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.