A model is proposed for nonlinearly hardening materials under complex loading conditions. Observations on the macroscopic behavior of materials under uniaxial random cyclic loading are generalized to develop a model for complex multiaxial loading, particularly cyclic loading. The model introduces the concept of a bounding surface in stress space that always encloses the loading surface. A parameter defined by the relative position of the loading and bounding surfaces, and the plastic work done during the most recent loading, determines the value of the plastic modulus. The paper discusses the importance of accurately describing material behavior in the plastic range, especially for complex loading histories. Existing models for simple histories are insufficient for complex loading, requiring constitutive relations that include realistic dependence on loading history. The basic step in considering this history dependence is the formulation of constitutive laws in differential or incremental form. The material response is obtained by integrating the incremental relations. Conventional models inadequately describe hardening or softening properties. The paper emphasizes the need for a more accurate model to represent material behavior. While mathematically complex models are difficult to solve analytically, advanced numerical methods and computers can help overcome practical difficulties. The model should contain two basic features: the flow rule, which is an incremental plastic stress-strain relation, and the hardening rule, which defines the change of the loading surface and the change of hardening (softening) properties. The part of the hardening rule concerned with the change of the plastic modulus is the main subject of this paper. Historical remarks discuss various models for defining changes in the loading surface. These include isotropic hardening, kinematic hardening, and more complex models involving deformation and rotation of the initial yield surface. The paper also notes that while much attention has been given to the change of yield-loading surfaces, less has been done on how the work-hardening plastic moduli change. A function is proposed for kinematic hardening to clarify this.A model is proposed for nonlinearly hardening materials under complex loading conditions. Observations on the macroscopic behavior of materials under uniaxial random cyclic loading are generalized to develop a model for complex multiaxial loading, particularly cyclic loading. The model introduces the concept of a bounding surface in stress space that always encloses the loading surface. A parameter defined by the relative position of the loading and bounding surfaces, and the plastic work done during the most recent loading, determines the value of the plastic modulus. The paper discusses the importance of accurately describing material behavior in the plastic range, especially for complex loading histories. Existing models for simple histories are insufficient for complex loading, requiring constitutive relations that include realistic dependence on loading history. The basic step in considering this history dependence is the formulation of constitutive laws in differential or incremental form. The material response is obtained by integrating the incremental relations. Conventional models inadequately describe hardening or softening properties. The paper emphasizes the need for a more accurate model to represent material behavior. While mathematically complex models are difficult to solve analytically, advanced numerical methods and computers can help overcome practical difficulties. The model should contain two basic features: the flow rule, which is an incremental plastic stress-strain relation, and the hardening rule, which defines the change of the loading surface and the change of hardening (softening) properties. The part of the hardening rule concerned with the change of the plastic modulus is the main subject of this paper. Historical remarks discuss various models for defining changes in the loading surface. These include isotropic hardening, kinematic hardening, and more complex models involving deformation and rotation of the initial yield surface. The paper also notes that while much attention has been given to the change of yield-loading surfaces, less has been done on how the work-hardening plastic moduli change. A function is proposed for kinematic hardening to clarify this.