This article studies adaptive modulation for QR decomposition and successive interference cancellation receivers in multiple-input multiple-output systems over slow- and fast-fading channels. In slowly fading channels, adaptive modulation schemes with finite-rate feedback under the constraints of a constant total transmit power, discrete-rate and a target bit-errorrate (BER) are proposed. Specifically, the authors first develop adaptive modulation with modulation order feedback only. For power allocation and modulation order feedback, the authors establish an optimisation scheme that can be solved easily and analyse the effect of power-level quantisation on the achievable data rates. For the fast fading channel case, the authors analyse the probability distribution of the 'R' matrix and derive a scheme that only requires feedback of the statistical information of the channel for adaptive modulation with optimal bit loading to guarantee that the BER target is met.