Given a distinction of endogenous and exogenous population cyc1es, this paper searches the ways of characterizing the‘endogenous’cycles with the dynamics of changing age composition.1t is argued that while the size of parental cohort is related to the size of off spring cohort by the renewal process, fluctuations in size are correspondingly transmitted and averaged time after time. It is shown that as the population transition in Taiwan is approaching the final stage of completion, population cycles appear to becoming the principal component of the population change. Though the cycles tend to converge in the long-run, the compression in age pattern of maternity has nevertheless effected a trend to the contrary. A decomposition of the crude birth rate is introduced to capture the cycle component of population renewal.