A race of giant Gastropods has taken over the planet Jaconda. Their leader, Mestor, now intends to cause an enormous explosion in order to spread his people's eggs throughout the galaxy, and he kidnaps juvenile twin geniuses from Earth to work out the necessary mathematical equations. Space fighters led by Lieutenant Hugo Lang are dispatched to get the twins back, but they come under attack and Lang is the sole survivor when his ship crashes on the asteroid Titan III. A newly regenerated Doctor and Peri become involved and help Jaconda's elderly former ruler Professor Edgeworth, who is really a Time Lord named Azmael, to defeat Mestor and free the planet's bird-like indigenous people from the gastropods' reign of terror. Azmael, however, sacrifices his life in the process.

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