Time-series analysis, a valuable tool in studying population dynamics, has been used to determine the periodicity of smallpox epidemics during the seventeenth and eighteenth centuries in two contrasting representative situations: 1) London, a large city where smallpox was endemic, and 2) Penrith, a small rural town. The interepidemic period was found to be two years in London and five years in Penrith. Equations governing the dynamics of epidemics predict 1) a two-year periodicity and 2) that oscillatory epidemics die out quickly. It is suggested that epidemics were maintained by a periodic variation in susceptibility linked either to a five-year cycle of malnutrition or to an annual cycle. Computer modeling shows how the very different patterns of epidemics are related to population size and to the magnitude of the oscillation in susceptibility.