AbstractAn approach to nonlinear viscoelasticity is described which is based on the “coupling model” of relaxation. A brief review of nonlinear viscoelasticity models is given to put the present approach into historical perspective. The physical basis of the coupling model is then described, and the quantitative predictions that the model has made in linear viscoelasticity and other areas of relaxation are discussed. The relaxation function predicted by the coupling model is used as a time‐dependent kernal in a constitutive equation for a description of nonlinear viscoelasticity. The model incorporates the strain history dependence and allows for the evolution of material structure. Simulations are presented showing how the model reproduces the essential features of constant strain‐rate, strain‐rate change, and strain‐step experiments. Experiments are described that can partially characterize the coupling model parameters and lead to quantitative tests o