The study of one-dimensional combined longitudinal and torsional plastic wave propagation in a thin-walled cylindrical tube of isotropic-hardening material was first carried out by Clifton. In this paper, the same problem is studied for a combined kinematic and isotropic hardening material. Simple wave solutions are obtained. In some cases, a discontinuity in shear stress occurs, propagating at the elastic shear-wave speed c2, followed by a slow plastic simple wave.