The roughness of fault surfaces is important in the mechanics of fault slip and could play a role in determining whether sliding occurs via earthquakes or fault creep. We have made preliminary measurements of the power spectral density of several fault surfaces over the wavelength range from 10-5 to 1 m, using field and laboratory scale profilimeters. The fault surfaces are strongly anisotropic; profiles parallel to the slip direction have amplitudes about one order of magnitude lower than those perpendicular to the slip direction over most of the wavelength interval measured. Fault roughness perpendicular to the slip direction is similar to the roughness of natural joints; the greater smoothness in the slip direction presumably represents wear resulting from slip. Combining our data with previous measurements of the roughness spectrum of the San Andreas fault shows that fault surfaces are fractal over nearly eleven orders of magnitude in wavelength. ¿ American Geophysical Union 1987