A local lightwave network can be constructed by employing two-way fibers to connect nodes in a passive-star physical topology, and the available optical bandwidth may be accessed by the nodal transmitters and receivers at electronic rates using wavelength-division multiplexing (WDM). The number of WDM channels, w, in such a network is technology-limited and is less than the number of network nodes, N, especially if the network should support a scalable number of nodes. We describe a general and practical channel sharing method, which requires each node to be equipped with only one transmitter-receiver pair, and in which each WDM channel is shared in a time-division multiplexed fashion; optical fiber LANs are discussed in particular. We also develop a general model for analyzing such a shared-channel, multi-hop, WDM network. Our analysis yields a counterintuitive result: it is sometimes better to employ fewer channels than a larger number of channels. We explore bounds on the ranges of w which admit queueing stability-using too few or too many channels can lead to instability. We also obtain an estimate for the optimal number of channels that minimizes network-wide queueing delay.