  We consider the two-dimensional t-t' Hubbard model with the Fermi level being
close to the van Hove singularities. The phase diagram of the model is
discussed. In a broad energy region the self-energy at the singularity points
has a nearly-linear energy dependence. The corresponding correction to the
density of states is proportional to ln^3(e). Both real- and imaginary part of
the self-energy increase near the quantum phase transition into magnetically
ordered or superconducting phase which implies violation of the Fermi-liquid
behavior. The application of the results to cuprates is discussed.
