Abstract: The constitutive equations of cyclic plasticity and cyclic viscoplasti- city of metallic matcrials have been a very important field of solid mechanics for morc than ten years,In the paper, bounding surface constitutive theories,the endochronic lheory and viscoplastic theories of metallic materials under non- proportional cyclic loadingsnre prcsented together with recent advances,The definitions of nonproportionality, the mcmory effects on complex strain am- plitude history,and material hardcning and flow r...