Mad scientist Dr. Krelmar is working on a machine that allows two people to swap minds and enemy agents Basil and Lola intend to use it with the Avengers to get them to destroy their network. Basil exchanges personalities with Steed but Mrs. Peel is suspicious that the man who looks like her partner is acting out of character and has to persuade the real Steed what is going on.

Paul Beresford, the brother of Clement Armstrong, the creator of the Cybernauts, blames Steed and Mrs. Peel for his brother's death at the cold hands of his own creations. Aided by Armstrong's assistant Benson, he abducts several scientists who are blackmailed into producing a new batch of Cybernauts. Whilst he is the perfect gentleman towards Mrs. Peel, his aim is to turn her and Steed into human robots.

Sir Andrew Boyd, the British delegate at a European peace conference has a dream in which he is run over and killed by a car. The dream comes true. The Avengers are charged with the safety of his successor, Lord Melford. He too is beginning to have bad dreams, involving a sinister man who turns out to be a member of the Eastern bloc. There is a plot afoot to derail the conference and Steed and Mrs. Peel intend to foil it.