  The fourth-gradient model for fluids-associated with an extended molecular
mean-field theory of capillarity-is considered. By producing fluctuations of
density near the critical point like in computational molecular dynamics, the
model is more realistic and richer than van der Waals' one and other models
associated with a second order expansion. The aim of the paper is to prove-with
a fourth-gradient internal energy already obtained by the mean field
theory-that the quasi-linear system of conservation laws can be written in an
Hermitian symmetric form implying the stability of constant solutions. The
result extends the symmetric hyperbolicity property of governing-equations'
systems when an equation of energy associated with high order deformation of a
continuum medium is taken into account.
