In the paper, taking into account the empirical research of different authors, the chosen pedagogical, sociological as well as psychological aspects of the on-line teaching and learning processes in the university education are presented. It has been shown that the use of on-line education causes a significant influence on the didactic process in contemporary university. The typical features of the asynchronous learning networks have been discussed in the framework of cognitive psychology, based on the constructivist theory of learning by Jerome Bruner, cognitive constructivist theory by Jean Piaget and the social constructivist theory by Lev Vygotsky. Special attention has been focused on chosen critical variables for successful on-line learning and such groups of problems as: networked collaborative classrooms, community-building paradigm and types of networked interactions. The functions fulfilled by teachers in the asynchronous learning: organizational, social and intellectual, and their competences, have been described.