<p>In this paper, we address semi-blind two-way non-orthogonal multiple access (NOMA) networks. Two time slots are used to perform NOMA transmissions between the source and two users via two relay nodes. Unlike existing works where channel state information (CSI)- assisted relay is used, two semi-blind relays are employed, which require only the statistics of the first hop to amplify the source signal, thereby significantly reducing the system overhead and complexity, with a slight decrease in performance compared to CSI- assisted two-way NOMA networks. We provide the upper-bound of the sum-rate for the proposed semi-blind two-way NOMA with amplify-and-forward (AF) under Rayleigh fading channels. We also derive an asymptotic expression for the sum-rate of semi-blind two-way NOMA-AF schemes. Numerical results prove the accuracy of the theoretical analysis and show that the proposed system performs similarly to the CSI-assisted two-way NOMA-AF system, with the benefit of reduced processing complexity and system overhead. Numerical results further reveal that, in the high-SNR regime, the sum-rate of both the semi-blind two-way NOMA-AF and the CSI-assisted two-way NOMA-AF schemes is independent of the source transmit power, assuming fixed transmit powers at the relays and users. Moreover, the sum-rate is unaffected by changes in the power allocation factor, illustrating the robustness of the schemes to power allocation variations.</p>