This paper deals with asymptotic rejection of individual frequency modes in nonlinear systems under general periodic disturbances. An iterative observer design is proposed for disturbance estimation, and it is shown that the proposed observer design successfully extracts individual frequency modes from general periodic disturbances. The proposed iterative observer design is then applied to asymptotic rejection of nonlinear systems under general periodic disturbances. (c) 2008 Elsevier Ltd. All rights reserved.