Most mylonitic rocks are characterized by a fine grainsize and it is now widely accepted that the grainsize reduction commonly takes place by dynamic recrystallization. This reduction in grainsize will favour a number of deformation mechanisms whose strain rate depends inversely on grainsize (e.g., diffusion flow, grain boundary sliding - GBS). We have constructed deformation maps to illustrate the effect of these mechanisms, especially GBS, on flow strength. It is shown that, if the recrystallized grainsize equilibrates with the steady state dislocation flow stress, the grainsize reduction is insufficient to cause extensive strain softening. In general, a monomineralic rock that has undergone dynamic recrystallization by dislocation creep will continue to deform by the same basic mechanism with limited strainrate acceleration (1-10 times) due to GBS. Extensive diffusion flow will only take place if the grainsize is held below the equilibrium value by some means (e.g., impurity pinning of grain boundaries). Several microstructural characteristics of mylonites are found to be consistent with flow by dislocation creep-accommodated GBS. It is suggested that the strain softening implied by the geometry of mylonite zones is the result of a variety of phenomena that are generally only indirectly related to the reduction in grainsize.