  In this paper we deal with curves with degeneration degree two in
pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show
a correspondence between the evolute of a null curve and the involute of a
certain spacelike curve in the $6-$dimensional pseudo-Euclidean space of index
two. Also we characterize pseudo-spherical null curves in the $n-$dimensional
pseudo-Euclidean space of index two in terms of the curvature functions.
