The propagation equations with transient parameters are the only time-domain equations able to represent, without approximations, the skin effect in the line and in the earth. These equations were completed with a nonlinear term taking into account a simplified model of the impulsive corona effect, based on previous laboratory studies. A computer program for numerical integration of the new equations, for a unifilar line with earth return, was developed, and some applications were carried out, for various wave shapes and earth conductivities, involving lightning overvoltage propagation. The calculated results from tests on a high-voltage transmission line are in good agreement with the measured values. This shows that the attenuation, as well as the distortion, of the propagated lightning waveshape can be predicted by means of calculation for a unifilar line with earth return.