Based on a story from the BBC TV serial "Doctor Who". Scientist Dr. Who accidentally activates his new invention, the Tardis, a time machine disguised as a police telephone box. Dr. Who, his two grand-daughters, and Barbara's boyfriend Ian are transported through time and space to the planet Skaro, where a peaceful race of Thals are under threat of nuclear attack from the planet's other inhabitants: the robotic mutant Daleks.

While absentminded Dr. Who is demonstrating his latest invention, a time machine, the apparatus is accidentally set in motion, and the doctor, his two granddaughters (Barbara and Susan), and Barbara's boyfriend, Ian, all land in a petrified forest on a huge planet in the future. They are quickly captured by the Daleks, a hostile form of life encased in metal cones which protect them from the radiation caused by a massive neutron war. Also living on the planet are the Thals, friendly creatures who are able to live without the protective cones because they possess a drug which immunizes them against radioactivity. Since the Daleks desperately want the drug, they send Susan to invite the Thals to their stronghold; but when she returns, the Daleks discover that the drug is fatal to them. They decide to explode a giant neutron bomb which will increase radiation and exterminate the Thals. Dr. Who and his friends escape from their captors, warn the Thals, and help launch an attack in which the Daleks are vanquished moments before the bomb is set to explode. With the Thals free to live in peace, Dr. Who and his party return to their time machine.