A new approach is presented for the transient simulation of lossy transmission lines in high-speed circuits. The approach is based on developing a model for the transmission line which is structured around natural modes of oscillation unlike other transmission-line models which are based on travelling waves. The principal advantage of the new approach is that conversion of frequency-domain prototype models for the transmission lines to the time domain for use in circuit simulators is particularly straightforward and obviates the need for numerical convolution. An illustrative case is given to confirm the efficacy of the new approach.