  The problem of pairing in anisotropic electron systems possessing patches of
fermion condensate in the vicinity of the van Hove points is analyzed.
Attention is directed to opportunities for the occurrence of non-BCS pairing
correlations between the states belonging to the fermion condensate. It is
shown that the physical emergence of such pairing correlations would
drastically alter the behavior of the single-particle Green function, the
canonical pole of Fermi-liquid theory being replaced by a branch point.
