Let G be a complex, connected and simply connected semisimple Lie group with Lie algebra g . Let σ and τ be two involutions of g such that (1) the algebras g σ and g τ of points fixed by σ and τ, respectively, are real forms of g , (2) the group G τ of points fixed by τ is quasisplit, and (3) the automorphism σ τ is inner. We characterize the stable invariant integral of a C ∞ function with compact support on G/ G σ. Then, we generalize the results of Harinck to the case of a reductive symmetric space of type G C / G R . This allows us to construct stable spherical distributions on G/ G σ. Afterward, we construct a correspondence between stable spherical distributions on G/ G τ and those of G/ G σ.