Abstract : This work deals with eulerian compressible multi-specie fluid dynamics, the species beeing either mixed or separated (with interfaces). The document is composed of three parts. The first part is devoted to the numerical resolution of model problems: advection equation, Burgers equation, and Euler equations, in dimensions one and two. The goal is to find a precise method, especially for discontinuous initial conditions, and we developp non dissipative algorithms. They are based on a downwind finite-volume discretization under some stability constraints. The second part treats of the mathematical modelling of fluids mixtures. We contruct and analyse a set of multi-temperature and multi-pressure models that are entropic, symmetrizable, hyperbolic, not ever conservative. In the third part, we apply the ideas developped in the first part (downwind discretization) to the numerical resolution of the partial differential problems we have constructed for fluids mixtures in the second part. We present some numerical results in dimensions one and two.