  A comprehensive study is performed of two-loop Feynman diagrams with three
external legs which, due to the exchange of massless gauge-bosons, give raise
to infrared and collinear divergencies. Their relevance in assembling realistic
computations of next-to-next-to-leading corrections to physical observables is
emphasised. A classification of infrared singular configurations, based on
solutions of Landau equations, is introduced. Algorithms for the numerical
evaluation of the residues of the infrared poles and of the infrared finite
parts of diagrams are introduced and discussed within the scheme of dimensional
regularization. Integral representations of Feynman diagrams which form a
generalization of Nielsen - Goncharov polylogarithms are introduced and their
numerical evaluation discussed. Numerical results are shown for all different
families of multi-scale, two-loop, three-point infrared divergent diagrams and
successful comparisons with analytical results, whenever available, are
performed. Part of these results has already been included in a recent
evaluation of electroweak pseudo-observables at the two-loop level.
