The economy is the basis for political processes, while the contradictions arising in the system of socio-economic relations determine the cyclical nature of social development, in particular, cyclical economic and political processes that have become global under the conditions of the capitalist world-system. The cyclic nature of geo-economic and geo-political processes is manifested primarily in the cyclical nature of the change of the world hegemon, whose presence indicates the existence of a global political and economic system. The prerequisites for the formation of the world political and economic system, which develops cyclically, arose already in the most ancient times. The historical prototypes of world hegemony were the Roman and Chinese empires, as well as the Mongolian empire, after whose fall the Western European civilization from the beginning of the "long" XVI century became a source of contradictions, giving rise to a cyclical process of struggle for world leadership, which is reflected in the main provisions of the theory of long cycles of world politics by J. Modelski and U. Thompson, theories of cycles of hegemony by I. Wallerstein, etc. The unfolding of long cycles of world politics and cycles of hegemony is coordinated with the unfolding of Kondratiev cycles, whose beginning and end are marked by wars, generated by political and economic contradictions and serving as a way of their partial resolution. The competition of the leading actors of geopolitics gives rise to global military-economic cycles, whose rhythm is set by world wars, and global geo-economic and geopolitical cycles create the basis for the deployment of cycles derived from them on a regional scale. The rhythm of cyclical geo-economic and geopolitical processes on a regional scale is determined by the dynamics of global cycles. Today, the increasing instability in the capitalist world-system indicates the beginning of crisis-militaristic phases of global cycles, whose unfolding leads to a cyclical change of the leader in the capitalist world-system, and the reformatting of the world geopolitical system, and creates the basis for the development of deep geo-economic and geopolitical contradictions, which are the internal driving force of the cyclicality of global political and economic processes.