Analytical expressions of shear stress evolution for arbitrary transient flows are obtained, based on a rate-dependent network (RDN) model as well as on a nonaffine network (NAN) model. Predictions of both models are evaluated for various step histories against experimental results on linear and branched polyethylene melts (LDPE and HDPE). Agreement with experiments justifies the usefulness of the computed stress functions regarding the predictions of shear responses in melt processing. A slow transient process is more adequately simulated by an NAN model than by an RDN model. The very slow reentanglement process following cessation of flow is poorly described by either model. This fact implies that additional relaxation mechanisms are involved. In the linear viscoelasticity of small deformation, elastic relaxation occurs. In processes involving large shear rates, additional parameters are needed to account for the structural changes accompanying the relaxation process.