For the first time, we report on using dynamic mechanical analysis (DMA) to directly follow molecular mobility in PMMA and PC deformed by small constant tensile stress (a) over the temperature interval from T-g - 60 K to T-g + 60 K. At T-alpha' > T-g, a pronounced secondary alpha'-relaxation was observed exhibiting larger frequency shift and stronger alpha-dependence compared to the main alpha'-relaxation. After reaching its maximum at approximately the T-g, the strain rate was progressively reduced at the onset of the alpha'-relaxation, attaining its minimum value at approximately the T-alpha'. Above the T-alpha', the strain rate increased gradually again, suggesting that mobility has again been enhanced: 0,4 0,1 We ascribe the observed variation in mobility to the strain-induced transition of 0,2 Segments from less mobile into more mobile domains, resulting in the alteration of conformational and orientational distribution. The macroscopic deformation (epsilon) dependence of the transient Modulus, defined to characterize the system stiffness between the alpha and alpha' relaxation (Gamma*(epsilon)) and above the a'-relaxation (Omega*(epsilon)), collapsed to a single linear master curve for Gamma*(epsilon) and the nonlinear Omega*(epsilon) master curve. Our results seem to indicate that the observed alpha'-relaxation may be caused by the process of intrabasin jump diffusion of small portions of the backbone chain over the characteristic length scale smaller than or equal to the dynamic Kuhn segment length (l(K)). The existence of the alpha'-relaxation may be a manifestation of the large strain-altered chain packing associated with the polyamorphic phase transition as the process accompanying yielding in polymer glasses.