Summary: We derive the governing equations and the Rankine-Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton’s principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions, we use two reference frames related to the Lagrangian coordinates of each component. Under some hypotheses on flow properties, we prove the hyperbolicity of the governing system for small relative velocity of phases.