  We define the notion of affine Anosov representations of word hyperbolic
groups into the affine group $\mathsf{SO}^0(n+1,n)\ltimes\mathbb{R}^{2n+1}$. We
then show that a representation $\rho$ of a word hyperbolic group is affine
Anosov if and only if its linear part $\mathtt{L}_\rho$ is Anosov in
$\mathsf{SO}^0(n+1,n)$ with respect to the stabilizer of a maximal isotropic
plane and $\rho(\Gamma)$ acts properly on $\mathbb{R}^{2n+1}$.
