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A general time-(distance-) domain representation of unidirectional multipass processes is presented which describes all previously identified examples.1 It is then shown that systems of multiple machines in which the signal flow is unidirectional could be simulated by the repeated simulation of a single machine, and that such a procedure is described by the same general time-domain formulation. The stability of this multipass-simulation sequence, and hence that of the multimachine system, can therefore be investigated analytically using the frequency-response approach previously applied1 to real life multipass processes. It is demonstrated how the approach can be applied also to discretised spatially-distributed processes, provided again that signal flow is unidirectional. The modelling and analysis techniques presented in the paper are shown to be unsuitable, however, in the presence of either counterflow signals or feedback controllers which are not of a local nature and uniformly distributed along the process. The identification of these limitations is an important objective and provides the motivation and starting point for a companion paper in which the multipass-systems approach is adapted to cope with this much wider class of processes.