Flow of non-Newtonian fluids between rough walls is of interest in several geophysical and industrial applications. In this work (mainly geared toward fractured media) a governing equation for creeping flow of a purely viscous power law fluid of flow behavior index n in a rough-walled fracture is obtained, generalizing past results for a Newtonian fluid. An equivalent fracture aperture is defined, in analogy to the well-known hydraulic aperture valid for n=1. Tortuosity is introduced as a vectorial quantity, thereby distinguishing between true and apparent fracture aperture. Examples are provided to illustrate the utility of the proposed approach. It is demonstrated that tortuosity effects significantly decrease the equivalent fracture permeability. Depending on the specific geometry considered, the flow behavior index may or may not have a significant impact on the equivalent fracture permeability. When it does, the reduction effect due to tortuosity is enhanced as the flow behavior index decreases. ¿ 2001 American Geophysical Union