Abstract The problems of the asymptotic behavior of age-dependent population models with interior and spatial structures are considered. It is proved that the existence and uniqueness of the stable state and its exact form is founded for general linear models. Problems on the speed of convergence to stable state and transitional effects are investigated. Methods of solving two special classes of nonlinear models (separate models and models of the Gurtin-MacCami type) are suggested. A model of forest stand dynamics on the basis of conception of layer-mosaic characteristics of the spatial-temporal structure of stands is examined as an example of the application of given results.