The article deals with methodological problems of studying evolutionary dynamics of political systems, as well as with problems of conceptualization of the interrelated development of single polities and of the international political system as a whole. The authors point out "non-equilibriousness" as a fundamental characteristic of the sociopolitical process; they suggest - for the sake of comprehension of the causes and mechanisms of transformation of the dynamic structures of politics - to make use of visions of the theory of non-equilibrious processes. Possibility is discussed, to give an account of the complication of political processes with resort to the idea of "evolutionary cycles". The authors also discuss the role of globalization as a factor conducive to acceleration of political development.