The paper deals with the moving horizon control of systems subject to input delays and affected by input and state and/or output constraints. The robustness of the control law with respect to the uncertainties introduced by the discretization is considered. The stability of the closed-loop system is guaranteed by forcing the state trajectories to attain a robust positively invariant terminal set on the prediction horizon. Illustrative examples complete the paper. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.