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One hundred years have elapsed since Charles Elton (1924) described the periodic fluctuations in North American snowshoe hare abundance, yet mechanisms underlying 9-11-year population cycles in snowshoe hares continue to be debated. We applied multistate capture-mark-recapture models to long-term field data (1977-2020) based on >20,000 captures of >7000 unique snowshoe hares (Lepus americanus) from Kluane Lake, Yukon, Canada, to estimate and model state-specific demographic parameters. Juveniles had the lowest and reproductive adult females the highest apparent survival. Apparent survival of all sex-age classes was highest during the mid- and late-breeding seasons and was generally better during the increase phase. Conditional probability of females transitioning from non-reproductive to reproductive state, and reproductive females remaining in the reproductive state, increased substantially as the population transitioned from low to increase phase throughout the breeding season. Analysis of stage-structured matrix population models revealed that population-dynamic characteristics were strongly phase-specific, and also varied across seasons, with the increase phases being characterized by high monthly asymptotic population growth rate. Snowshoe hares experienced short stage-specific generation time during the early breeding season across all phases; they experienced relatively long generation time during the increase and low phase of the mid-breeding season, and the increase and peak phase of the late breeding season. Elasticity analyses showed that asymptotic population growth rate was proportionately most sensitive to changes in survival of adult females across all phases and seasons. However, retrospective life table response experiment analysis showed that rapid growth of the snowshoe hare populations during the increase phase was due to improvements in reproductive transitions and pre-weaning survival, whereas population declines are caused primarily by reduced survival (primarily, pre-weaning survival), with reduced reproductive transitions and smaller litter sizes playing a secondary role. Our results suggest that cyclic populations of snowshoe hares are characterized by complex demographic and population-dynamic patterns, depending on phase of the cycle and reproductive season, and that different demographic mechanisms underlie rapid population growth during the increase phase, and swift population declines as the population transitions from the peak to the decline phase. Because our study represents the first comprehensive demographic and population-dynamic study of a cyclic population, similar studies would be needed to test the generalities of our conclusions. Whereas density-dependent predation has been shown to be the primary cause of phase-related changes in survival, future research should focus on identifying mechanisms underlying phase-related changes in reproductive parameters.