  We review a certain class of ("nearly") exactly solvable models of electronic
spectrum of two-dimensional systems with fluctuations of short range order of
"dielectric" (e.g. antiferromagnetic) or "superconducting" type, leading to the
formation of anisotropic pseudogap state on certain parts of the Fermi surface.
The models are based on recurrence procedure for one- and two-electron Green's
functions which takes into account of all Feynman diagrams in perturbation
series with the use of the approximate Ansatz for higher-order terms in this
series. These models can be applied to calculation of spectral density, density
of states and conductivity in the normal state, as well as to calculation of
some properties of superconducting state.
