  Two-dimensional system of the fermions with the indirect Einstein
phonon-exchange attraction and added local four-fermion interaction is
considered. It is shown that in such a system at resulting attraction between
particles a new nonsuperconducting phase arises along with the normal and
superconducting phases. In this, called "abnormal normal", or pseudogap, phase
the absolute value of the order parameter is finite but its phase is a random
quantity. It is important that the new phase really exists at low carrier
density only, i.e. it shrinks with doping increasing in the case of phonon
attraction. The relevance of the results for high-temperature superconductors
is speculated.
  Key words: 2D metal, arbitrary carrier density, normal phase, abnormal normal
phase, pseudogap, suderconducting phase, Berezinskii-Kosterlitz-Thouless phase,
electron-electron and electron-hole pairing
