The article deals with the necessity of formation of intercultural competence of future specialists in the process of their professional training in higher educational institutions. Studying foreign theories of intercultural interaction can significantly help in understanding the theoretical foundations and developing practical principles for the formation of intercultural competence of future specialists, which is especially important in the context of globalization and migration processes in the current stage of development of the world community. The article presents information on foreign theories of intercultural interaction, which are rightly recognized as leading in the interpretation of the essence of intercultural interaction and characteristics of human behavior in the process of intercultural communication. The essence and the possibilities of creative use of the basic principles of the Communication Accommodation Theory and Cultural Schema Theory in the process of understanding theoretical aspects of intercultural competence and analysis of practical approaches to forming the readiness of future specialists in the process of professional development are characterized in higher educational institutions to work in a multicultural environment.