A model for dynamic steady state friction between two rough surfaces is developed in which the transfer of momentum from the horizontal to the vertical direction by collisions between asperities on opposing surfaces leads to a friction law which is independent of the detailed mechanism of energy dissipation. For nonfractal surfaces the model applies above a lower critical velocity which increases exponentially with smoothness. At high velocities there is velocity weakening and, as the smoothness of the surfaces increases, the velocity dependence rapidly approaches the experimentally observed logarithmic dependence, in agreement with phenomenological state variable friction laws. For fractallike surfaces the model applies over the whole velocity range above V=0, showing velocity strengthening at low velocities and velocity weakening at high velocities, implying the existence of a stick-sliplike instability. ¿ American Geophysical Union 1991