  We investigate the superconformal transformation properties of the
supercurrent as well as of the superconformal anomalies themselves in d=4, N=1
supersymmetric quantum field theory. Matter supercurrent and anomalies are
coupled to a classical background of minimal supergravity fields. On flat
superspace, there exist two different types of the superconformal Ward identity
(called S and B) which correspond to the flat space limits of old resp. new
minimal background supergravity fields. In the present publication we give
particular importance to the new minimal case. A general formalism is set up
which is then applied to the massless Wess-Zumino model.
