  We investigate the influence of electron-phonon coupling on the superexchange
interaction of magnetic insulators. Both the Holstein-Hubbard model where the
phonons couple to the electron density, as well as an extended Su, Schrieffer,
Heeger model where the coupling arises from modulation of the overlap integral
are studied using exact diagonalization and perturbative methods. In all cases
for both the adiabatic (but non-zero frequency) and anti-adiabatic parameter
regions the electron-phonon coupling is found to enhance the superexchange.
