A new constitutive model is derived for the nonlinear viscoelastic behavior of polymers which do not possess the separability property. The model is based on the concept of adaptive links (a version of the theory of transient networks). It is assumed that the response of a link is essentially nonlinear, and the rates of breakage and reformation depend on the strain intensity. With reference to the Eyring concept of thermally activated processes, a new equation is proposed to describe the effect of strains on reformation of adaptive links. Adjustable parameters of the model are found by using experimental data for polycarbonate and an epoxy glass in the standard relaxation tests. Comparison of experimental data in dynamic tests with results of numerical simulation shows that the model correctly predicts the nonlinear viscoelastic response.