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This paper considers effective capacity region of two-user opportunistic spectrum access in fading channel under discrete transmission rate policy. Although opportunistic spectrum access has been regarded as a promising solution to the the problem of spectrum inefficiency and scarcity, little attention is given to capacity analysis under QoS constraint. Since discrete transmission rate policy is more preferable in practice, we firstly extend the finite state channel model to the opportunistic spectrum access by taking the occupancy of primary user into consideration. Then by means of effective capacity, we investigate the capacity region for the two-user opportunistic spectrum access under QoS constraint. Finally, we present numeric results and draw conclusions.