We develop a microscopic description of the contribution to stress relaxation in entangled polymer melts of convective constraint release, which is the release of entanglement constraints due to the effects of convective flow on chains surrounding a given chain. Our theory resolves three of the main shortcomings of the Doi-Edwards model in nonlinear rheology, in that it predicts (1) a monotonically increasing shear stress as a function of shear rate, (2) shear stress independent of molecular weight at sufficiently high shear rates, and (3) only modest anisotropies in the single chain scattering function, in agreement with experiment. In addition, our approach predicts that a stress maximum and resulting shear-banding instability would occur for living micelle solutions, as observed. (C) 2001 Thr Society of Rheology.