A model is developed that describes the complicated rheology and morphology of thermoplastic polymers blended with relatively small amounts of liquid-crystalline polymers (LCPs). Such blends typically display properties superior to, but more complicated than, those of ordinary thermoplastic polymers. Viscosity predictions are obtained with this model that exhibit the wide range of behavior that is observed experimentally in these blended materials for both shear and elongational flows. For example, the viscosity-composition curve can display a minimum at low compositions of LCP, and the addition of an LCP to a thermoplastic polymer can result in a reduction in the shear viscosity but an increase in the elongational viscosity. Corresponding morphological descriptions are also obtained for the internal microstructure of the blends that provide information about the underlying causes of the complicated rheological behavior.