In this unusual offbeat black comedy directed by Ugo Tognazzi, Giuseppe (Tognazzi) is a middle-aged industrialist obsessed with gadgets. When his nose starts to whistle uncontrollably, he checks into a clinic to resolve the problem. What begins as a minor affliction worsens, and Giuseppe is placed on a different floor as his ailments multiply. The sicker he gets, the higher he goes up in the floors of the clinic, until he is near death's door.

Four extraterrestrials, X-1, X-2, X-3 and X-4, arrive on Earth in the early sixties. Here they decide to take on human features to study the terrestrials incognito, but end up getting involved in the Roman "dolce vita".