In this paper, we study the long wave approximation for quasilinear
symmetric hyperbolic systems. Using the technics developed by
Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that
under suitable assumptions the long wave limit is described by
KdV-type systems. The error estimate if the system is coupled appears to
be better. We apply formally our technics to Euler equations with free
surface and Euler-Poisson systems. This leads to new systems of KdV-type.