Thermally stimulated depolarization currents (TSDC) and differential scanning calorimetry (DSC) are performed on thermoplastic polyesters and dimethacrylate resins over temperature ranges covering the alpha and beta relaxation regions. The noncooperative beta relaxation is characterized by a continuous variation of activation energies as a function of temperature and follows the activated states equation with a zero activation entropy. The cooperative alpha relaxation shows a prominent maximum of the activation energies at the glass transition temperature. Compensation behavior is often observed by TSDC for many polymers in the glass transition temperature range. We show that this behavior is not systematic and that it appears for the alpha relaxation if the increase of the apparent activation enthalpy is strong and if the width of the glass transition is weak.