Persona (1966)
Persona is a 1966 Swedish film written and directed by Ingmar Bergman and starring Bibi Andersson and Liv Ullmann. Persona’s story revolves around a young nurse named Alma (Bibi Andersson) and her patient, a well-known stage actress named Elisabet Vogler (Liv Ullman), who has suddenly ceased to speak. The relationship between the two women becomes strained and the border between dream and reality becomes blurred. By the end of the film the identities of Alma and Elisabeth appear to merge.
More at Wikipedia.