This paper investigates the performance of a two-way amplify-and-forward(AF)relay system with adaptive modulation over independent and non-identical Nakagami-m fading channels.The tight closed-form cumulative distribution function(CDF)expression of the instantaneous end-to-end signal-to-noise ratio(SNR)is provided.Further,approximate closed-form expression for the average spectral efficiency of the two-way AF system with adaptive modulation is obtained.Then,a tight lower bound of outage probability is derived.Finally,we use numerical simulations to verify the tightness of our analytical results.