.On the other hand ,although stochastic partial functional differential equations also seem very important as stochastic models of biological, chemical, physical and economical systems, the corresponding properties of these systems have not been studied in great detail (cf.[23]and[24]).As a matter of fact, there exist extensive literature on the related topics for deterministic age-dependent population dynamic system. There has been much recent interest in application of deterministic age-structures mathematical models with diffusion, For example ,Cushing[3] investigated hierarchical age-dependent populations with intra-specific competition or predation.