  In this paper we discuss some aspects of the behavior of superconformal N=1
models under Seiberg's duality. Our claim is that if an electric gauge theory
is superconformal on some marginal subspace of all coupling constants then its
magnetic dual must be also superconformal on a corresponding moduli space of
dual couplings. However this does not imply that the magnetic dual of a
completely finite N=1 gauge theory is again finite. Moreover we generalize this
statement conjecturing that also for non-superconformal N=1 models the
determinant of the beta-function equations is invariant under Seiberg duality.
During the course of this investigation we construct some superconformal N=1
gauge theories which were not yet discussed before.
