  To understand the role of electron-phonon interaction in superconducting
MgCNi$_{3}$ we have performed density functional based linear response
calculations of its lattice dynamical properties. A large coupling constant $%
\lambda $= 1.51 is predicted and contributing phonons are identified as
displacements of Ni atoms towards octahedral interstitials of the perovskite
lattice. Instabilities found for some vibrational modes emphasize the role of
anharmonic effects in resolving experimental controversies.
