  Results about the phase structure of certain N=1 supersymmetric gauge
theories, which have been obtained as a consequence of holomorphy and
`electric-magnetic' duality, are shown to be in quantitative agreement with
corresponding consequences of analyticity and superconvergence of the gauge
field propagator. This connection is of interest, because the superconvergence
arguments for confinement are not restricted to theories with supersymmetry.
The method of reduction in the space of coupling parameters is used in order to
define, beyond the matching conditions, an asymptotically free, dual magnetic
theory involving Yukawa couplings.
