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In this paper, we present a new approach to the global output regulation problem. In this approach, a controller should be designed in such a way that the closed-loop system is uniformly convergent. This requirement allows to extend the theory developed for the local output regulation problem to what we call the uniform global output regulation problem. Such extension is made using global invariant manifold theorems, which serve as global counterparts of the center manifold theorems. It is shown that within the proposed approach solvability of the (extended) regulator equations is a basic necessary condition for the solvability of the uniform global output regulation problem. As an illustration, we present a solution to the uniform global output regulation problem for a class of nonlinear systems.