We consider the pulsar velocity problem and relate it to some unconven
tional neutrino oscillation mechanisms based on the violation of the e
quivalence principle by neutrinos. We show that the observed pulsar ve
locities may be explained by violations at the level from 10(-9) to 10
(-10) in the case of a non-universal tensor neutrino-gravity coupling,
whereas there is no solution in the case of a non-universal scalar ne
utrino-gravity coupling. Neutrinos may remain massless and the requisi
te magnetic field strength is similar to that in the conventional mass
oscillation mechanism.