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This paper argues for the need to address the issue of multi-channel network performance under constraints on channel switching. We present examples from emergent directions in wireless networking to motivate the need for such a study, and introduce some models to capture channel switching constraints. For some of these models, we study connectivity and capacity of a wireless network comprising n randomly deployed nodes, equipped with a single interface each, when there are c=O(logn) channels of equal bandwidth W/c available. We consider an adjacent (c,f) channel assignment where a node may switch between f adjacent channels, but the adjacent channel block is randomly assigned. We show that the per-flow capacity for this channel assignment model is Theta(Wradic(f/cnlogn)). We then show the adjacent (c,2) assignment maps to the case of untuned radios. We also consider a random (c,f) assignment where each node may switch between a pre-assigned random subset of f channels. For this model, we prove that per-flow capacity is O(Wradic(prnd/nlogn)) (where prnd=1-(1-f/c)(1-f/(c-1))...(1-f/(c-f+1)) and Omega(Wradic(f/cnlogn))).