Chain mobility in multiphase polymeric materials is studied by thermally stimulated depolarization currents and dielectric spectroscopy in poly(styrene)-b-poly(butadiene)-b-poly(c-caprolactone) triblock copolymers and poly(carbonate)/poly(c-caprolactone) blends. The variation in the relaxation time distribution of the dielectrically active components and in the number of orientable dipoles in the amorphous phases of these materials is interpreted as the result of the existence of a rigid amorphous phase constrained by the crystalline regions or in the case of the blends by a phase segregation which takes place when the crystallization process of the blend components advances. The mean relaxation times for the secondary and segmental motions are not affected when the phases are segregated.