In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold $ ilde{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of $ ilde{M}$ is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.