In this paper, the shear and extensional rheology of fumed silica nanoparticles dispersed in an aqueous polyethylene oxide (PEO) solution is investigated. The role of particle concentration, polymer concentration, and polymer molecular weight on both the shear and the elongational behavior of the dispersions was examined. The fumed silica dispersions were found to strongly shear thicken. Increasing particle concentration was found to increase the degree of shear thickening. The effect of polymer concentration and polymer molecular weight on shear-thickening behavior was found to be nonmonotonic. The data showed a maximum in shear thickening at an optimum polymer concentration and molecular weight. Increasing the polymer concentration and molecular weight was found to reduce the critical shear rate for the onset of shear thickening. Linear viscoelastic measurements showed a qualitatively similar trend in the elastic modulus. Extensional rheology was conducted using a capillary breakup extensional rheometer. The dispersions showed strong strain-hardening behavior with thickening magnitudes similar to that observed under shear. The trends in the magnitude of extensional hardening with particle and polymer concentration were found to be similar to shear. In some cases, extensional thickening of nearly 1000 times was observed. However, in contrast to shear, increasing the molecular weight of the PEO corresponded to a sharp increase in extensional strain-hardening likely due to the role of polymer-induced elasticity which was shown to cause extensional hardening even in the absence of nanoparticles. (C) 2014 The Society of Rheology.