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This paper concerns the numerical evaluation of transmission line transient response using travelling-wave methods in which the effects of frequency dependent parameters are taken into account. Transmission line behaviour is considered in terms of forward and backward response functions, special emphasis being placed on the latter, which is introduced because of the time dependent nature of the line characteristic impedance. Relatively simple formulae are derived so that both response functions may be included in a general purpose computer program without difficulty. The validity of the approach is confirmed by comparing results with those obtained from the modified Fourier transform method.