The influence of storm motion on runoff is explored, with a focus on dimensionless hydrologic similarity parameters. One- and two-dimensional physically based runoff models are subjected to moving rainstorms. A dimensionless storm speed parameter Ute/Lp, where U is the storm speed, te is the runoff plane kinematic time to equilibrium, and Lp is the length of the runoff plane, is identified as a similarity condition. Storm motion effects on the peak discharge are greatest when the storm is traversing a one-dimensional runoff plane in the downslope direction at a dimensionless speed of Ute/Lp=0.5. This conclusion holds for all values of the dimensionless storm sizes Ls/Lp where Ls is the length of the storm in the direction of motion. Simulations with a two-dimensional rainfall-runoff model confirm the applicability of this similarity parameter on natural watershed topography. Results indicate that the detailed simulation of storm motion is necessary when the storm is moving near the velocity of maximum effect, which is considerably slower than typical storm velocities. ¿ American Geophysical Union 1995