The film is a parody of Disney's Fantasia, though possibly more of a challenge to Fantasia than parody status would imply. In the context of this film, "Allegro non Troppo" means Not So Fast!, an interjection meaning "slow down" or "think before you act" and refers to the film's pessimistic view of Western progress (as opposed to the optimism of Disney's original).

Snowball, a dolphin, gets into trouble when it swallows a bottle with the records of pension payments owed to Billy Bolla, an aged cruise ship entertainer. If the performer cannot quickly catch Snowball and induce him to produce the papers, he will have no retirement.

Aliens send a hypnotic signal through a TV channel, and the signal makes people dance and makes them forget their fears.

Maurizio wakes up after sleeping for twenty years and goes to live with his cousin Carlina, who shares her apartment with two other women: one an actress, the other unemployed.

Right after she moves in with him, Frederico's new girlfriend Francesca sends him back to her former boyfriend's apartment to fetch her something she forgot - but he's surprised to find him lying there - dead. Assuming that Francesca killed him and sent him for cleaning up, he cuts him up in pieces, puts him in a suitcase and tries to get rid of it... but he has a hard time finding a suitably quiet place. Unfortunately there's a witness, who comes back on him. One thing leads to another, and the normally shy and overly fearful Frederico has to rid himself of more and more corpses until this black comedy ends.

Maurizio works in a dubbing studio and puts sound effects into cartoons. One day his hands turn into cartoon ones, with a life of their own.