Observations are reported in relaxation tests under tension and retraction on polypropylene/clay nanocomposites with various contents of filler. A two-phase constitutive model is developed in cyclic viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters in the stressstrain relations are found by fitting the observations. Ability of the constitutive equations to describe characteristic features of the time-dependent behavior of nanocomposites under cyclic deformation is confirmed by numerical simulation. POLYM. ENG. SCI., 2013 (c) 2012 Society of Plastics Engineers