While many populations of large mammals are stable from year to year, some show persistent oscillations associated with high mortality. This article investigates the causes of variation in population stability in ungulates by comparing the contrasting dynamics of two naturally regulated island populations: the Soay sheep population of Hirta (St. Kilda), where numbers fluctuate by 60%-70% every 3 or 4 yr as a result of overcompensatory winter mortality, and the red deer population of the North Block of Rum, where numbers have been stable for over a decade. We suggest that the contrasting dynamics of these two populations are caused by differences in fecundity and maturation rate. Red deer show relatively low fecundity and slow maturation, and increases in population density depress both fecundity and juvenile survival. In contrast, the relatively rapid development of Soay sheep allows them to evade density-dependent effects on reproduction and survival until the population exceeds winter carrying capacity by a substantial margin, subsequently triggering overcompensatory mortality in late winter in all age classes.