In this paper, the hydrodynamic equations and the associated transport coefficients are derived for a simple binary fluid from molecular considerations. This is a generalization of the methods of Felderhof and Oppenheim and of Selwyn to multicomponent systems. A linear response formalism is used to describe the relaxation of the binary system from an initial nonequilibrium state. Explicit molecular expressions are given for the transport coefficients in terms of time correlation functions of generalized current densities. These densities have the useful property of not containing a conserved part. The correlation functions are then related to a set of phenomenological coefficients in the theory of nonequilibrium thermodynamics. This explicit identification enables one to relate the correlation functions to experimentally measured transport coefficients.