In this paper, the nonlinear (orbital) stability of static 180^\circ N\'eel
walls in ferromagnetic films, under the reduced wave-type dynamics for the
in-plane magnetization proposed by Capella, Melcher and Otto [CMO07], is
established. It is proved that the spectrum of the linearized operator around
the static N\'eel wall lies in the stable complex half plane with non-positive
real part. This information is used to show that small perturbations of the
static N\'eel wall converge to a translated orbit belonging to the manifold
generated by the static wall.Comment: 45 page