Abstract : We study the geometry of lightlike hypersurfaces $M$ of an indefinite cosymplectic manifold $\bar{M}$ such that either (1) the characteristic vector field $\zeta$ of $\bar{M}$ belongs to the screen distribution $S(TM)$ of $M$ or (2) $\zeta$ belongs to the orthogonal complement $S(TM)^{\bot}$ of $S(TM)$ in $T\bar{M}$.
