  We develop a thorough description of neutrino oscillations in a magnetized
protoneutron star, based on a resonance layer for neutrinos with different
momentum directions. We apply our approach to the calculation of the asymmetry
in the neutrino emission during the birth of a neutron star and the pulsar
acceleration in the case of an active-sterile neutrino resonant conversion. The
observed velocities can be obtained with the magnetic fields expected in the
interior of a protoneutron star, for sterile neutrino masses of the order of
KeV and small mixing angles.
