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This note deals with asymptotic rejection of periodic disturbances in a class of nonlinear systems via output feedback. The disturbance undertaken is unmatched but the period of the disturbance is known. A novel method for estimating periodic disturbances is proposed, which ensures convergence of the estimation error to zero. By applying such estimation, a controller is constructed such that all the signals in the closed loop are bounded and the output converges to zero. A numerical example is presented to show the utility of the results presented in the note.