In this paper nonuniform multiconductor trans-mission lines are considered to be equivalent to a cascaded chain of many multiport subnetworks which are made of short sec-tions of uniform lines. The ABCD matrices of the subnetworks can be obtained by the matrix series expansions of their ana-lytic expressions. As long as the number of the subnetworks is large enough to reflect the line nonuniformity fully, the expan-sions will converge so fast that a few of low-order series terms will be good approximations. After the overall ABCD matrix of the cascaded network chain is evaluated from that of each sub-network, the time of response of transmission lines can be ana-lyzed. The lines may have frequency-dependent parameters and arbitrary nonlinear terminals. Furthermore, transmission sys-tems with branches uniform and nonuniform transmission lines can be studied with this method conveniently. The analysis ac-curacy and efficiency are discussed in detail.