  In this paper, we initiate the study of lightlike hypersurfaces of an
$(\epsilon)$-almost paracontact metric manifold which are tangent to the
structure vector field. In particular, we give definitions of invariant
lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, and
give some examples. Integrability conditions for the distributions involved in
the screen semi-invariant lightlike hypersurface are investigated when the
ambient manifold is an $(\epsilon)$-para Sasakian manifold.
