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In this paper,the existence of periodic solutions for a time dependent agestructured population model is studied.The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model.The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space.The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained.The dynamics of the linear time-periodic model is similar to that of the linear model.