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This paper concs the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations.By using the Fourier localization argument and the Littlewood-Paley theory,we get local well-posedness results of the GMHD equations with large initial data (u0,b0) belonging to the critical Fourier-Besov-Morrey spaces FN1-2α+3/pl+λ/p p,λ,q (R3).Moreover,stability of global solutions is also discussed.