  Four-point functions of gauge-invariant operators in D=4, N=4 supersymmetric
Yang-Mills theory are studied using N=2 harmonic superspace perturbation
theory. The results are expressed in terms of differential operators acting on
a scalar two loop integral. The leading singular behaviour is obtained in the
limit that two of the points approach one another. We find logarithmic
singularities which do not cancel out in the sum of all diagrams. It is
confirmed that Green's functions of analytic operators are indeed analytic at
this order in perturbation theory.
