  We analyze a number of ``nearly exactly'' solvable models of electronic
spectrum of two-dimensional systems with well-developed fluctuations of short
range order of ``dielectric'' (e.g. antiferromagnetic) or ``superconducting''
type, which lead to the formation of anisotropic pseudogap state on certain
parts of the Fermi surface. We formulate a recurrence procedure to calculate
one-electron Green's function which takes into account all Feynman diagrams in
perturbation series and is based upon the approximate Ansatz for higher-order
terms in this series. Detailed results for spectral densities and density of
states are presented. We also discuss some important points concerning the
justification of our Ansatz for higher-order contributions.
