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We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationarydoi:10.4064/am-27-1-21-34 fatcat:6ozrwxhjxzhh7fxyrhohj4iw6e