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In this paper we introduce the notion of Gorenstein X-flat R-module and study a kind of stability of the class of Gorenstein X-flat R-modules. A ring R is called right GXF-closed if the class of all Gorenstein X-flat right R-modules is closed under extensions. We give an answer for the following natural question in the setting of a right GXF-closed ring R: Given an exact sequence of Gorenstein X-flat right R-modules G = · · ·→G ₁ → G ₀ → G ⁰ → G ¹ →· · · such that the complex G ⊗ _R H is exact for each Gorenstein X-injective left R-module H, is themodule M:= im(G ₀ → G ⁰) a Gorenstein X-flat R-module?