This paper proposes a new adaptive feedforward cancellation (AFC) control that achieves periodic tracking and/or periodic disturbance rejection. The new control design is a direct scheme in the sense that it adaptively updates the desired control without estimating the unknown disturbance. The proposed new control has several advantages. First, its adaptation gain can be arbitrarily chosen without upsetting the system stability if given the exact system model. Second, it can be applied to not only minimum-phase systems, but also non-minimum phase systems. Third, the new control law is independent of where the disturbance enters the system. Finally, a robustness analysis is made to show that the proposed control is robust with respect to un-modelled dynamics. (C) 2011 Elsevier Ltd. All rights reserved.