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Let T be a tilting module. In this paper, Gorenstein Td n-injective and Gorenstein Td n-flat modules are introduced. If G∈ CogenT (resp; G∈ GenT), then G is called Gorenstein Td n-injective (resp; Gorenstein Td n-flat) if there exists the exact sequence M=···→ M1→ M0→ M0→ M1→··· of ET-modules (resp; FT-modules) with G= ker (M0→ M1) such that Ed