Cyclic viscoplastic constitutive equations are formulated starting from classical models which are modified in order to follow the general principles of thermodynamics with internal variables. The state variables associated to various kinds of kinematic and isotropic hardening are selected. The total plastic work is separated into energy dissipated as heat and energy stored in the material. A systematic comparison is given between the model predictions and experimental data for both the mechanical response and the energy stored in the material.