The fluid mechanics of the movement of the contact line region for non-Newtonian fluids has been analyzed using the method of Joanny and de Gennes [C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Univers Terre 299, 279 (1984)] where under lubrication theory approximation the rate of viscous dissipation is equated to the rate of surface work to get the expression for the rate of spreading. Two kinds of fluids are considered, one where the viscosity is dependent on shear rate but there are no normal stresses, and another where there are normal stresses but the coefficients are not dependent on the shear rate. Both show the spreading rates to be independent of the non-Newtonian nature of the fluids to a good approximation, with the zero shear viscosity replacing the Newtonian viscosity in the result of Joanny and de Gennes. This appears to be in keeping with the available experimental data.