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Abstract-We consider an asymmetrical two-way relay channel (TWRC) which consists of one relay node and two user nodes in this paper. In TWRCs, we can efficiently use the channel by using the network coding at the relay with the exclusive OR (XOR) operation. However, due to the nature of the XOR, the rate from the relay to a user node should be the same as the rate from the relay to the other user node. When the channel is asymmetrical, this results in the waste of the channel capacity in the channel with a better channel gain. In this paper, we propose using a superposition coding on top of the XOR operation to utilize the better channel. By using the hybrid network-superposition coding, we can achieve more rate region than that of the XOR-based systems.