The influence of shear thinning and viscoelasticity on the power required for the mixing of viscous liquids using six different helical ribbon agitators has been investigated. Four Newtonian and 12 non-Newtonian fluids prepared using several polymers dissolved in varying concentrations in different solvents cover a wide range of rheologicalproperties. By a careful choice of test media, thespecific and combined effects of shear thinning and viscoelasticity on the power requirement have been examined. Simple models are proposed to predict the effective shear rate in the tank from the knowledge of the torque or power number. The effective shear rate predictions compared with the effectiveshear rate estimated using thescheme of Metzner and Otto (1957) show that they slightly depend on the shear thinning properties. Fluid's elasticity increases appreciably the power requirement, and departures from the generalized Newtonian power curve in the laminar regime are observed at smaller Reynolds numbers for viscoelastic fluids. Bottom wall resistance of the mixing vessel makes a negligible contribution to the power consumption.