  The formalism of flavor conversion of supernova neutrinos is generalized to
include possible differences in the fluxes of the muon and tau neutrinos
produced in the star. In this case the radiatively induced difference of the
nu_mu and nu_tau potentials in matter becomes important. The nu_mu and nu_tau
flux differences can manifest themselves in the effects of the Earth matter on
the observed nu_e (antinu_e) signal if: (i) the neutrino mass hierarchy is
normal (inverted); (ii) the solution of the solar neutrino problem is in the
LMA region; (iii) the mixing U_{e3} is relatively large: |U_{e3}|>10^{-3}. We
find that for differences in the nu_mu - nu_tau (antinu_mu - antinu_tau)
average energies and/or integrated luminosities < 20 %, the relative deviation
of the observed nu_e (antinu_e) energy spectrum at E > 50 MeV from that in the
case of the equal fluxes can reach 20 - 30 % (10 - 15 %) for neutrinos crossing
the Earth. It could be detected in future if large detectors sensitive to the
nu_e (antinu_e) energy spectrum become available. The study of this effect
would allow one to test the predictions of the nu_mu, nu_tau, antinu_mu,
antinu_tau fluxes from supernova models and therefore give an important insight
into the properties of matter at extreme conditions. It should be taken into
account in the reconstruction of the neutrino mass spectrum and mixing matrix
from the supernova neutrino observations. We show that even for unequal nu_mu
and nu_tau fluxes, effects of leptonic CP violation can not be studied in the
supernova neutrino experiments.
