This chapter argues that 'assemblages', although rooted in a deep skepticism of grand theory, could also be useful for re-thinking structure and models of structure in international relations. IR models of structure usually restrict themselves to how subjects are ordered. The idea of an ordering principle that concerns objects as well as subjects has not been much considered. But what if not only subjects but also assemblages play a critical role in structuring international relations? I argue that ‘polities’ are basically constituted, not by the emergence of a hierarchy, but by the emergence of a common governance-object and that a ‘global polity’ is therefore a situation where actors orient themselves toward the governing of specifically global governance-objects.