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In token passing protocols of local area networks, we assume that a user transmits a message which is divided into several packets, and that each packet is transmitted in a round of the circulating token. This transmission from a certain station is interleaved with possible transmissions from other stations. In this paper, a new queueing model is provided to evaluate the mean message delay in contrast to the mean packet delay given by the past studies. The same model is also used to evaluate the mean packet delay in error-prone transmission systems.