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A priority-queueing-based router in WDM networks with multiple lightpaths between nodes under traffic with two priority classes is analyzed. A priority-queueing-based router transports a high-prioritized packet prior to a low-prioritized one. Therefore, it can handle a variety of traffic having different requirements for queueing delay. Our analysis can clarify the effect of system parameters such as the number of lightpaths and the ratio of traffic with high priority class on the delay performance. It is shown that class 1 packet delay is liable to be affected by the routing processing speed and the ratio of the class 1 traffic to all traffics.