In this paper, the authors consider a mixture of two gases consisting of hard spheres having different masses and radii and evolving according to Newton’s laws. Starting from the microscopic dynamics of the two gases, they rigorously derive a Boltzmann equation for mixtures. First of all, they prove that the microscopic flow is measure preserving and global in time for almost every initial configuration. After that, they introduce two parameter mixed marginals which satisfy a Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of which they prove the well-posedness. Suitably taking the numbers of particles of the two gases going to infinity and their radii going to zero (Boltzmann-Grad scaling), the authors formally obtain an infinite two parameter hierarchy of equations called the Boltzmann hierarchy of which they prove the well-posedness too. Tensor form densities are formal solutions to this latter hierarchy if each factor solves the Boltzmann system for mixtures. Given a sequence of initial data for the Boltzmann hierarchy and its approximation for the BBGKY hierarchy, the authors prove that the corresponding solutions of the BBGKY hierarchy converge to those of the Boltzmann hierarchy in the sense of observables. Moreover, if the initial data for the Boltzmann hierarchy have the form of a tensor product of one particle densities, then the solutions of the BBGKY hierarchy converge to the tensor product of the solutions of the Boltzmann system having as initial data the above-specified factors As a corollary of the derivation, the authors prove Boltzmann’s propagation of chaos assumption for the case of a mixture of gases. In addition to the theoretical framework developed for a single type gas, the authors exploit new techniques for multiple gases able to keep track of the evolution and correlation of one type of gas to the other.