This work reports the relaxation behavior of amorphous polymers the spectra of which do not explicitly present the secondary, relaxation. Poly(2,4-difluorobenzyl methacrylate), a polymer with complex motions in the side groups, was chosen to carry out this study. The apparent distribution of retardation times of the polymer calculated from dielectric loss isotherms in a wide range of temperatures (T > T-g) presents two peaks which do not merge into a single absorption at moderate temperatures. The, absorption appearing as a shoulder of the R relaxation in global thermal stimulated depolarization current experiments is not at first sight detected in the retardation spectra. Separation of the hidden, absorption from the longest time peak in the retardation spectra was carried out by fitting the inverse of the Havriliak-Negami equation to the peak using b = 1 and b < 1 for the skewness shape parameter of the, and R relaxations, respectively. Moreover, the shortest time peak in the retardation spectra was found to be the result of two overlapping peaks, named in increasing order of time gamma and gamma'. Arrhenius plots for the R and, absorptions present a new scenario characterized for displaying both relaxations the same temperature dependence at temperatures not far above Tg. To investigate how small differences in the chemical structure may influence the dielectric response of polymers to perturbation fields, the results obtained for poly(2,4-difluorobenzyl methacrylate) are compared with those previously reported for poly(3-fluorobenzyl methacrylate). The differences in the responses of both polymers are interpreted in terms of molecular motions of the side groups.