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We consider in this paper relay assignment for cooperative systems with multiple two-way relay channels. The nodes corresponding to one two-way relay channel (henceforth referred to as pair) communicate with each other through a relay. The relays use network coding to simultaneously transmit the signals corresponding to the pairs they are assigned to. We propose two relay assignment schemes. One scheme considers all possible relay assignment permutations and selects the one that yields the best performance, and the other one considers only a subset of these permutations and selects the best one. The advantage of the latter is that it results in a significant reduction in computational complexity, in addition to making the analysis more tractable. We analyze the performance of these schemes over asymmetric independent Rayleigh fading channels. We also consider semi-symmetric and symmetric channels as special cases. We derive closed-form expressions for the end-to-end bit error rate performance for all scenarios and show that the full diversity order is achieved, which is the number of available relays. We present several examples to verify the theoretical results.