The complex storage modulus components G'(omega) and G "(omega) were studied as functions of the frequency for the glassy polycarbonate (PC) and PMMA samples upon preliminary room-temperature plastic deformation by uniaxial compression to epsilon(def) approximate to 40-45%. The G'(omega) and G "(omega) values were measured at room temperature in the frequency range omega = 10(-2)-10(2) Hz. It was found that G'(omega) of the predeformed samples was lower than the modulus of the initial samples in the entire frequency range studied, whereas the G "(omega) values markedly increased after deformation, especially in the low-frequency region. By partially annealing the residual deformation at temperatures below the glass transition temperature, it is possible to release the anelastic deformation component in PMMA and PC while retaining the elastic component. It is established that all changes in the G' and G " values observed in the frequency range studied are related completely to the anelastic component of the residual deformation. The plastic deformation component does not affect the G' and G " values, although the amount of plastic deformation markedly exceeds the anelastic deformation level. It is concluded that an increase in the molecular mobility in predeformed polymeric glasses is due to the appearance of the plastic sheer transformation (PST) regions that serve as elementary carriers of anelastic deformation component in glassy polymers. It is suggested that this pattern is typical of all noncovalent low- and high-molecular-mass glasses, The PC samples were additionally characterized by positronium annihilation lifetime spectroscopy (PALS). It was found that the appearance of anelastic deformation component and its carriers (PST regions) is related to a small (2-3%) decrease in the free volume of the glass, while the size of the free volume elements are virtually not affected by the deformation. Therefore, an increase in the molecular mobility and the deformation-induced softening of predeformed PC cannot be explained in terms of the free volume increase in the polymeric glass upon deformation (which is possible for PMMA). Some physical factors responsible for the anelastic-deformation-induced activation of the molecular mobility in glassy polymers are considered. A general phenomenological scheme explaining the effect of anelastic deformation of glasses on the molecular mobility in these materials is proposed. A decrease in the storage modulus G' in predeformed samples (deformation-induced softening) is probably related to the fact that PST regions are less rigid formations compared to the surrounding nondeformed glassy matrix. The PST accumulation in the course of deformation of a polymeric glass sample leads to a growth in the concentration of "soft" inclusions and, hence, to a decrease int he overall macroscopic rigidity of the system.