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In this paper, we investigate the weak Gorenstein global dimension. We are mainly interested in studying the problem when the left and right weak Gorenstein global dimensions coincide. We first show, for GFclosed rings, that the left and right weak Gorenstein global dimensions are equal when they are finite. Then, we prove that the same equality holds for any two-sided coherent ring. We conclude with some examples and a brief discussion of the scope and limits of our results.