Jack Bohlen is a repairman who emigrated to Mars to flee from his bouts of schizophrenia. He lives with a wife and a young son. His father Leo visits Mars to stake a claim to the seemingly worthless Franklin D. Roosevelt mountain range after receiving an insider tip that the United Nations plans to build a huge apartment complex there. The complex will be called "AM-WEB", a contraction of the German phrase "Alle Menschen werden Brüder" (All men become brothers) from Schiller's An die Freude (Ode to Joy).
Bohlen has a chance encounter with Arnie Kott, the hard-nosed leader of the Water Worker’s Union, when both Bohlen’s and Kott’s helicopters are called to assist a group of critically dehydrated Bleekmen, the "original" inhabitants of Mars who are thought to be genetically similar to the African Bushmen of Earth. Bohlen rebukes Kott for his hesitance to help the Bleekmen, an act that angers Kott.
After visiting with his ex-wife Anne Esterhazy about their own "anomalous" child, Kott hears of the theories of Dr. Milton Glaub, a psychotherapist at Camp Ben-Gurion, an institution for those afflicted with pervasive developmental disorders. Glaub believes that mental illnesses may be altered states of time perception. Kott becomes interested in Manfred Steiner, an autistic boy at Camp B-G in the hopes that the boy can predict the future—a skill Kott would find useful to his business ventures. Since Camp B-G is scheduled for closure, Kott offers to take Manfred off Glaub's hands. Manfred in turn is afraid of a future only he can see, in which Mars is derelict and the AM-WEB is a dumping ground for forgotten people like him, wherehe will eventually be confined as a decrepit old man to a bed on life-support.
Kott leases Bohlen's contract from his current employers and hires him to build a video device that can help Manfred perceive time at a regular pace (Kott is also ultimately intent on getting revenge on Bohlen). Bohlen takes a liking to Manfred but the assignment stresses him out because he fears that contact with the mentally ill may cause him to relapse. Bohlen also begins an affair with Kott’s mistress.
As an assignment from his regular job as a repairman, Bohlen is sent to service the simulacra at the Public School, where lessons are taught by robotic simulations of historical figures. These figures are deeply disturbing to Bohlen as they remind him of his own schizoid episodes where he perceived people around him as non-living mechanisms. When he takes Manfred to the school during an assignment, the simulacra begin acting strangely, as it seems Manfred is altering their reality. Eventually Bohlen is asked to take Manfred away. In light of other events it is not entirely clear, however, whether Manfred is actually affecting the simulacra or whether he is merely influencing Jack Bohlen's perception of them.
Only Heliogabalus, Kott's Bleekman servant, is able to connect with Manfred. From Manfred's point of view, humans are strange beings who live in a world of fractured time where they disappear from one place and reappear in another and otherwise move in a jerky, uncoordinated manner. Heliogabalus, to Manfred, moves smoothly and gracefully. He seems to talk to Manfred without words.
The precipitating event of the story is the suicide of Manfred Steiner's father Norbert which has the effect of connecting Kott to Manfred and also depriving Otto Zitte, a colleague of Norbert's, of his livelihood. The crux of the story is a meeting between Kott, Bohlen and Kott's mistress, Doreen Anderton, at Kott's home, with Manfred in tow. This episode is previewed three times before it actually occurs, apparently through Manfred's eyes but with participation by Bohlen. Each time the events are more surreal, the perceptions more hallucinatory. When the events of the story finally reach the crucial point, which Bohlen fears after having foreseen the outcome, Bohlen himself does not experience it. His awareness stops as he and Doreen arrive at Kott's home and picks up after they leave. He only knows that he and Kott parted ways, superficially friends but actually enemies.
Pressured by Kott, Heliogabalus reveals that the Bleekmen's sacred rock, "Dirty Knobby", can be used as a time travel portal that Manfred may be able to open. Kott centers his interest in altering the past on two goals: Revenge on Jack Bohlen and claiming the FDR mountains before Leo Bohlen does.
Somewhat predictably, the scheme goes badly awry. Returned in time to the point where he first appeared in the novel, emerging from the sybaritic bath-house run by the Union, Arnie Kott finds himself repeating the actions which led him to meeting Bohlen while simultaneously dealing with perceptual distortions which seem to be emanating from Manfred's mind. He is unable to get to the FDR mountains to plant his stake, being compelled by law to go the aid of Bleekmen just as he did before. He encounters Bohlen, as he did originally, but in attempting to shoot him he is "killed" by a Bleekman's arrow.
Waking from the vision, Kott realizes he has failed. He decides to give up on his schemes, abandon Doreen and let Bohlen get on with his life. He still desires to help Manfred who has wandered off during the purported "time-travel" episode. Leaving the cave in Dirty Knobby where they performed Heliogabalus's strange ritual, he encounters Otto Zitte. After the suicide of Norbert Steiner, Kott, his best customer, elected to take over Norbert's business. Zitte was competing, so Kott's men destroyed the smuggler's storage facility and the adjacent property, leaving a message that "Arnie Kott doesn't like what you stand for". Zitte has pursued Kott, following his helicopter to Dirty Knobby. He shoots Kott, who thinks he might still be stuck in another one of Manfred's hallucinations. Bohlen and Doreen land in Kott's own helicopter and take Kott back to Lewistown. Kott dies, believing to the last that he was only experiencing another hallucination.
Bohlen returns to his wife, Silvia, who had been seduced by Zitte on his sales round. Despite both admitting to infidelity, Jack with Doreen and Silvia with Zitte, they decide to maintain their marriage. There is a disturbance in the Steiner home, and Steiner's widow runs screaming into the night. Barging in, Bohlen and his father see Manfred, old and in a wheelchair, festooned with tubes, accompanied by Bleekmen. Manfred joined a group of Bleekmen after leaving Dirty Knobby, and has saved himself from AM-WEB. He has come back through time to see his family and thank Bohlen for saving him.
In a subdued final scene, Bohlen and his father are out searching for Steiner's widow in the darkness, with voices "business-like and competent and patient."