This  article  is  about  the  world  system  as  one  form  of  social  organization  humankind  can  assume.  It  provides  a  valuable,  conceptual  and  historical  introduction  into  the  structural  components  of  the  world  system,  such  as  economic  or  political,  as  well  as  global  and  national,  each  of  which  might  be  expected to be subject to evolutionary process. The nature of global leadership is among the most hotly contested issues in contemporary political science. The article is devoted to the problem of interaction of various regional and cultural models of space organization in the history of mankind. Particular attention is paid to the study of сenter-periphery hierarchies and center-periphery relations as  a  constant  structural  feature  of  world  system.  The  focus  is  on  the  work  of  leading  Western  and  domestic  theorists  of  international  relations.  The  article  deals  with  the  theory  of  the  demographic  transition  of  S.  Kapitsa,  long  waves  in the world politics of D.Modelsky. In the modern period, the concentration of global forces in one location is gradually decreasing, and the 'unipolar' model of center-periphery relations is giving way to 'multipolar center-periphery relations. Observed earlier in the last century, the domination of superpowers is inferior to the decrease in the influence of centers of power. The rigidity of confrontation between leaders and challengers is replaced by greater flexibility in the behavior of alliances and the reorganization of alliance systems. The stability of political alliances  is  built  on  the  commitment  to  shared  values.  The  system  of  world  politics is gradually entering a period of transition from the state of leadership of one superpower to a "cultural balance".