As known that the effective capacity theory offers a methodology for exploring the performance limits in delay constrained wireless networks, this article considered a spectrum sharing cognitive radio (CR) system in which CR users may access the spectrum allocated to primary users (PUs). Particularly, the channel between the CR transmitter (CR-T) and the primary receiver and the channel between the CR-T and the CR receiver (CR-R) may undergo different fading types and arbitrary link power gains. This is referred to as asymmetric fading. The authors investigated the capacity gains achievable under a given delay quality-of-service (QoS) constraint in asymmetric fading channels. The closed-form expression for the effective capacity under an average received interference power constraint is obtained. The main results indicate that the effective capacity is sensitive to the fading types and link power gains. The fading parameters of the interference channel play a vital role in effective capacity for the looser delay constraints. However, the fading parameters of the CR channel play a decisive role in effective capacity for the more stringent delay constraints. Also, the impact of multiple PUs on the capacity gains under delay constraints has also been explored.