An analysis of the electronic structure and bonding in the superconducting LnNi2B2C and nonsuperconducting LnNiBC phases is made, using extended Huckel tight-binding calculations. The results show that these compounds are highly covalent and can be considered as intermetallic materials. Oxidation formalisms of (Ln2+)(Ni0)2(B2C)2- for LnNi2B2C and (Ln3+)(Ni0)(BC)3- for LnNiBC constitute good starting points to describe their electronic structure. The Fermi level cuts a narrow and sharp peak in the DOS for LuNi2B2C, mainly composed of sigma-type Ni-B bonding states. This allows us to conclude that electrons transferred from the (B2C)2- entities into sigma-type metal-non-metal bonding states are responsible for the superconducting properties encountered for certain LnNi2B2C compounds. Flat bands are calculated in the planes perpendicular to the stacking c axis. These materials should be 2-D-like superconductors. The absence of superconductivity for LuNiBC seems to be associated with the rather weak DOS at the Fermi level, compared to that of LuNi2B2C.