  In this paper, we study the hydrodynamic limit transition from the Boltzmann
equation for gas mixtures to the two-fluid macroscopic system. Employing a
meticulous dimensionless analysis, we derive several novel hydrodynamic models
via the moments' method. For a certain class of scaled Boltzmann equations
governing gas mixtures of two species, we rigorously establish the two-fluid
incompressible Navier-Stokes-Fourier system as the hydrodynamic limit. This
validation is achieved through the Hilbert expansion around the global
Maxwellian and refined energy estimates based on the Macro-Micro decomposition.
