An efficient method for frequency-domain and transient analysis of the nonuniform lossless coupled microstrip transmission lines excited by external electromagnetic waves is presented. The nonuniform coupled microstrip transmission lines system is first decomposed into a large number of uniform sections called steplines. Using the modal decomposition method, each step is modeled as a linear system with matrix coefficients. The effects of the external excitation are then modeled as inputs in the proper positions of the system. Finally, the solution in the frequency domain is obtained, and the fast Fourier transform algorithm is used to find the time-domain response of the lines. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 215–228, 2003.