Abstract   The problem of understanding the tolerance, which has fundamental importance especially for the system of education, lies at the heart of cross-cultural sustainability of multiethnic societies. The crisis of multiculturalism has revealed the problematic nature of understanding tolerance from the perspective of positive interactions with the ethnically different. The aim of the study is to identify and substantiate a new principle of cross-cultural tolerance, which would take into account the fundamental nonremovability of dissonance existence of different cultural groups. The article reveals that an attempt to eclectically merge classic models of social integration is the source of multiculturalism failures. The reasons behind their psycho-social groundlessness in the development of stable social connection are considered as well. Reasons have been exposed of problematic nature of positive tolerance. The notion of “dissonance tolerance” have been defined, its relation to cross-cultural sustainability has been shown, particularly in education.