Gramsci’s concept of hegemony is applied to interstate relations to account for both the invariance and the evolution of the modern world-system from its beginnings in Late-Medieval Europe to our days. It is argued that what made the United Provinces, the United Kingdom, and the United States hegemonic in their respective “worlds” was not their military might or superior command over scarce resources as such, but their predispositions and capabilities to use either or both to solve the problems over which system-wide conflicts raged. The changes in the nature of these problems and, therefore, in the conditions of the rise and decline of world hegemonies are explored, and some provisional hypotheses concerning the future of the modern world-system are advanced.