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We first propose and research a multi-class multi-queue system single server under polling table, which is more proper for modeling token-based communication systems. Then we deduce its common stability condition through analyzing the procedure of message service and message queue in this system. Further, we obtain stability conditions with services, such as limited and gated service, from the common stability condition. Besides, both queue stability and system stability are considered for some systems whose exact analyses have not been obtained yet. The analysis indicates that system stability and queue stability depend on the service styles.