Many field investigations have documented the existence of significant spatial variability of the saturated hydraulic conductivity Ks in typical catchments, and several modeling studies have examined the effects of this variability on Hortonian surface runoff. However, these modeling studies had limitations, and some could not deal adequately with possible runoff/run-on phenomena where areas of low saturated hydraulic conductivities Ks are upstream of areas of higher Ks. The kinematic wave equations with interactive Smith-Parlange infiltration are solved by a finite-difference scheme on a characteristic computational net. It is shown that runoff hydrographs are strongly affected by trends in hydraulic conductivity, particularly for small runoff events. The results also show that Smith and Hebbert <1979> mislabeled outflow hydrographs, resulting in incorrect conclusions about the effects of linear trends in Ks. A simple technique is introduced to account for flow concentration in rills and the resulting reduced effective wetted areas subject to infiltration after rainfall ceases. It is shown that this mechanism has a major impact on runoff peaks, volumes, and time to peak for cases where Ks increases downslope. ¿ American Geophysical Union 1996