Molecular-level modelling of linear viscoelastic properties of a polymer melt is combined with a continuum-based model for the recoverable deformation in domains of fluid in a flow field to predict nonlinear viscoelastic properties. A nonlinear differential constitutive equation is derived, whose parameters are elemental linear viscoelastic properties which can be calculated as a function of polymer composition and environmental conditions. The model is demonstrated by means of examples of important nonlinear effects: recoverable strain and Non-Newtonian shear viscosity, extrudate swell, nonlinear stress relaxation, the onset of shear, and elongational viscosity.