This paper addresses the application of nonorthogonal multiple-access techniques (NOMA) to those satellite relayed communications for which a significant imbalance in the link quality of user terminals can be expected. The Signal-to-Interference and Noise Ratio (SINR) imbalance could be caused by the coexistence of different types of terminals, possibly with different antenna sizes, and offering different classes of service. This link SINR asymmetry can be exploited to outperform orthogonal access schemes under different rate metrics, paying special attention to fairness in the service provision. Both forward and asynchronous return link are addressed, with minimum signaling information and emphasis on some relevant implementation issues such as framing and synchronization.