  Properties of strongly correlated two-dimensional (2D) electron systems in
solids are studied on the assumption that these systems undergo a phase
transition, called fermion condensation, whose characteristic feature is
flattening of the electron spectrum $\epsilon({\pf p})$. Unlike the previous
models in the present study, the decay of single-particle states is properly
taken into account. Remarkably, the value of the topological charge ($N=1/2$)
remains unchanged, supporting the view that systems with a fermion condensate
form a separate class of Fermi liquids. Results of calculations are found to be
in qualitative agreement with ARPES data.
