  It is shown that in 2D system of the fermions with simplest indirect
boson-induced attraction (through the Einstein phonon exchange as an example)
along with the normal and superconducting phases there arises a new (called
"abnormal normal" or pseudogap) one where the absolute value of the order
parameter is finite but its phase is a random quantity. It is important that
this new phase really exists at low carriers density only, i.e. it shrinks when
doping increases. The relevance of the results obtained with dependence of
pseudogap on doping in high-temperature superconductors is speculated.
