At a social gathering at a château or baroque hotel, a man approaches a woman. He claims they met the year before at Marienbad and is convinced that she is waiting there for him. The woman insists they have never met. A second man, who may be the woman's husband, repeatedly asserts his dominance over the first man, including beating him several times at a mathematical game (a version of Nim). Through ambiguous flashbacks and disorientating shifts of time and location, the film explores the relationships among the characters. Conversations and events are repeated in several places in the château and grounds, and there are numerous tracking shots of the château's corridors, with ambiguous voiceovers.
The characters are unnamed in the film; in the published screenplay, the woman is referred to as "A", the first man is "X", and the man who may be her husband is "M".