This article provides a new characterization of stages of the demographic transition from the perspective of children competing for resources within families and cohorts. In Stage 1 falling mortality increases the size of both families and birth cohorts. In Stage 2 falling fertility overtakes falling mortality to reduce family size, but population momentum causes continued growth in cohort size. In Stage 3 falling fertility overtakes population momentum to produce declining cohort size. We apply our framework to census microdata for eight countries and to United Nations population projections for a larger set of countries. The results suggest that most countries spend two to three decades in Stage 2, with declining family size offset by increasing cohort size. From the perspective of children aged 9–11, many countries enter Stage 3 between 2000 and 2010. Other countries, especially in Africa, will continue to experience increasing cohort size for several more decades.