A new test, known as antistress relaxation, allows us to study, exclusively, the anelastic deformation, i.e. one which is recoverable with time, of various polymers over a wide range of stresses and temperatures until the yield flow point is reached. In the linear regime, this test is linked with certain viscoelastic properties, such as the loss tangent, tan Phi and the loss dynamic compliance, J", which are usually measured using dynamic spectrometry techniques. Thus, the isochronal J" and tan Phi spectra of poly(methyl methacrylate) (PMMA) and polycarbonate (PC) are obtained by performing this test at several different temperatures. These spectra are very similar to those obtained using classical techniques and clearly display the beta-relaxation and the anelastic part of the alpha-relaxation. When carried out at high stress levels, the antistress relaxation test allows us to obtain these spectra in the non-linear regime, and therefore, carry out observations of the two relaxations under high stresses. In particular, it is noticeable that the stress increase leads to an important shift of the anelastic part of the alpha-relaxation towards low temperatures and, eventually, to merging of the alpha- and beta-relaxations. On the other hand, there is no clear evidence for any effect of the stress on the beta-relaxation, which, in any case, appears to remain weak. Taking into account these observations, different models, describing the non-linear anelastic deformation during creep experiments, are discussed. Finally, from the hypothesis and the concepts developed in the molecular model of Perez, an energy scheme is proposed for representing the energy state of the microregions of the material participating in anelastic and plastic deformation. This energy representation is able to describe the experimental results concerning the alpha- and beta-relaxations under high stress, and also various other previous experimental observations.