By appropriately adding nanoparticles to a polymer matrix can lead to materials with dramatically improved properties, especially under conditions of good dispersion. From a rheological point of view, polymer nanocomposites are typically considered to be soft colloidal dispersions, with an intrinsically disordered structure that greatly affects their viscoelastic or mechanical properties. Despite that the rheological properties of nanocomposites in the melt can be predicted or explained via entanglement network simulations based on multiscale simulation strategies, large-scale macroscopic calculations of their processing flows requires reliable constitutive (viscoelastic) equations which are currently missing. Our objective in the proposed project is to develop such constitutive models guided by principles of nonequilibrium thermodynamics. In particular, we propose to develop a new family of differential models capable of describing the complicated rheologicalbehavior of polymer nanocomposites as a function of the viscoelastic properties of the native polymer matrix and a few parameters describing polymer-filler interactions. The new models will be thermodynamically admissible and will be validated against experimentally measured data for the linear and non-linear viscoelastic properties of selected systems. They will also be employed in large scale finite- or spectral-element calculations in flows such as extrusion and calendering. The outcome of our work will be new differential constitutive equations capable of explaining or describing a number of intricate phenomena typically observed in the preparation and processing of polymer-matrixnanocomposites: filler alignment for anisotropic fillers, particle clustering, network formation, jamming etc., and their effect on the observed rheological properties (yield stress, stress overshoot, etc.)