We explore the use of large amplitude oscillatory shear (LAOS) deformation to probe the dynamics of shear-banding in soft entangled materials, primarily wormlike micellar solutions which are prone to breakage and disentanglement under strong deformations The state of stress in these complex fluids is described by a class of viscoelastic constitutive models which capture the key linear and nonlinear theological features of wormlike micellar solutions, including the breakage and reforming of an entangled network At a frequency-dependent critical strain, the imposed deformation field localizes to form a shear band, with a phase response that depends on the frequency and amplitude of the forcing. The different material responses are compactly represented in the form of Lissajous (phase plane) orbits and a corresponding strain-rate and frequency-dependent Pipkin diagram Comparisons between the full network model predictions and those of a simpler, limiting case are presented (c) 2010 Elsevier B V All rights reserved.