Sociocultural-interdeterminist dialogical approach focuses attention on the caused interdeteministic character of mutual relations of situational, personal and activity determinants of the behaviour, staticized in concrete historical cultural context. For example, a change in a situational context leads to changes both in the person, and in his or her activity. Achievement of changes in the person and his or her activity assumes creation of the special conditions promoting to their actualization, etc. For understanding of the nature of progress in culture and science the theoretical construct “cultural-scientific tradition” is offered, allowing to trace changes in common cultural and scientific worldview throughout the human history. Consideration of personality problems is carried out in a three-dimensional continuum conscious-unconscious-existential, allowing to capture all variety of displays of psychological phenomenology. Proceeding from understanding of culture as orientational and normative structure of behaviour and as communicative matrix by means of which the behaviour is interpreted, integrated, coordinated and authorized (R. Priest), efficiency of use of the conceptual device of the epistemic approach of Michel Foucault and cultural framing of E. Goffman to understanding of intercultural interaction specificity is proved. The epistemic differences of European (graphic), Chinese, and classic Arabic languages are demonstrated. Intercultural competence is considered in aspect of ability of formation of shared meanings and experiences on the basis of mastering by knowledge about originalities of language, values and norms, experiences and behavioral algorithms of each other. The basis of such mutual understanding creates the dialogue that assumes unconditional acceptance of another based on tolerance and pluralism, the joint extension of the horizons directed on formation and development of coordinated and mutually endured values and senses. As unit of the analysis of intercultural interaction the evaluation of a sharedness of meanings and experiences is offered. Results of empirical research of the given approach on the example of formation of interpersonal mutual understanding of the Belarus and Chinese students are presented.