This paper explores the relations between persistence and dynamics in measles epidemics. Most current models, including the stochastic seasonally forced and age-structured models examined here, fail to capture simultaneously the observed dynamics and persistence characteristics of epidemics in large urban populations before vaccination. Summary measures of persistence and trienniality allow us to compare epidemics in England, New York and Copenhagen with results of non-spatial and spatial stochastic models. Spatial (metapopulation) structure allows persistence and triennial dynamics to coexist in this class of models. The spatial dynamics of measles, for which detailed spatiotemporal data are available, may serve as a useful test of ideas applicable to other epidemiological and ecological systems with an important spatial component.