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.

Valentin and Valentina love each other and want to marry. But their mothers are strongly against this marriage. So strong is their hate that they can use any possible means.

A young aristocrat, Aleksei Fedyashev, is languishing in his family's country estate, spending his days reading poetry and confessing his love... to a statue. Upon hearing that famous Count Cagliostro is touring Russia and has created quite a buzz in high society with his "magic", he decides to ask the Count to bring the statue to life...