Dielectric spectra of the polyester poly(propylene succinate) were measured upon crystallization. For this model aliphatic polyester the alpha and beta relaxations appear simultaneously and are well resolved in the experimental frequency window. During isothermal crystallization, this fact allows one to use the beta relaxation to characterize the crystalline structural development while the alpha relaxation provides information about the evolution of the amorphous phase dynamics. In this way structure development and dynamics evolution can be characterized by a single experiment during the crystallization process. The unambiguous analysis of the dielectric loss clearly supports the existence of precursors of crystallization in the induction period.