The rheological behavior of micellar solutions is analyzed under nonhomogeneous velocity and stress flow conditions. The framework is based on the extended irreversible thermodynamics and the transient network formulation coupled to the underlying kinetics embodying two relevant processes: formation of wormlike chains from a free micellar solution through a thermally activated process and their flow induced degradation. The second kinetic process consists in the formation of entanglements from the free wormlike chains and their flow-induced breakage. These processes are modeled in a coupled kinetic scheme constituted by a set of reversible kinetic equations describing the evolution in average of the three microstates (free short rod-like micelles, free wormlike chains, and entangled wormlike chains) that reflect the complexity of macromolecular interactions. The predictions of the shear stress and first normal stress difference as a function of shear-rate under banded flow are in good agreement with experimental data. (c) 2018 American Institute of Chemical Engineers AIChE J, 64: 2277-2292, 2018