We are now moving into a new era of great power relations that is profoundly unlike both the Western dominated, centered globalist one we have been in for the past two centuries, and the classical, premodern one before that. The core of modern industrial, bureaucratic states is getting both bigger and more global, and includes many states with big populations. As a result, the period of Western hegemony, which lasted from the second quarter of the 19th century to the first quarter of the 21st century, is coming to an end. The world is shifting from an era of globalism centered on a mainly Western core, to one of decentered globalism in which power is much more diffused. There are six new conditions that will set the context for great power relations within the new structure of decentered globalism: a diffuse distribution of power and status, a transformed problematic of violence, a relatively narrow ideological bandwidth, a quite robust international society, a variety of “shared fate” issues, and a very complex dynamic of identity. Therefore, future great power behavior should be in consistence with such prescriptions as global non-hegemony, responsible great powers, ideological humility, etc.