Abstract A nonlinear kinematic hardening rule with back stress decomposed into components is transformed to a multisurface form. First it is shown under isothermal conditions that the multisurfaces generated by the transformation are nested and obey a Mroz-type translation rule. It is also shown that the multisurface form can be specialized to a piecewise linear kinematic hardening rule. The transformation is then applied to a time recovery term describing thermal softening and a temperature-rate term operating in nonisothermal inelasticity. A multisurface model is thus derived for nonisothermal, as well as isothermal, plasticity and viscoplasticity.