The classical von Smoluchowski equation predicts that the electroosmotic mobility generated by the wall zeta potential could be suppressed if the viscosity of the solution adjacent to the wall were extremely high. When performing runs in capillaries filled with polymer solutions (2% methyl cellulose solutions with viscosities of 25 cP), however, one consistently finds that the quenching of electroosmotic mobility is substantially less than predicted by the von Smoluchowski relationship. The electroosmotic flow is progressively suppressed with subsequent electrophoretic runs, suggesting a "dynamic coating" of the polymers onto the capillary wall. This progressive reduction of electroosmotic mobility tends to a plateau value which is still substantially higher than the value derived on the basis of the von Smoluchowski relationship. The following explanation is proposed: due to the very high shear rate in the electric double layer, the polymer molecules change their orientation and/or conformation, which lowers the fluid viscosity in this region. A scaling equation for electroosmotic mobility taking into account the non-Newtonian properties of polymer solutions is derived. It predicts electric field dependence of the electroosmotic mobility as the shear rate in the double layer is proportional to the electric field. Experimental measurements confirm the dependence of the electroosmotic mobility on the electric field.