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The overall outage probability of a two-way amplify-and-forward relaying system with opportunistic relay selection is investigated over Nakagami-m fading channels, and a tight closed-form approximation is derived. Further, closed-form expressions for the overall diversity and coding gains are obtained. Simulation results are presented to verify the analysis. Using these expressions, one can evaluate the outage performance, diversity and coding gains of a two-way relaying system easily and fast.