  We generalize the dynamical-mean field (DMFT) approximation by including into
the DMFT equations some length scale via a (momentum dependent) ``external''
self-energy \Sigma_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+\Sigma_k 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+\Sigma_k 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+\Sigma_k show a pseudogap formation near the Fermi level of the
quasiparticle band.
