The article presents the theory of cross-cultural communicative competence. The purpose of the article was to allocate components of cross-cultural communicative competence. Components of competence are the cultural knowledge and skills; adequacy in cross-cultural contacts, tolerance, assertiveness and sensitivity. The article analyzes the philosophical principles of human interaction, psychological foundations of intercultural communication. Four social-psychological principles of contributing to the success of partners in cross-cultural communication have been proposed. It is proved that in complex modern migration processes it is currently better to move from tolerance behavior to assertiveness based on the ability to protect their own interests without ignoring the interests of the partners. As a result of theoretical research, the socio-psychological tricks in assertive behavior have been described. In conclusion the most effective tactics of assertiveness are given: the search for common interests, non-discrimination, focus on the achievement of your own objectives, the reliance on rules of interaction, activity and kindness in communication.