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In this study, the authors analyse the average end-to-end packet delay for a cognitive ad hoc network where multiple secondary nodes randomly contend for accessing the licensed bands of primary users in non-slotted time mode. Before accessing the licensed bands, each node must perform spectrum sensing and collaboratively exchange the sensing results with other nodes of the corresponding communication as a means of improving the accuracy of spectrum sensing. Furthermore, the medium access control with collision avoidance mechanism based distributed coordination function specified by IEEE 802.11 is applied to coordinate spectrum access for this cognitive ad hoc network. To evaluate the system performance, the authors model the considered network as an open G/G/1 queuing network and utilise the method of diffusion approximation to analyse the end-to-end packet delay. The authors' analysis takes into account not only the number of secondary nodes, the arrival rate of primary users and the arrival rate of secondary users but also the effect of the number of licensed bands when assessing the average end-to-end packet delay of the networks.