The proposed work aims to extend and develop methods for projection and dynamic analysis of human populations. Part of the work focuses on populations with fixed mortality and fertility patterns which are in theprocess of convergence to a stable age distribution (for example, following a baby boom). The process of convergence can alternatively be described in a probabilistic way; using this description, amplitudes of cycles in population age structure will be studied in relation to the population's initial state. In addition, a quantitatively and qualitatively useful description of the rate of convergence will be developed using an entropy statistic. The larger part of the work focuses on calculation of statistical quantities which describe populations whose fertility and mortality vary stochastically over time. Such variation is likly to strongly influence prediction and dynamics in populations near stationarity. Analytical approximation methods will be applied, and where necessary, extended to develop useable projection schemes. Time series models of vital rate fluctuation will be incorporated into this computational scheme. The effects of stochastic vital rates on population convergence will be analyzed. Finally, exogenous cycles in fertility and endogenously driven cycles (for example, as in the Easterlin effect) will be studied in the presence of superimposed stochastic change in vital rates.