Police Comissioner Datti is investigating the murder of a female doctor whose murderer seems to be a thirty-fivish year old man. Soon another murder follows: Pianist Robert Dominici's girlfriend is found killed. The killer also challenges Datti on the phone and says he can't be caught since he has a secret which makes him invulnerable. In the meantime the clues seems to point in strange directions...

Christmas holidays on the snow of Cortina D'Ampezzo. Mario, a guy from Rome who has not much money, falls in love with the American Samantha, the girlfriend of hypochondriac Roberto. Billo, a singer and a playboy, meets Ivana: she's married with a rich man, Donatone, but in the past she had a flirt with Billo, who wants to reignite the flame.