A stable method for the analysis of lossy transmission lines with nonlinear loads is presented. The simulation employs the time marching (TM) method for solving the convolution equations in the time domain. To cope with the late-time instability of the TM method, a novel approach based on the application of Z-transform analysis and cepstrum is presented. The efficiency of the proposed method is demonstrated by comparing its results with simulations obtained using (i) a full-wave FDTD approach, and (ii) CST Cable Studio.