In this article, a new, discrete time, non-linear flow control strategy for a connection-oriented, multi-source communication network is proposed. The strategy effectively exploits the Smith principle in order to avoid data loss in the network, and to ensure full utilisation of the bottleneck link available bandwidth. The desirable properties of the proposed control strategy are preserved, even though the connection round trip times may be determined imprecisely. Furthermore, an enhanced strategy, which employs extra feed-forward bandwidth compensation, and reduces the influence of the available bandwidth variations on the steady state queue length in the network, is introduced. Finally, the proposed strategy is modified to be appropriate for application when the number of active connections changes during the control process, and new conditions for no data loss and full bandwidth utilisation are formulated and strictly proved. Since the modified strategy allows for arbitrary resource allocation among the controlled virtual circuits, the max-min fairness criteria can be satisfied.