Abstract-Non-Orthogonal Multiple Access (NOMA) has the potential to increase the spectral efficiency of fifth generation (5G) networks by allowing simultaneous transmission to/from multiple users in the same wireless channel. In this work, a Buffer-Aided (BA) NOMA multiple relay network is considered, where the source transmits with fixed rate towards two users. By adopting BA relays, increased robustness can be achieved, as additional degrees of freedom are provided to relay selection. In order to increase the diversity of NOMA transmissions, two BA Half-Duplex (HD) relay selection algorithms are developed, considering the required transmission rate for each user, for Successive Interference Cancellation (SIC) at the reception and the Buffer State Information (BSI) at the relays. Then, results are provided in terms of outage probability, average throughput and average delay for the two algorithms. Finally, conclusions and possible future directions are given.