Nonlinear electrodynamic characteristics of the return-stroke wave of cloud-to-ground lightning equivalent Zeq impedance and phase v velocity are estimated on the basis of the approximate description of the return stroke using quasi-linear partial differential equations. These equations contain nonlinear parameters which depend on instantaneous values of the current in the front of the wave. Besides, a method for the calculation of overvoltages on the high-voltage lines is worked out for the case of direct lightning strokes, taking into account nonlinear impedance of lightning and wave processes in the line. ¿ American Geophysical Union 1994