This study analyses the performance of a non‐orthogonal multiple access‐based two‐way relaying system. Analytical expressions are obtained to characterise the outage probability and outage floor of the system for end‐to‐end communication over Rayleigh fading channels. Furthermore, results are also presented for the resulting individual user and sum ergodic capacities. A user power allocation technique is proposed for sum‐rate maximisation with user quality of service constraints by transforming the original non‐convex problem into a difference of convex program that can be readily solved. Finally, simulation results are presented to authenticate the analytical expressions obtained for the various quantities and illustrate the efficacy of the proposed scheme.