  In earlier work \cite{bedeaux/vdW/I, bedeaux/vdW/II, bedeaux/vdW/III} a
systematic extension of the van der Waals square gradient model to
non-equilibrium one-component systems was given. In this work the focus was on
heat and mass transfer through the liquid-vapor interface as caused by a
temperature difference or an over or under pressure. It was established that
the surface as described using Gibbs excess densities was in local equilibrium.
Heat and mass transfer coefficients were evaluated. In our first paper
\cite{glav/gradient/eq/I} we discussed the equilibrium properties of a
multi-component system following the same procedure. In particular, we derived
an explicit expression for the pressure tensor and discussed the validity of
the Gibbs relation in the interfacial region. In this paper we will give an
extension of this approach to multi-component non-equilibrium systems in the
systematic context of non-equilibrium thermodynamics. The two-dimensional
isotropy of the interface is discussed. Furthermore we give numerically
obtained profiles of the concentration, the mole fraction and the temperature,
which illustrate the solution for some special cases.
