  The weak coupling spectrum of BPS saturated states of pure $N=2$
supersymmetric SU$(n)$ gauge theory is investigated. The method uses known
results on the dyon spectrum of the analogous theory with $N=4$ supersymmetry,
along with the action on these states of the semi-classical monodromy
transformations. For dyons whose magnetic charge is not a simple root of the
Lie algebra, it is found that the weak coupling region is divided into a series
of domains, for which the dyons have different electric charge, separated by
walls on which the dyons decay. The proposed spectrum is shown to be consistent
with the exact solution of the theory at strong coupling in the sense that the
states at weak coupling can account for the singularities at strong coupling.
