This paper considers a novel polling system with two classes of message which can experience an upper bounded time before being served . The station serves these two classes with mixed service discipline , one class with exhaustive service discipline, and the other with gated service discipline. Using iterative method, we have developed an approximation method to obtain the mean waiting time for each message class . The performance of approximation has been compared with the simulation results . The expression for the upper bound of waiting time is given too .