It is demonstrated that a large number of solid polymers (PMMA, PLLA, iPP, PS) display a pronounced change in kinetics (strain-rate and temperature dependence) after yield. The phenomenon finds its origin in the fact that, in specific ranges of temperature and strain rate, two different molecular processes may contribute to the yield stress. Because of strain softening, the post-yield response is only controlled by one of the two, resulting in a strain-rate dependence of the yield drop. The universality of the phenomenon is discussed in connection to the alleged influence of secondary transitions on the impact response of polymer glasses. A modification of the finite-strain elasto-viscoplastic EGP-model is proposed to enable an accurate description of the mechanical response of solid polymers in the transition range. The versatility of the model is demonstrated on the temperature and strain-rate dependence of the intrinsic mechanical behavior of PMMA, iPP, PS, and PLLA.