The time-dependent mechanical response of flax fiber-reinforced thermoplastic starch matrix composite and neat starch is analyzed. It is demonstrated that the response is highly sensitive to the relative humidity (with specific saturation moisture content in the composite) and special effort has to be made to keep it constant. It was found that the accumulation of micro-damage and the resulting reduction of the elastic modulus in this type of composite is limited. The highly nonlinear behavior of composites is related to the nonlinear viscoelasticity and viscoplasticity. These phenomena are accounted for by simple material models, as suggested in this study. The stress-dependent nonlinearity descriptors in these models are determined in creep and strain recovery tests at low as well as by high stresses.