In this paper, we analyze the performance of adaptive modulation with single-cell multiuser scheduling over independent but not identical distributed (i.n.i.d.) Nakagami fading channels. Closed-form expressions are derived for the average channel capacity, spectral efficiency, and bit-error-rate (BER) for both constant-power variable-rate and variable-power variable-rate uncoded/coded M-ary quadrature amplitude modulation (M-QAM) schemes. We also study the impact of time delay on the average BER of adaptive M-QAM. Selected numerical results show that the multiuser diversity brings a considerably better performance even over i.n.i.d. fading environments.