The crystal structures of the layered host lattices, β-ZrNBr and β-HfNCl have been determined. They have been found to be isostructural with rhombohedral SmSI. New lithium intercalation compounds (Li _x MNX; M=Zr, Hf; X=Cl, Br, I) have been prepared by treatment of either β-ZrNBr, β-HfNCl, α-ZrNBr or α-ZrNI with an excess of BuLi in hexane. These intercalates are all superconducting and show transition temperatures (T _c ) of 12, 20, 11 and 11 K respectively. The lithium intercalates of the host lattices β-ZrNBr, α-ZrNBr and α-ZrNI are the first examples of intercalation into these materials.