Protected operators in Nu=2, 4 supersymmetric theories

The anomalous dimension of single and multi-trace composite operators of scalar fields is shown to vanish at all orders of the perturbative series. The proof hold for theories with N =2 supersymmetry with any number of hypermultiplets in a generic representation of the gauge group. It then applies to the finite N =4 theory as well as to nonconformal N =2 models.