Two Soviet humans previously unknown to each other are transported to the planet Pluke in the Kin-dza-da galaxy due to a chance encounter with an alien teleportation device. They must come to grips with a language barrier and Plukian social norms (not to mention the laws of space and time) if they ever hope to return to Earth.
A young Russian store clerk has a drab existence in times of shortages and is berated by her ailing mother for not seeing men. So she brings home an unknown young man who she met on the tram. She dreams many things but pines for this man.
The story begins when Alice Postique, who had to stay late at work, discovers her boss Roche with a knife in his back. When the police detective arrives, Alice recognizes him as her old friend.