Several processes are nonlinear and operate under input constraints. Their effective control requires model-based techniques whose performance is often affected by modelling uncertainties. The paper addresses the control of single-input single-output nonlinear systems with input constraints in the presence of modelling errors. A nonlinear internal model control based on input output linearisation is designed, and an internal model control with antiwindup which removes the nonlinear mismatch due to input constraints is given. An adaptive internal model control with anti-windup to account for parameter uncertainty and an augmented internal model control with anti-windup to attenuate the effect of modelling errors, are proposed and analysed theoretically. Simulation results on temperature control of a continuous stirred tank reactor demonstrate the benefits of the proposed anti-windup schemes.