In previous papers [1, 2], we presented hyperbolic governing equations and jump conditions for barotropic fluid mixtures. Now we extend our results to the most general case of two–component media. We obtain governing equations for each component. This is not a system of conservation laws. Nevertheless, using Hamilton's principle we are able to obtain a complete set of Rankine–Hugoniot conditions. For the two–fluid case, the jump relations do not involve the conservation of the total momentum and the total energy.