  One derives 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 one uses
two reference frames related with the Lagrangian coordinates of each component.
Under some hypotheses on flow properties one proves the hyperbolicity of the
governing system for small relative velocity of phases.
