  We generalize the dynamical-mean field (DMFT) approximation by including into
the DMFT equations some length scale via a momentum dependent ``external''
self-energy S(k). This external self-energy describes non-local dynamical
correlations induced by short-ranged collective SDW-like antiferromagnetic spin
(or CDW-like charge) fluctuations. At high enough temperatures these
fluctuations can be viewed as a quenched Gaussian random field with finite
correlation length. This generalized DMFT+Sk approach is used for the numerical
solution of the weakly doped one-band Hubbard model with repulsive Coulomb
interaction on a square lattice with nearest and next nearest neighbour
hopping. The effective single impurity problem in this generalized DMFT+Sk is
solved by numerical renormalization group (NRG). Both types of strongly
correlated metals, namely (i) doped Mott insulator and (ii) the case of
bandwidth W~U (U - value of local Coulomb interaction) are considered.
Densities of states, spectral functions and ARPES spectra calculated within
DMFT+Sk show a pseudogap formation near the Fermi level of the quasiparticle
band.

Strongly Correlated Electrons