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This study analyses a cognitive radio scenario based on non-persistent carrier sense multiple access (CSMA) and time division multiple access (TDMA) systems sharing a single-channel wireless network. TDMA users are considered as primary users who can access the channel at any time, and non-persistent CSMA users are considered as secondary users who can share the channel when it is free. New expressions for the individual and aggregate throughput performance of this combined system have been developed, and the system performance is evaluated for a variety of proportions of non-persistent CSMA and TDMA traffic levels. Simulation and analytical results are presented and the ways in which both schemes suffer negative effects as a result of the interaction are shown, primarily caused by increased number of collisions arising from the other scheme.