ASSA is set in Crimea during the winter in the mid eighties. A young musician (Bananan) falls for mobster's (Krymov) young mistress (Alika). The parallel story line involves an 18th century assassination plot.

The story happens mainly around "The Old Arbat Street" in the center of Moscow, where always concentrate vendors, poor young artists and musicians. The hero of this film is a boy named Mitiya,who lives with eccentric elder friend in an apartment house on "The Old Arbat". In fact, people who then appear around Mitiya are all unique, eccentric and the space of the apartment house begins to have an unrealistic character as a miniature of unstable society in the end of Soviet Union.

Old scientist Bashkirtsev is very surprised to discover the possible contacts with other world...