Future 6G mobile networks are expected to provide ubiquitous communication to a wide range of mobile devices through heterogeneous networks including non-terrestrial networks (NTNs). As an important complement to terrestrial networks, unmanned aerial vehicles (UAVs) based NTNs offer benefits such as flexible deployment, mobility control, and strong line-of-sight links. In this paper, a cognitive radio (CR) assisted cooperative non-orthogonal multiple access (NOMA) UAV system is proposed and its performance is analysed. In this system, the base station uses power-domain NOMA regarding the UAVs. The UAVs act as decode-and-forward relays serving clusters of user equipments (UEs). The CR concept is applied to reduce the interference caused by the UAVs to adjacent clusters of UEs. Analytical expressions of the outage probability and sum rate of this system are derived for the case of Nakagami-m fading. Numerical results are provided to reveal the impact of system parameters on the outage probability and sum rate. Further, design options and trade-offs between orthogonal multiple access and CR assisted cooperative NOMA UAV systems are illustrated. © 2024 IEEE.