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 νμ and ντ potentials in matter becomes important. The νμ and ντ flux differences can manifest themselves in the effects of the Earth matter on the observed νe (ν̄e) 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 Ue3 is relatively large: |Ue3| >∼ 10−3. We find that for differences in the νμ – ντ (ν̄μ – ν̄τ ) average energies and/or integrated luminosities <∼ 20%, the relative deviation of the observed νe (ν̄e) 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 νe (ν̄e) energy spectrum become available. The study of this effect would allow one to test the predictions of the νμ, ντ , ν̄μ, ν̄τ 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 νμ and ντ fluxes, effects of leptonic CP violation can not be studied in the supernova neutrino experiments. PACS: 14.60.Pq, 97.60.Bw.