Eulerian and Lagrangian hydrodynamic equations for multicomponent gases are derived from generating kinetic equations and the advantages of Lagrangian transport equations are discussed in connection with the problem of particles slowing down in moving host media. Then a general theory which incorporates both, hydrodynamic and transport formalisms is formulated in a consistent and flexible way. Applications to Inertial Confinement Fusion (ICF) are shown. Although new ideas are proposed, the main aim of this paper is to help the users of existing hydrodynamic and transport codes when they face problems of coupling. However, it is shown that in the general case a few modifications must be introduced in such codes.