The TARDIS materialises on board a vast and advanced alien spacecraft, observed by a hovering surveillance device which conveys the arrival of the Doctor, Tegan, Nyssa and Adric to an observing being that is in control of the vessel. The TARDIS crew become separated and the Doctor and Tegan reach the bridge of the vessel where the green-skinned commander introduces himself as Monarch, ruler of Urbanka, and his associates and fellow Urbankans are the Ministers of Enlightenment and Persuasion. The leader is intrigued by talk of current Earth civilisation and reveals their ship is bound for Earth. Shortly afterward Enlightenment and Persuasion seemingly regenerate into human form, dressed in garments Tegan designed to demonstrate contemporary Earth fashions.
The TARDIS crew are reunited as guests aboard the ship and it soon becomes apparent that there are four distinct human cultures represented on the vessel by a small group of humans – Ancient Greeks, the leader of whom is the philosopher Bigon; Chinese Mandarins and their leader Lin Futu; Princess Villagra and representatives of the Mayan people; and Kurkutji and his tribesmen, of the very ancient Australian Aboriginal culture. The Urbankans have made periodic visits to Earth, each time getting speedier in their journeys. This time they have left their homeworld after erratic solar activity, storing three billion of their species on slides aboard their craft, and it seems the current journey is their last and they now wish to settle on Earth, which they are due to reach in four days time.
The Doctor becomes suspicious of Monarch and soon learns that the Urbankan does not plan on peaceful co-existence: instead, he has developed a toxin to wipe out humanity, and this will be unleashed before the Urbankans disembark. He also finds out that the humans aboard are not descendents of the original abductees, but are the original people taken from Earth and converted into androids like the three Urbankans walking around on board (Monarch's actual status, whether partly cybernetic or completely organic, is not stated explicitly. Monarch described the era prior to Monarch's conversion of Urbankan life forms into cyborgs as the 'flesh-time'). The four leaders of the peoples have been given additional circuits to help them reason, but this facility can be taken away, as Bigon learns when he rebels against Monarch, and his neural circuit is removed and placed in a container for 5 centuries. He explained to the Doctor that Monarch strip-mined and destroyed Urbanka in a quest for minerals to improve the ship, and now plans to do the same to Earth. Monarch believes that if he can move the ship faster than the speed of light, he can pilot it back to the beginning of time and discover himself as God.
Adric, nevertheless, is rather taken with Monarch, and tensions between him and the Doctor become very strained. It takes the truth to break the alien’s hold over the boy. The Doctor now sets about over-throwing Monarch and, with the help of the human androids led by a restored Bigon, a revolution is put into effect. Enlightenment and Persuasion are de-circuited, while Monarch himself (evidently still constrained by the weaknesses of 'flesh-time') is exposed to the deadly toxin and killed. The humanoid androids decide to pilot the vessel to a new home on a new world, while the TARDIS crew departs. Back in the console room, Nyssa suddenly collapses to the floor in a dead faint.