Abstract A model originally suggested by Gurtin and Levine  and later modified by Thompson et al.  is considered but with a general fecundity rate function. The same model is also studied under the assumption that the age-specific fecundity function is a function of the total population size of predator and prey species. Our basic model equations turn out to be integrodifferential equations. The stability and instability of equilibria are studied. It is found that Thompson et al.'s results stay valid even for a general fecundity function. Sufficient conditions are given for the stability of equilibria in the case of density-dependent fecundity function.