The mathematical theory that has been developed for populations with nonoverlapping generations has provided a framework for gaining some understanding of the effects of various forces on the genetic structure of populations. One objective of our research has been to examine the extent to which predictions from this theory remain valid when a population with overlapping generations is considered. Accordingly, further research will be done on both natural and artificial selection in age-structured infinite populations. Research has also been done on stochastic theory for populations with overlapping generations and this line of work will be pursued. We also propose to study genetic theory for interacting populations, so as to gain further understanding of the ways in which such populations evolve jointly. Finally, we note that, associated with pure genetic theory is the application of the theory to many species, including humans. Thus, statistical problems of interpreting data arise and it is relevant to examine the logic of data analysis in relation to quantitative genetics. BIBLIOGRAPHIC REFERENCES: Ghai, G. L. and E. Pollak (1975). On some results for a bivariate branching process. Biometrics 31:761-763. Pollak, E. (1976). A stochastic theory for rare genes in large populations with overlapping generations. Theoretical Population Biology 10:109-126.