In both systemic and realist theories, hegemons are expected to deter major intra-core wars that would upset their favored position in the status quo. Yet the conceptions, measures, and units of analysis for hegemony differ within and between the theoretical perspectives. We compare three conceptions of hegemony: economic efficiency in the world economy, global reach via sea power, and relative total power of states. Extrapolating from power transition theory, we also include the effects of rapid transitions in hegemony. In addition, we examine a central thesis in world system theories that long expansion periods produce the resources necessary for fielding large armies and sustaining long conflicts. We employ time series regression analyses for the entire period of 1496–1967 and for periods before and after the industrial revolution to explain the intensity of major wars between great powers. All hegemony measures have negative effects after the industrial revolution except hegemonic transition, which is rejected in all models. In preindustrial times, the Dutch failed and the Hapsburgs succeeded in functioning as hegemons with regard to major war. This suggests deficiencies in world economy theory and calls into question its generality across the history of the system. We find consistent positive effects of long-wave economic expansions on war intensity, and we reject Marxist crises theories. A novel finding is that imperial expansion, in the form of colonial conquest, lessens intra-core war by displacing internal pressures hierarchically onto the periphery.