Three relay selection techniques, aiming at achieving secure non-orthogonal multiple access in cooperative energy-harvesting (EH) communications, are proposed and compared. In the cooperative relaying system, the source node communicates with multiple users through amplify-and-forward EH relays in the presence of a passive eavesdropper. The relay selection is a two-stage strategy, where the first stage aims at achieving the users’ target data rate, and the second aims at optimizing the secrecy outage probability. New explicit analytical expressions for the secrecy outage probability are derived for three operating scenarios: i) when the channel state information (CSI) of the eavesdropper is unknown, and a two-stage conventional relay selection scheme is considered, ii) when CSI of the eavesdropper is known, and a two-stage optimal relay selection scheme is used, and iii) when multiple relays participate in forwarding the signal to the end users. Monte-Carlo simulations are provided to confirm the derivations, and the effects of the main system parameters on its secrecy are investigated. In particular, it is shown that the optimal relay selection scheme outperforms the conventional and the multiple-relays schemes in terms of secrecy outage probability, and that this superiority becomes more obvious when the number of the relays increases.