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This study considers an underlay cognitive radio (CR) system, where the secondary network employs cooperative non‐orthogonal multiple access (NOMA) to transfer information for downlink secondary users (SUs). Here the near user is enabled to act as a full duplex/half duplex (FD/HD) decode‐and‐forward (DF) relay for the far user. We derive analytical expressions for the outage probabilities experienced by the SUs in the considered FD/HD – CR‐NOMA network. The maximum transmit power constraint of the secondary nodes and the tolerable interference power constraints at the primary receiver are considered for the analysis. We provide numerical and simulation results to identify the impact of key system parameters on the outage performance of SUs. Further, we provide insights on the selection of key system parameters such as NOMA power allocation coefficient for ensuring that both the SUs experience …