The Doctor and his companions Ben and Polly arrive in the TARDIS at the South Pole in the year 1986, near the Snowcap base. The base is supervising the mission of the Zeus IV spaceship, running a routine probe on the Earth's atmosphere.
Unusual readings on the spaceship's instruments lead to the discovery of a new planet suddenly approaching Earth. The spaceship begins to experience power losses, and Snowcap personnel begin arrangements to abort its mission.
Back on the base, the Doctor reveals what he knows about the tenth planet: it is Mondas, Earth's former sister planet and its inhabitants will soon be visiting Earth. True to his prediction, three robotic creatures land outside, killing the guards and disguising themselves in the dead men's furs to gain access.
While everyone is distracted by their efforts to land Zeus IV safely, the creatures are easily able to take over the base. The base personnel and Polly plead with the invaders to allow them to save the lives of the Zeus IV crew, but the creatures say that their lives are irrelevant to them. They explain that they are Cybermen, who were once like human beings, but gradually replaced their bodies with mechanical parts, including eliminating the "weakness" of emotion from their brains. The Cybermen allow the men to make contact with Zeus IV, but it is too late as the ship is dragged away by Mondas and explodes.
The Cybermen explain that Mondas is absorbing energy from Earth and will soon destroy it. They propose to take humans back to Mondas and turn them into Cybermen.
Ben, who has been imprisoned in the projection room after attempting to kill a Cyberman, rigs up the projector to blind incoming Cybermen, allowing him to steal his guard's weapon and kill him. Sneaking back into the Tracking Room, he hands the cyberweapon to General Cutler, the base commander, who kills the remaining two Cybermen. Cutler contacts Space Command HQ in Geneva and is informed that they have sent his son on a mission to rescue the doomed Zeus IV.