In Cold War Vienna, Milena (Theresa Russell), a young American woman in her twenties, is rushed to the emergency room after apparently overdosing. With her is Alex Linden (Art Garfunkel), an American psychiatrist who lives in the city as a teacher. Through myriad fragmented Flashback (literary technique), the narrative depicts the story of their romance, which ultimately amounts to an unhealthy obsession on the part of Alex.