  We study two-flavor neutrino oscillations in homogeneous neutrino gases in
which neutrinos and anti-neutrinos are in nearly pure weak interaction states
initially. We find that the monopole and dipole oscillation modes can trigger
flavor instabilities in the opposite neutrino mass hierarchies in a nearly
isotropic neutrino gas. For a class of simple neutrino systems we are able to
identify the normal modes of neutrino oscillations in the linear regime. Our
results provide new insights into the recently discovered multi-azimuthal angle
(MAA) instability of neutrino oscillations in supernovae.
