  We study a pseudogap region of the mixed boson fermion system using a recent
formulation of the renormalization group technique through the set of
infinitesimal unitary transformations. Renormalization of fermion energies
gives rise to a depletion of the low energy states (pseudogap) for temperatures
$T^{*}>T>T_{c}$ which foreshadows appearance of the pairwise correlations with
their long range phase coherence being missed. With a help of the flow
equations for boson and fermion operators we analyze spectral weights and
finite life times of these quasiparticles caused by interactions.
