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In this paper we analyze the behavior of communication networks in which packets are generated dynamically at the nodes and routed in discrete time steps across the edges. We focus on a basic adversarial model of packet generation and path determination for which the time-averaged injection rate of packets requiring the use of any edge is limited to be less than 1. A crucial issue that arises in such a setting is that of stability-will the number of packets in the system remain bounded, as the system runs for an arbitrarily long period of time? Among other things, we show: (i) There exist simple greedy protocols that are stable for all networks. (ii) There exist other commonly-used protocols (such as FIFO) and networks (such as arrays and hypercubes) that are not stable. (iii) The n-node ring is stable for all greedy routing protocols (with maximum queue-size and packet delay that is linear in n). (iv) There exists a simple …