Abstract: ‍ ‍In the presence of multiple non-colluding eavesdroppers， a non-orthogonal multiple access （NOMA） scheme is proposed for physical layer secure communications based on full-duplex relay and two-stage relay selection （TSRS）. Each communication process contains a transmission time slot. At the beginning of each time slot， the system selects the optimal relay by the TSRS strategy. While receiving the NOMA superimposed signal from the source node， the selected relay forwards the re-encoded superimposed signal of the previous time slot to two destination nodes. The two destination nodes decode their respective desired signals from the relayed superimposed signal by using successive interference cancellation （SIC）. The approximated expression for the secrecy outage probability of the system under imperfect SIC is derived and validated by Monte-Carlo simulations. Meanwhile， the relationship between some simulation parameters （SIC residual interference coefficient， target secrecy rate， number of relays， etc） and the secrecy outage probability of the system is analyzed. Theoretical analysis and simulation results show that the combined FD-TSRS scheme can effectively improve the secrecy outage performance of the system. When the scheme is applied to the design of practical communication system， some measures， such as selecting appropriate transmit signal-to-noise ratio （SNR）， enhancing the capability of successive interference cancellation or appropriately increasing the number of relays， can help to achieve better secrecy performance.