Bigon reprogram the servitors to act in unison, and a fail-safe intended to prevent a rebellion causes their programming to lock in recreational mode. But Monarch realizes what's going on and furiously sends Enlightenment and Persuasion to deal with the Doctor. In the ensuing struggle, the Doctor and Adric manage to decircuit Persuasion and throw his control circuits out into space, but before Adric can stop her Enlightenment detaches the Doctor's lifeline, leaving him floating helplessly in space. Adric is able to overpower Enlightenment and decircuit her, and the Doctor saves himself by throwing a cricket ball at the wall of the Urbankan ship; the ball bounces off and returns to the Doctor's hands, and its momentum carries him to the door of the TARDIS.