  We introduce two classes of null hypersurfaces of an indefinite Sasakian
manifold, $(\overline{M}, \overline{\phi},\zeta, \eta)$, tangent to the
characteristic vector field $\zeta$, called; {\it contact screen conformal} and
{\it contact screen umbilic} null hypersurfaces. These hypersurfaces come in to
fill the existing gap in screen conformal and screen totally umbilic null
hypersurfaces. We prove that such hypersurfaces are contained in indefinite
Sasakian space forms of constant $\overline{\phi}$-sectional curvature of $-3$.
