  We investigate the diffusion asymptotics of the Boltzmann equation for
gaseous mixtures, in the perturbative regime around a local Maxwellian vector
whose fluid quantities solve a flux-incompressible Maxwell-Stefan system. Our
framework is the torus and we consider hard-potential collision kernels with
angular cutoff. As opposed to existing results about hydrodynamic limits in the
mono-species case, the local Maxwellian we study here is not a local
equilibrium of the mixture due to cross-interactions. By means of a
hypocoercive formalism and introducing a suitable modified Sobolev norm, we
build a Cauchy theory which is uniform with respect to the Knudsen number
$\eps$. In this way, we shall prove that the Maxwell-Stefan system is stable
for the Boltzmann multi-species equation, ensuring a rigorous derivation in the
vanishing limit $\eps\to 0$.
