  We continue the investigation from a previous paper concerning the
super-renormalizablity of gauge models going to the third order of the
perturbation theory. Here we consider only the Yang-Mills case and we prove
that this property is true iff some supplementary restrictions are imposed on
the constants appearing in the interaction Lagrangian. The usual standard model
does not verify these restrictions, but there is hope that such models do exist
and they are in agreement with the phenomenology. We consider here only the
even-parity contributions.
