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An effective method for computing the time-domain response of lossless multiconductor transmission lines with branches in cross-sectionally inhomogeneous dielectric media is presented. Lines of this type are characterized by multiple propagation modes having different velocities. The theory of wave propagation on lossless multiconductor transmission lines with inhomogeneous dielectrics is used to obtain the modal amplitudes on the uniform sections of the line. The scattering matrix for the junction is used to compute the transmitted and reflected waves in the different branches at the junction. Each mode arriving at the junction excites multiple modes in all branches. The method described in this paper identifies all propagation modes in all branches of the line, and leads to the direct physical interpretation of the results. The method is general and can be applied to either partially or completely nondegenerate cases. Experimental results for a six-conductor transmission line with a single branch are found to be in good agreement with the results computed using the described method.