The paper argues that Leslie Matrix models are very useful for studying a range of archaeological problems associated with past man-animal relationships. Following a brief description of the Leslie Matrix model it outlines the types of heuristic and substantive contributions that may be expected from its use. Some of these are illustrated by examples from the study of hunting behavior during the Upper Palaeolithic in Franco Cantabria. Specifically, the following issues are examined: the relationships between hunting intensity, yields and variability in yields for the exploitation of reindeer and red deer, the effects on yields from hunting in a multi-predator community and certain aspects of assemblage formation processes.