This paper gives a characterization of nonexpansive mappings from the unit sphere of ℓβ (Γ) onto the unit sphere of ℓβ (Δ) where 0<β≤1. By this result, we prove that such mappings are in fact isometries and give an affirmative answer to Tingley’s problem in ℓβ (Γ) spaces. We also show that the same result holds for expansive mappings between unit spheres of ℓβ (Γ) spaces without the surjectivity assumption.