  Given a positive function $F$ on $S^n$ which satisfies a convexity condition,
we define the $r$-th anisotropic mean curvature function $H^F_r$ for
hypersurfaces in $\mathbb{R}^{n+1}$ which is a generalization of the usual
$r$-th mean curvature function. Let $X:M\to \mathbb{R}^{n+1}$ be an
$n$-dimensional closed hypersurface with $H^F_{r+1}=$constant, for some $r$
with $0\leq r\leq n-1$, which is a critical point for a variational problem. We
show that $X(M)$ is stable if and only if $X(M)$ is the Wulff shape.
