  In this paper, we rigorously derive a Boltzmann equation for mixtures from
the many body dynamics of two types of hard sphere gases. We prove that the
microscopic dynamics of two gases with different masses and diameters is well
defined, and introduce the concept of a two parameter BBGKY hierarchy to handle
the non-symmetric interaction of these gases. As a corollary of the derivation,
we prove Boltzmann's propagation of chaos assumption for the case of a mixtures
of gases.
