This note deals with asymptotic rejection of general periodic disturbances in nonlinear systems. A novel approach based on integrations over the half of disturbance period is proposed to estimate disturbances which may not be harmonic or even smooth. The proposed algorithm uses the period and the knowledge of the basic disturbance patterns, while the amplitude and phase of the disturbances are unknown, and they are estimated. Based on the estimated disturbance, the disturbance rejection algorithm is then proposed for linear systems and nonlinear systems in the output feedback format, which asymptotically rejects the periodical disturbances. The proposed algorithm extends asymptotic rejection of unknown disturbances from sinusoidal disturbances to a more general class of periodical disturbances which includes zero-mean square waves, symmetric triangular waves etc.