A secret US navy research project is founded to investigate the existence of paranormal powers, bringing together a variety of men and women who have shown indications of telepathic ability. As a result of the experiment they make mental contact with the Tyrenni, strange alien beings resembling winged squids who dwell in the upper atmosphere of their tempestuous world.

The aliens' world, Tyree, is being threatened by a huge being, the Destroyer, which is moving inexorably towards them, obliterating whole solar systems in its path. When the Tyrenni realise that it threatens to exterminate life on Tyree, they are forced into the decision - contrary to all their moral beliefs - to take over the bodies of their human contacts in order to preserve their race.