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Let R be a ring, X a class of R-modules and n>1 an integer. In this paper,via special finitely presented modules, we introduce the concepts of Gorensteinn-X-injective and n-X-flat modules. And aside, we obtain some equivalentproperties of these modules on n-X-coherent rings. Then, we investigate therelations among Gorenstein n-X-injective, n-X-flat, injective and flat moduleson X-FC-rings (i.e., self n-X-injective and n-X-coherent rings). Several knownresults are generalized to this new context

Gorenstein n-X-injective and n-X-flat modules with respect to a special finitely presented module