sentences:  In addition, it correctly defines the Generalized Mean Field (GMF), that determine "elastic" scattering renormalizations and, in general, are not functionals of the mean particle densities only.Applications to the lattice fermion models such as Hubbard/Anderson models and to the Heisenberg model of ferro- and antiferromagnet, which manifest the operational ability of the method were given.It was shown that the IGF method provides a powerful tool for the construction of essentially new dynamical solutions for strongly interacting many-particle systems with complex spectra.