  We study Weyl structures on lightlikes hypersurfaces endowed with a conformal
structure of certain type and specific screen distribution: the Weyl screen
structures. We investigate various differential geometric properties of
Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for
ambiant Lorentzian space $\mathbb{R}^{n+2}_{1}$ and a totally umbilical screen
foliation, there is a strong interplay with the induced (Riemannian)
Weyl-structure on the leaves. Finally, we establish necessary and sufficient
conditions for a Weyl structure defined by the $1-$form of an almost contact
structure given by an additional complex structure in case of an ambiant
Kaehler manifold to be closed.
