Nonlinear creep is one of the generic features of deformation response of glassy polymers, where a rich set of strain vs time responses is observed that depend upon the applied stress and the thermal history used to form the glass. Although existing constitutive models may be able to describe some aspects of nonlinear creep, these models are unable to provide a unified description of the diverse nonlinear creep behaviors exhibited by glassy polymers, where predicting the effects of thermal history has proved especially challenging. In this paper the ability of a recently developed Stochastic Constitutive Model (SCM) to describe nonlinear creep is critically examined, where it is demonstrated that the SCM qualitatively captures all of the major features of nonlinear creep of glassy polymers, including the tertiary creep. In particular the SCM predicts how the duration of the secondary creep and the range of the tertiary creep depend on the aging time prior to deformation. The SCM predicts the existence of Stage IV creep, which comes after the tertiary creep - where examination of nonlinear creep data clearly indicate the presence of Stage IV creep, although heretofore not recognized, in the experimental data. The SCM unifies the description of nonlinear creep, and provides a detailed mesoscopic picture of the processes that underlie both strain controlled and stress controlled experiments. (C) 2015 Elsevier Ltd. All rights reserved.