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This is the second part of a two-part paper considering bidirectional relay networks with half-duplex nodes and block fading where the nodes transmit with a fixed transmission rate. In Part I, it was shown that a considerable gain in terms of sum throughput can be obtained by optimally selecting the transmission modes or, equivalently, the states of the nodes, i.e., the transmit, the receive, and the silent states, based on the qualities of the involved links. To enable adaptive transmission mode selection, the relay has to be equipped with two buffers for storage of the data received from the two users. The protocol proposed in Part I was delay unconstrained and provides an upper bound for the performance of practical delay-constrained protocols. In this paper, we propose two heuristic but efficient delay-constrained protocols, which can approach the performance upper bound reported in Part I, even in cases where only a …