  A model of a Fermi liquid with the fermion condensate (FC) is applied to the
consideration of quasiparticle excitations in high temperature superconductors,
in their superconducting and normal states. Within our model the appearance of
the fermion condensate presents a quantum phase transition, that separates the
regions of normal and strongly correlated electron liquids. Beyond the phase
transition point the quasiparticle system is divided into two subsystems, one
containing normal quasiparticles and the other --- fermion condensate localized
at the Fermi surface and characterized by almost dispersionless single-particle
excitations. In the superconducting state the quasiparticle dispersion in
systems with FC can be presented by two straight lines, characterized by
effective masses $M^*_{FC}$ and $M^*_L$, respectively, and intersecting near
the binding energy which is of the order of the superconducting gap. This same
quasiparticle picture persists in the normal state, thus manifesting itself
over a wide range of temperatures as new energy scales. Arguments are presented
that fermion systems with FC have features of a quantum protectorate.
