  In this paper a hyperbolic system of partial differential equations for
two-phase mixture flows with $N$ components is studied. It is derived from a
more complicated model involving diffusion and exchange terms. Important
features of the model are the assumption of isothermal flow, the use of a phase
field function to distinguish the phases and a mixture equation of state
involving the phase field function as well as an affine relation between
partial densities and partial pressures in the liquid phase. This complicates
the analysis. A complete solution of the Riemann initial value problem is
given. Some interesting examples are suggested as bench marks for numerical
schemes.
