Causes of cyclic fluctuations in abundance (population cycles) of some small-mammal populations remain poorly understood despite 6 decades of research and >20 hypotheses. Population cycles are demographic processes and cannot be fully explained without considering demographic mechanisms that underlie cyclic fluctuations in abundance. From simulation studies, we have recently shown that phase-related, density-dependent changes in age at maturity, abetted secondarily by changes in juvenile survival, are likely the main demographic causes of cyclic fluctuations in population size. The suggested mechanism of population cycles is based primarily on changes in age at maturity (α); we refer to this idea as the α-hypothesis. Here, we fully develop the α-hypothesis and present a testable, demographically based, mechanistic explanation of population cycles. The α-hypothesis identifies the demographic basis of population cycles and provides a mechanistic explanation of how changes in key demographic variables (age at maturity and juvenile survival) might cause cyclic fluctuations in abundance and biologic attributes of the cycles. The α-hypothesis is supported by, and logically consistent with, empirical patterns of life history and dynamics of cyclic populations of small mammals. Future research should focus on empirically determining causes of phase-related changes in age at maturity and juvenile survival.