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In this paper, we consider the global robust output regulation problem for a class of output feedback systems with nonlinear exosystems. Like the special case with linear exosystems, we have shown that the problem can be converted into a global robust stabilization problem of a lower triangular system. But unlike the special case with linear exosystems, the inverse dynamics of the lower triangular system is time-varying. We have derived a set of sufficient conditions for the solvability of the problem.