In this paper, we investigate the outage performance of a multiuser two-way relaying system over Nakagami-m fading channels. In particular, we consider the amplify-and-forward (AF) relay system with beamforming at the base station. Furthermore, the base station and mobile users have asymmetric traffic requirements. We fist derive a tight lower bound for the outage probability (OP). Moreover, the asymptotic outage probability expression is derived to shed light on the system's diversity order. Finally, Monte Carlo simulations are conducted to verify the analytical results.