The viscoelastic characterization of agro-filler based plastic composites is of paramount importance for these materials' long-term commercial success. To predict creep, it is imperative to derive a relationship between deformation, time, temperature, and stress. This work is the harbinger in modelling of the nonlinear creep behaviour of two-phase materials, where an extended "theory of mixtures" has been used to describe all the creep related parameters. The stress- and temperature-related shift factors were estimated in terms of the activation energy of the constituents. The combined effect of temperature and stress on creep strain was accommodated in a single analytical function where the interaction was shown to be additive. The model was validated under rigorous conditions and is unique because it describes creep not through curve fittings, but in terms of the creep constants of the constituents. This constitutive model is not only a vanguard in the prediction of long term creep of many biocomposites but also in the modelling of creep under step loading of temperature.