The nuclear magnetic relaxation dispersion profiles of lyophilized globular proteins were measured in the frequency range of 10 kHz-30 MHz at temperatures from 156 to 302 K. The existent theory of proton relaxation in immobilized protein systems was critically tested and expended to include contributions of rapid motions of protein side-chain groups. The new theory takes into account the strong coupling between the side-chain protons and the protein backbone, when correlation function cannot be written as a product of the contributions. The measurements showed that while the relaxation rate constant of the protein backbone protons is a linear function of the absolute temperature the side-chain groups exhibit an exponential temperature dependence corresponding to an activated process. Measurements carried out on simple homopolypeptides, polyglycine and polyalanine, provide strong support of the proposed new theory.