In a metric g.f.f-manifold we study lightlike hypersurfaces M tangent to the characteristic vector fields, and owing to the presence of the f-structure, we determine some decompositions of TM and of a chosen screen distribution obtaining two distributions invariant with respect to the structure. We discuss the existence of a g.f.f
Nearby in the stack
-structure on a lightlike hypersurface and, under suitable hypotheses, we obtain an indefinite
S
-structure on the leaves of an integrable distribution. The existence of totally umbilical lightlike hypersurfaces of an indefinite
S
-space form is also discussed. Finally, we explicitely describe a lightlike hypersurface of an indefinite