We expand our analytical modeling strategy for polymer non-linear stress relaxation (A) to specify the remaining steps to accurately deal with the nonaffine nature of the materials' local strains and stresses relative to their average overall values, and (B) to make it consistent with a new cooperative theory of amorphous materials dynamics, providing a model of tunable fragility that sheds light to most aspects of the behavior, including the glass transition. The stress relaxation models (1) describe a nonlinear (strain-dependent) behavior that becomes linear at very low strains, (2) quantify the effect of temperature, (3) may quantify the effects of changes in free volume, and (4) ensure very fast computations of the materials' response irrespective of the experimental time scale. The models are sensitive to the influence of different initial states of the material, as may result from varying degrees of molecular orientation and aging levels, and are able to predict from experimental stress relaxation moduli (for a poly (methylmethacrylate)PMMA and a bis-phenol-A polycarbonatePC) the values of the crossover frequency, (c), crossover temperature, T-c, and the minimum activation energy, in addition to the initial and long-time plateau moduli, in agreement with independently measured values. POLYM. ENG. SCI., 56:348-360, 2016. (c) 2016 Society of Plastics Engineers