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Let be a ring, a class of -modules and an integer. We introduce the concepts of Gorenstein --injective and --flat modules via special finitely presented modules. Besides, we obtain some equivalent properties of these modules on --coherent rings. Then we investigate the relations among Gorenstein --injective, --flat, injective and flat modules on --rings (i.e., self --injective and --coherent rings). Several known results are generalized to this new context.