Julia (Faye Dunaway), a divorced American fashion designer, is dying of a tragic, incurable disease. With only ten days to live, she spends her time vacationing in an Italian villa and watching television. She spots a TV interview with an Italian engineer Valerio (Marcello Mastroianni), who designs plastic air bags to protect passengers in automobile collisions. She recognizes his face as having met him before at the airport and calls him up to invite him over to her villa where they decide to spend the next several days together, making love. Julia’s friend Maggie (Caroline Mortimer) reappears and reveals that Julia is actually an escapee from the hospital where she was being treated for her disease. Maggie urges Julia to return to the hospital where she can die a painless death. Julia ignores her and returns to the villa and the arms of her lover. Maggie then telephones Valerio and tells him about Julia’s condition. Valerio is willing to stay for the duration but Julia is so upset by the fact that her lover knows her secret that she runs to a nearby mountaintop with the intention of committing suicide.