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Recent work in wireless sensor networks implies possibilities of concurrent support of multiple applications. In this paper, we discuss a novel scheme called hybrid computation in two-way relaying, which introduces cooperation of three sensor nodes to support bi-directional communications of two applications. Applications in wireless sensor networks require different computations and forms of aggregation. In the proposed scheme, different computations at the intermediate node are integrated in a two-way relaying scheme. For computations and transmissions in the proposed scheme, data from all three nodes are considered.We propose a superposition coding protocol and a time division protocol to handle the transmission of the messages from the intermediate node. The problem of maximizing the sum rate is discussed. The results show that the superposition coding protocol outperforms the time division protocol.