  An electron-phonon interaction arising from the modulation of the
superexchange interaction by phonons is studied within the theoretical
framework of Kondo lattices. It is relevant in strongly correlated electron
liquids in cuprate oxide superconductors, which lie in the vicinity of the
Mott-Hubbard metal-insulator transition. It is enhanced by antiferromagnetic
and superconducting fluctuations, which are developed mainly because of the
superexchange interaction. When the enhancement of the electron-phonon
interaction is large enough, it can explain the softening of phonons and kinks
in the quasiparticle dispersion in cuprate oxide superconductors. However, the
superexchange interaction itself must be mainly responsible for the formation
of Cooper pairs.
