Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (that is, fully associative) potential-based multiaxial, unified viscoplastic model is obtained. This model possess one tensorial internal state variable that is associated with dislocation substructure, with an evolutionary law that has nonlinear kinematic hardening, and both thermal- and strain-induced recovery mechanisms. A unique aspect of the present model is the inclusion of nonlinear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This nonlinear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated) and greatly influences the multiaxial response under nonproportional loading paths. In addition to this nonlinear compliance operator, a new, consistent, potential-preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves that are present with nonlinear hardening formulations during unloading and reversed loading of the external variables. Specification of an experimental program for the complete determination of the material functions and parameters for characterizing a metallic matrix, for example, TIMETAL 21S, is given. The experiments utilized are tensile, creep, and step-creep tests. Finally, a comparison of this model and a commonly used Bodner-Partom model is made on the basis of predictive accuracy and numerical efficiency.