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A hostparasitoid system with overlapping generations is considered. The dynamics of the system is described by differential equations with a control parameter describing the behavior of the parasitoids. The control parameter models how the parasitoids split their time between searching for hosts and searching for non-host food. The choice of the control parameter is based on the assumption that each parasitoid maximizes the instantaneous growth rate of the number of copies of its genotype. It is shown that optimal individual behavior of parasitoids, with respect to time sharing between hosts and food searching, may have a stabilizing effect on the hostparasitoid dynamics.] 1997 Academic Pres