The TARDIS arrives some ten million years in the future on a giant spaceship carrying all the Earth's surviving plant, animal and human life (much of it miniaturised and in suspended animation) on a 700 year voyage to a new home on the planet Refusis II. Dodo is suffering from a cold - an unknown affliction in this era - and as the human Guardians of the ship and their servant race the Monoids have no resistance, a plague breaks out.
The Guardians place the travellers on trial and Steven is forced to defend them against allegations that they spread the disease deliberately. Fortunately, the Doctor finds a cure. The TARDIS leaves the spaceship, which Dodo has nicknamed the Ark, only to arrive back there as it is approaching the end of its voyage. Partly as a result of the earlier plague, the Monoids have now grown strong and enslaved the humans.
They plan to make Refusis II their own but, with the help of the invisible Refusians, the Doctor is able to persuade the two races to live together in peace.