  In this paper we present the complete two-loop vertex corrections to scalar
and pseudo-scalar Higgs boson production for general colour factors for the
gauge group ${\rm SU(N)}$ in the limit where the top quark mass gets infinite.
We derive a general formula for the vertex correction which holds for conserved
and non conserved operators. For the conserved operator we take the
electromagnetic vertex correction as an example whereas for the non conserved
operators we take the two vertex corrections above. Our observations for the
structure of the pole terms $1/\epsilon^4$, $1/\epsilon^3$ and $1/\epsilon^2$
in two loop order are the same as made earlier in the literature for
electromagnetism. However we also elucidate the origin of the second order
single pole term which is equal to the second order singular part of the
anomalous dimension plus a universal function which is the same for the quark
and the gluon. [3mm]
