  We analyse the critical behaviour of anomalous currents in N=1
four-dimensional supersymmetric gauge theories in the context of
electric-magnetic duality. We show that the anomalous dimension of the Konishi
superfield is related to the slope of the beta function at the critical point.
We construct a duality map for the Konishi current in the minimal SQCD. As a
byproduct we compute the slope of the beta function in the strong coupling
regime. We note that the OPE of the stress tensor with itself does not close,
but mixes with the Konishi operator. As a result in superconformal theories in
four dimensions (SCFT$_4$) there are {\sl two} central charges; they allow us
to count both the vector multiplet and the matter multiplet effective degrees
of freedom. Some applications to N=4 SYM are discussed.
