The authors consider the problem of controlling stable linear plants subject to input saturation constraints and parametric uncertainties, A globally stable adaptive controller which performs well in the presence of such constraints is designed, using a specific pole placement that accounts for the saturation constraint, an integral action to deal with the tracking problem, and an adaptive control law with an ad-hoc excitation capability together with a parameter adaptation to cope with the parametric uncertainty, The proposed controller allows one to track slowly varying reference sequences. particularly in the case of a constant reference, the output tracking error vanishes asymptotically and the control input does stop saturating after a finite time.