In this paper, we introduce a notion of a k-type null slant helices inMinkowski space-time, where kin0,1,2,3. We give the necessary andsufficient conditions for null Cartan curves to be k-type null slanthelices in terms of their curvatures kappa2 and kappa3. Inparticular, we characterize k-type null slant helices lying inpseudosphere S13(r). We find the relationships between 0-type and -type null slant helices, as well as between 1-type and 2-type nullslant helices. Moreover, we prove that there are no 3-type null slanthelices in Minkowski space-time