The electronic structure of the layered ternary nitrides CaMN₂ (M=Ta,Nb) has been studied and the results are compared with those for the related LiMoN₂ phase. It is shown that the former are two-dimensional metals, with a Fermi surface very similar to that of the 1T-TaX₂ (X=S,Se) dichalcogenides, whereas the latter is a three-dimensional metal. The three phases show strong covalent bonding within the layers but ionic bonding with the alkali atom sheets.