  The band structure of the new perovskite-like superconductor MgCNi$_{3}$ was
studied by the self-consistent FP-LMTO method. The superconducting properties
of MgCNi$_{3}$ are associated with an intensive peak in the density of Ni3d
states near the Fermi level. The absence of superconductivity for
nonstoichiometric compositions MgC$_{1-x}$Ni$_{3}$ is due to the transition of
the system to the magnetic state. The possibility of superconductivity was
discussed for intermetallics ScBNi$_{3}$, InBNi$_{3}$, MgCCo$_{3}$ and
MgCCu$_{3}$ which are isostructural with MgCNi$_{3}$.
