Existing demographic analyses do not explain the negative relationship between population growth and life-support systems that are now emerging in scores of developing countries. The demographic transition, a theory first outlined by demographer Frank Notestein in 1945, classified all societies into one of three stages. Drawing heavily on the European experience, it has provided the conceptual framework for a generation of demographic research. During the first stage of the demographic transition, which characterizes premodern societies, both birth and death rates are high and population grows slowly, if at all. In the second stage, living conditions improve as public health measures, including mass immunizations, are introduced and food production expands. Birth rates remain high, but death rates fall and population grows rapidly. The third state follows when economic and social gains, including lower infant mortality rates, reduce the desire for large families. As in the first stage, birth rates and death rates are in equilibrium, but at a much lower level. The theorists do not say what happens when developing countries get trapped in the second stage, unable to achieve the economic and social gains that are counted upon to reduce births. Nor does the theory explain what happens when second-stage population growth rates of 3% per year continue indefinitely and begin to overwhelm local life-support systems. (BZ)