  We compute four-point correlation functions of scalar composite operators in
the N=4 supercurrent multiplet at order g^4 using the N=1 superfield formalism.
We confirm the interpretation of short-distance logarithmic behaviours in terms
of anomalous dimensions of unprotected operators exchanged in the intermediate
channels and we determine the two-loop contribution to the anomalous dimension
of the N=4 Konishi supermultiplet.
