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In this paper, we examine the delay performance in cognitive radio networks (CRNs) over general fading channels where secondary users are allowed to simultaneously access the spectrum licensed by primary users. In particular, subject to the peak interference power constraint, we investigate the effect of general fading channels on the delivery delay of data packets and acknowledgements (ACKs). A lower bound of outage probability and an upper bound of average transmission time are derived by utilizing the concept of timeout. Specifically, we apply the above results to investigate the quality of experience (QoE) for various fading channels, such as one-sided Gaussian, Rayleigh, Nakagami-m and Weibull channels. The numerical results indicate that the delay of ACKs under severe fading leads to a degradation of system performance.