  In this paper we introduce radical transversal lightlike hypersurfaces of
almost complex manifolds with Norden metric. The study of these hypersurfaces
is motivated by the fact that for indefinite almost Hermitian manifolds this
class of lightlike hypersurfaces does not exist. We also establish that radical
transversal lightlike hypersurfaces of almost complex manifolds with Norden
metric have nice properties as a unique screen distribution and a symmetric
Ricci tensor of the considered hypersurfaces of Kaehler manifolds with Norden
metric. We obtain new results about lightlike hypersurfaces concerning to their
relations with non-degenerate hypersurfaces of almost complex manifolds with
Norden metric. Examples of the considered hypersurfaces are given.
