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The problem of flow control in fast connection-oriented communication networks supporting traffic generated by multiple sources is addressed. The network is modelled as a dynamic system with different delay times. A nonlinear strategy governing the behaviour of the sources is proposed. The strategy combines Smith's principle with a conventional relay controller. It ensures full bottleneck link utilisation and no cell loss in the controlled network, even if the round-trip times of the connections contributing to the bottleneck link queue are not known exactly, but can only be estimated within a certain level of accuracy. Furthermore, a modified strategy with extra feed-forward compensation is proposed. This strategy also guarantees no cell loss and full bottleneck link utilisation. Moreover, it helps to achieve a favourable quality of service in the controlled network.