Local network externalities are present when the network externalities associated with entering a certain network depends not only on the total number of agents in the network, but on the identity of the agents in the network. We explore the consequences of local network externalities within a framework where two networks compete on the Hotelling circle. We first show that local network externalities, in contrast to global network externalities, do not sharpen competition. Then we show that the equilbrium suffers from composition inefficiency, due to a coordination failure. We also study the effects of the systematic difference between the marginal and the average consumer that the local network externalities create. The consequences are too little traffic within the network, and too much interconnection between the networks.