13-13E

We investigated the fermion spectrum of the Bose-Fermi-Hubbard model, used for description of boson-fermion mixtures of ultra-cold atoms in optical lattices. We used the method based on Hubbard operator approach for on-site basis. The equation for fermion Green's function in the Bode-Fermi-Hubbard model was built; Green's functions of higher order were decoupled in Hubbard-I approximation approach (the case of strong on-site interaction). Appropriate spectral densities were calculated. For the case of hard-core bosons the condition of appearance of additional bands in fermion spectrum  was investigated. It's shown, that these bands exist only in the state with Bose-Einstein condensate and manifest themselves because of mixing of states with different number of bosons. These additional bands are reflection of composite excitations (when appearing of fermion on a site is accompanied by simultaneous creation (or disappearing) of boson).