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The generalized method is presented to calculate the transients in the hybrid systems composed of multiconductor transmission lines and linear lumped elements. Each transmission line may be either uniform or nonuniform in its configuration of conductors. A straightforward matrix formulation at the interface is derived in the complex frequency domain by Laplace transform. Skin effect losses of the conductors as well as the distributed sources are incorporated into the algorithm. Calculated examples by numerical inversion method demonstrate the validity of the method.