The viscosity of aqueous, charged alpha -Al2O3 suspensions with and without added polyelectrolytes (polyacrylic acid (PAA 1800)) is investigated over a wide range of volume fractions and shear rates. The Carreau-Yasuda model is used for both cases for examining the shear-rate dependence; for the electrostatically-stabilized suspensions the Krieger-Dougherty and Quemada models are used to determine the maximum packing fraction. The latter analysis shows that the suspension behavior changes from liquid-like to solid-like at a volume fraction of 0.71 in the low-shear limit and at 0.89 at the high-shear limit (because of the polydispersity of the suspension). The results with polyelectrolytes indicate that the dosage of the polymer plays an important role in the viscosity of suspensions and that there is an optimum dosage of polyelectrolyte that must he added to reduce the viscosity at high volume fractions of solids.