The interactions between a predator and prey species have been analyzed by computer simulation of a model in which there are discrete breeding seasons, separated by a winter during which the predator must be able to find prey at a certain minimum rate or starve. The model is intended to represent a warm—blooded vertebrate predator and its prey. The main conclusions are: (1) Coexistence of predator and prey is possible, but if so, the number of prey present will not be substantially below the equilibrium number in the absence of predators. Mutual regulation of predator and prey, with the latter substantially below the carrying capacity of the environment, is unstable. (2) Coexistence is more likely if there are differences in hunting ability between different individual predators–for example, between young and old predators. (3) Cover for the prey enables the prey species to survive the extinction of the predator, but does not make coexistence more likely.