It is the concept of global politics worked out by the well-known American researcher G.Modelski, its methodological principles and prognostic potentialities, that are critically analyzed in the article. The authors point to the high heuristic potential of Modelski’s approach to historical development of the world political system as to an integral non-linear evolutionary process, seeing in such approach a kind of intellectual challenge. In answer to this challenge, the authors offer their own vision of the main stages of the genesis and development of the global political system and retrace evolutionary continuity-succession of world centres from Roman empire through Arab caliphate and Byzantium to the cities of Northern Italy and further to the Netherlands, Great Britain and the USA. As still another research alternative, the authors put forward a hypothesis of shortening of the duration of world evolutionary cycles and are considering from this angle the prospects of world political development in the nearest decades.