We show that, up to homotheties and translations, the Wulff shape W F is the only compact embedded hypersurface of the Euclidean space satisfying H F r = aH F + b with a 0, b > 0, where H F and H F r are respectively the anisotropic mean curvature and anisotropic r-th mean curvature associated with the function F : S n −→ R * +. Further, we show that if the L 2-norm of H F r − aH F − b is sufficiently close to 0 then the hypersurface is close to the Wulff shape for the W 2,2-norm.