The Kondo divergences owing to interaction of current carriers with local m
oments in highly correlated electron systems are considered within the Hubb
ard and s-d exchange models with infinitely strong on-site interaction, the
many-electron Hubbard representation being used. The picture of density of
states containing a peak at the Fermi level is obtained. Various forms of
the self-consistent approximation are used. The problem of the violation of
analytical properties of the Green's function is discussed. Smearing of th
e "Kondo" peak owing to spin dynamics and finite temperatures is investigat
ed.