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In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with constraints.We provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.