Abstract A construction principle for the supercurrent emphasizing its transformation property under the superconformal group is applied to the supersymmetric extension of massless gauge theories. A suggestion for a superspace current containing all improved currents of the superconformal group is made. This current is obtained from the supercurrent as a certain moment involving the superspace transformation parameters of the superconformal group. The connection to Noether's theorem in superspace is pointed out. The one-loop anomalies for typical on-shell matrix elements of the components of the supercurrent are calculated, and their supertransformation behaviour is elucidated.