The evolution of the ol-relaxation during an isothermal crystallization process of a series of flexible copolyesters of hydroxybutyrate (HB) and hydroxyvalerate (HV) has been followed in real-time by wide-angle X-ray scattering and dielectric complex permittivity measurements. The change of the dielectric parameters with crystallization time can be phenomenologically described in terms of the Havriliak-Negami equation. The dielectric strength follows a sigmoidal-shaped pattern similar to that shown by the crystallinity. A reduction of the overall mobility with crystallization time of the polymeric chains in the amorphous phase has been observed. This slowing down effect depends on the HV molar content. The influence of the chain flexibility on the crystalline-induced restriction has been discussed in the light of similar studies carried out with more rigid polymers. Dielectric experiments suggest that the progressive immobilization of polymer segments as crystallization proceeds cannot be exclusively associated with the amount of crystalline material. Differences in microstructure, depending on the HV molar content, seem to be responsible for the observed behavior. The progressive broadening and symmetrization of the ol-relaxation with increasing crystallization time has been explained as due to a restriction of the large-scale motions of the polymeric chains, as the material is being filled in with crystals.