The deformation field surrounding a fault in a non-linear ductile medium is characterized by two components: a singularity in the stress field at the fault tip which is required by the zero shear stress and discontinuous velocity boundary conditions on the fault, and a non-singular component which is required to satisfy arbitrary stress or velocity boundary conditions on the external boundary. For regions closer to the fault tip than to the external boundary, the singular component dominates. Near the fault tip the strain rate component dominates. Near the fault tip the strain rate components decay as a power-law function of radius with an exponent of -n/(n+1) (where strain rate varies as deviatoric stress to the nth power) and the stress components decay as a power-law function of radius with an exponent of -1/(n+1). The behavior of the mechanical energy dissipation, however, is independent of the reology; it is inversely proportional to the radial distance from the fault tip for all values of n. These results are consistent with the prediction of Rice and Rosengren [1968> who obtained the corresponding power-law relations for the analogous case of a traction free crack in a nonlinear elastic medium. From both the radial and angular dependences of the components of shear strain rate, a localized shear zone will develop along the immediate extension of the fault, and the degree of localization increases with increasing n. ¿ American Geophysical Union 1992