The article is devoted to the theoretical analysis of the concepts of tolerance and assertiveness. Problem of contemporary cross-cultural interaction is the need to shift strategy of tolerance on strategy of assertiveness. Considered the practice of multiculturalism based on the idea of tolerance. Six barriers to cross-cultural communication. Comparison of understanding tolerance in European, Arab, Eastern cultures and in Russia. Boundaries are considered manifestations of tolerance. Developed rules of tolerant behavior. Proposed in scientific analysis and in actual practice, intercultural strategy move to assertiveness. Tolerance is respect for the views of another person, provided that he respects your opinion. Assertiveness is the respect for the rights of another person, provided that it also respects your rights. Describes the ways in assertive behavior: the willingness to cooperate, the openness of conduct, allocation of responsibilities, defend their rights and interests, defining the way forward. Tactics developed in assertive behavior: “interests”, “anti-discrimination”, “achievement”, “standards”, “activity”, “goodwill”.