From the points of spectral efficiency, low latency and massive connectivity, novel modulation and multiple access schemes have been proposed in fifth generation (5G) wireless networks. However, the combinations of multiplexing and multiple access techniques have not been widely investigated in most literatures. Therefore, we joint generalized frequency division multiplexing (GFDM) waveforms and power-domain non-orthogonal multiple access (NOMA) systems together in order to further extend the framework of multi-carrier NOMA, and also achieve performance evaluations for NOMA networks with one base station and two users. Basically, theoretical BER expressions of downlink and uplink GFDM assisted NOMA schemes are mathematically derived and then verified by simulation results. In addition, combined performance advantages, including higher achievable sum rate, lower peak-to-average power ratio (PAPR) and out of band power (OOBP) radiation, can be obtained in GFDM assisted NOMA networks. INDEX TERMS 5G, generalized frequency division multiplexing (GFDM), non-orthogonal multiple access (NOMA), multi-carrier NOMA, theoretical BER.