Plot summary

Sonny Malone (Michael Beck) is a frustrated artist. He has tried to leave a job he hates--painting large display versions of record-album covers--but he shreds his efforts and throws them out the window. The pieces blow past a mural of nine dancing women. THE WOMEN GLOW INTO LIFE AND LEAP FROM THE PAINTING! The women are the so-called Nine Muses of Olympus. They dance down the street and turn into streaks of neon light and fly up into the sky, with accompanying "whoosh" sounds. However, one of them, Terpsichore (Olivia Newton-John) stays on Earth.Sonny does not see this one muse who remains. He returns to his hated job. On the way there, he is kissed by Terpischore who rolls up on him on roller skates before skating away.At work, Sonny's co-workers lovingly chide him. His tyrannical boss orders him to paint just what he is told and nothing more. He seems beat down, but his next assignment is an album cover of a musical group called 'The Nine Sisters'. It is the one with one of the kissing woman on it! He asks around--who is the kissing album-cover woman? A guy behind the desk says she's not on the payroll. The photographer can't explain how she got into the shoot for the album cover--of a hundred pictures, she's in only one. A guy on a porch hasn't seen her (but tries to set Sonny up with one of his daughters). Sonny goes to look for her at the scene of the kiss which is the front of an abandoned art deco auditorium. Sonny goes inside the auditorium and finds Terpsichore, who introduces herself as Kira. The two of them fall in love, though Kira refuses to tell Sonny anything about herself.One day, Sonny hears a clarinet played by an older gentleman who sits on a rock by the ocean. The older man is Danny McGuire (Gene Kelly), a former big-band orchestra leader who is currently working as construction mogul. One thing leads to another, Danny and Sonny become friends. Danny tells Sonny that he once had a muse in the 1940s who looked significantly like Kira. Kira encourages Sonny and Danny to open a nightclub at the auditorium, and the two begin working on this project as partners. However, Kira eventually confesses to Sonny that she is a Muse and cannot stay in love with him. Kira/Terpischore tells Sonny that she is not supposed to fall in love with mortals. Rather, her purpose in the universe is to inspire people--men, it seems--to achieve a dream; then she moves on. So, sadly, she must leave. Sonny gets upset, and Kira leaves Earth. Danny tells Sonny to keep pursuing Kira, encouraging Sonny not to give up on his ambitions like he did after his own muse left him.Sonny finds the wall upon which Kira was, and is, a painting. He looks at the wall, then roller-skates quickly toward it and jumps into it! Inside the realm of the gods, Kira's father Zeus denies Sonny's plea to let Kira come back to Earth, and despite Kira's mother Mnemosyne interceding for Sonny and Kira, Zeus ultimately sends Sonny back to Earth. Kira then professes her feelings for Sonny, and her parents decide to let her go back to him for "a moment, or maybe forever."At the climax, Kira and the Muses perform at the grand opening of Sonny and Danny's nightclub Xanadu before returning to their realm. Sonny is saddened by their departure, but upon seeing a waitress who looks exactly like Kira, he stops her and asks to talk.