In this paper, we study a power domain non-orthogonal multiple access (NOMA) scheme for cognitive cooperative radio networks (CCRNs). In the proposed scheme, a secondary transmitter communicates with two secondary users (SUs) by allocating transmit powers inversely proportional to the channel power gains on the links to the respective SUs. A decode-and-forward (DF) secondary relay is deployed which decodes the superimposed signals associated with the two SUs. Then, power domain NOMA is used to forward the signals from the relay to the two SUs based on the channel power gains on the corresponding two links. Mathematical expressions for the outage probability and ergodic capacity of each SU and the overall power domain NOMA CCRN are derived. Numerical results are provided to reveal the impact of the power allocation coefficients at the secondary transmitter and secondary relay, the interference power threshold at the primary receiver, and the normalized distances of the SUs on the outage probability and ergodic capacity of each SU and the whole NOMA system. © 2018 IEEE.