Summary: It has been shown that the indiscriminate use of the Jaumann rate in constitutive equations for plastic materials gives rise to an oscillatory stress response in the presence of monotonically increasing strain. In this paper we discuss the use of the Jaumann rate in constitutive models with a back stress. More specifically we address the question of linear kinematic hardening given by the Prager-Ziegler rule in the context of large plastic deformation. We demonstrate that the Jaumann rate is a physically opaque mathematical differential operator which must be used with great care in intuitive, large deformation, generalizations of rate equations that apply to small strains. We then use integral constitutive laws, obtained in the context of endochronic plasticity, to derive rate equations of the Prager-Ziegler type for the back stress, that are free of invasive and unwanted oscillations, and give proper kinematic hardening behavior under conditions of large deformation. Lastly we bring the above conclusions into focus by solving exactly the problem of large plastic deformation in simple shear. Closed-form solutions are also obtained using more general memory integral formulations. We further show that the closed form solutions so obtained may serve as vehicles for determining the form of the memory function experimentally in constitutive formulations with path-dependent integrals.