The travellers learn from the Time-Space Visualiser taken from theMoroks' museum that Daleks equipped with their own time machine are on their trail with orders to exterminate them. They flee in the TARDIS.
The chase begins on the desert planet Aridius and takes in a number of stopping-off points, including a spooky haunted house which is actually a futuristic fun-fair attraction.
Eventually both time machines arrive on the jungle planet Mechanus, where the Daleks try to infiltrate and kill the Doctor's party with a robotic double of him. The travellers are taken prisoner by the Mechonoids — robots sent some fifty years earlier to prepare landing sites for human colonists who never arrived — and meet Steven Taylor, a stranded astronaut who has been the Mechonoids' captive for the past two years.
The Daleks and the Mechonoids engage in a fierce battle which ends in their mutual destruction. The Doctor's party seizes this opportunity to escape. The Doctor reluctantly helps Ian and Barbara to use the Daleks' time machine to return home.
Of note in this episode when the tardis lands in New York City on top of the Empire State Building, the cars in the street shot from the top of the building are going the wrong way for the US.