  We study the ordered "excitonic" states which develop around the quantum
critical point (QCP) associated with the electronic topological transition
(ETT) in a 2D electron system on a square lattice. We consider the case of
hopping beyond nearest neighbors when ETT has an unusual character. We show
that the amplitude of the order parameter (OP) and of the gap in the electron
spectrum increase with increasing the distance from the QCP, \delta_c - \delta,
where \delta = 1-n and "n" is an electron concentration. Such a behavior is
different from the ordinary case when OP and the gap decrease when going away
from the point which is a motor for instability. The gap opens at "hot spots"
and extends untill the saddle points (SP) whatever is the doping concentration.
The spectrum gets a characteristic flat shape as a result of hybrydization
effect in the vicinity of two different SP's. The shape of the spectrum and the
angle dependence of the gap have a striking similarity with the features
observed in the normal state of the underdoped high-T$_c$ cuprates. We discuss
also details about the phase diagram and the behaviour of the density of
states.
