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In this paper, we introduce a new approach to deadlock-free routing in wormhole-routed networks called the message flow model. This method may be used to develop deterministic, partially-adaptive, and fully-adaptive routing algorithms for wormhole-routed networks with arbitrary topologies. We first establish the necessary and sufficient condition for deadlock-free routing, based on the analysis of the message flow on each channel. We then use the model to develop new adaptive routing algorithms for 2D meshes.