  We review the results on neutrino propagation in neutral and charged media
under strong magnetic fields $M_{W}^{2}\gg B\gg m_{e}^{2}$. It is shown that
the neutrino energy density gets a magnetic contribution in both charged and
neutral media, which is linear in the magnetic field, of first order in
$G_{F}$, and independent of the charge density. This new term enters as a
correction to the neutrino kinetic energy and produces an anisotropic
contribution to the neutrino index of refraction. As a consequence, in a
neutral medium a highly anisotropic resonant level-crossing condition takes
place for the oscillation between electron-neutrinos and the other neutrino
species. Possible cosmological applications are presented.
