A new method for the simulation of fast transients on nonuniform transmission lines is proposed in this paper. The method is based on the method of characteristics of partial differential equations theory. It is shown that the proposed method can easily include resistive losses and wave speed variations. In addition, in order to bring the proposed method to practical usefulness, a Norton equivalent for transmission line ends is presented. At any given time, the Norton equivalent of each transmission line end is independent of the line's interior behavior at that time, therefore the model can readily be included into any electrical network transients simulation program. The advantages of the method are shown here by applying them to two problems. The first one consists of analyzing the effects of nonuniformities caused by the sagging of conductors on an aerial line. For this case, results from electromagnetic transients program and finite differences time domain simulations are included for comparison purposes. The second application consists of the simulation of a fast impulse propagating along a transmission tower modeled as a network of vertical and horizontal transmission lines.