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Greens relations and generalized Greens relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Greens relations and generalized Greens relations on GV-semigroups are considered by the structure of GV-semigroups.D=J andD (C)D* on GV-semigroups will be proved.