The theory of the existence of limiting fluxes and concentrations in the ultrafiltration of macromolecules is reviewed and extended to non-Newtonian power-law fluids. Recent work by Pritchard el al. (1995, J. Membrane Sci. 102, 223-235) has shown the existence of situations where the ultrafiltration flux can increase with concentration. The criterion for this occurring has been developed and evaluated using rheological data as a Function of concentration for a variety of fluids including xanthan gum, dextran, pectin and reconstituted whey. These were then concentrated to high concentrations by ultrafiltration to verify the validity of the criterion. Higher fluxes with increased concentration were only found for xanthan gum.