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Consider a network in which adjacent nodes exchange messages via multiple communication channels. Multiple channels between adjacent nodes are desirable due to their cost effectiveness and improved fault-tolerance. We consider the problem of providing deterministic quality of service guarantees in this network. We show that any scheduling protocol designed for a single channel can be converted into a multiple-channel scheduling protocol without significantly increasing the delay at the scheduling node. However, because there are multiple channels between adjacent nodes, the packets of a flow may be reordered. This in turn significantly increases the upper bound on the end-to-end delay of the flow. We show how this increase in delay can be avoided through the use of efficient sorting techniques.