The article discusses developmental character of cultural globalization processes taking into consideration variety of equal cultures throughincreasing the number of integral connections that promote mutual understanding between peoples, cultures, and traditions that take part in the dialogue. Relation between modernization processes and socio-cultural dynamics, ecologization and globalization of the society and national cultural tradition, values, and identifications are significant for this study. The article shows that modernization processes in Russia were slowed down by the national socio-cultural tradition. It was largely determined by rejection of innovations that is typical of the traditional society and acceleration of socio-cultural dynamics, which is characteristic of the Western civilization that caused the demand for adaptation and resistance to it. Emerging of the new world order is conditioned by the necessity that was caused by globalization. Its creation should not challenge preservation of national and cultural identity of peoples that participate in the globalization process, sovereignty of their countries, as well as preservation and realization of cultural uniqueness and personal sovereignty.