The article deals with the problem of determining the components of the teaching of cross-cultural communication at language universities in modern conditions, describes the difficulties of defining these components character and amount. The author states that the process of cross-cultural communication teaching consists of verbal, non-verbal and paraverbal components. Besides it includes the creating of the culturally-bound language personality having cross-cultural knowledge and skills, and capable of adequately acquiring, adapting and applying the knowledge obtained in the process of cross-cultural communication.