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An asymptotic rejection algorithm is proposed for nonlinear dynamic systems under nonharmonic periodic disturbances generated from nonlinear exosystems. The dynamic systems considered in this brief are in the normal form, a larger class of nonlinear dynamic systems than the output feedback systems. A new internal model design method is used to exploit the nonlinearities in the exosystem, together with high gain design to achieve asymptotic rejection of nonharmonic disturbances with the guaranteed semi-global stability of the overall system. An illustrative example demonstrates that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol circuit.