Several classes of multiple-mode rheological constitutive equations are examined for predicting the viscoelastic flow properties of a typical polymer melt in single and double step-strain flows. The phenomenological parameters appearing in these models have been obtained by the fitting of experimental data taken in small-amplitude oscillatory shear and steady shear flows. The performance of the models for predicting the experimental data in the step-strain experiments is examined in detail. Specifically, we examine whether or not mode coupling is necessary to describe the experimental behavior under step-strain flows. Furthermore, it is demonstrated that the reversing double step-strain experiment is a very powerful tool for testing viscoelastic constitutive equations. (C) 2007 Wiley Periodicals, Inc.