Behavior of massless feynman integrals near singular points

It is proved for some class of massless Feynman amplitudes including one-loop integrals that on the leading Landau surface these integrals can only have poles and logarithmic or square root-type singularities; the corresponding critical points (in the sense of the theory of singularities of differentiable mappings) are simple. Diagrams having nonisolated critical points are considered. The question of possible coincidence of leading Landau surfaces for the graph and its sub- or quotinent-graphs is studied.