A control structure is introduced for the purpose of rejecting periodic (or repetitive) disturbances on a tracking system. The objective of the proposed structure is to drive the output of the system to the reference input that will result in perfect following without any changing the inner configuration of the system. The structure includes an adaptation block which learns the dynamics of the periodic disturbance and forces the interferences, caused by disturbances, on the output of the system to be reduced. Since the control structure acquires the dynamics of the disturbance by on-line adaptation, it is possible to generate control signals that reject any slowly varying time-periodic disturbance provided that its amplitude is bounded. The artificial neural network is adopted as the adaptation block. The adaptation is done at an on-line process. For this , the real-time recurrent learning (RTRL) algoritnm is applied to the training of the artificial neural network.