Most preindustrial states experienced recurrent waves of political collapse and internal warfare. One possible explanation of this pattern, the demographic-structural theory, suggests that population growth leads to state instability and breakdown, which in turn causes population decline. Mathematical models incorporating this mechanism predict sustained oscillations in demographic and political dynamics. Here I test these theoretical predictions with time-series data on population dynamics and sociopolitical instability in early modern England, the Han and Tang China, and the Roman Empire. Results suggest that population and instability are dynamically interrelated as predicted by the theory.