  We show that four-dimensional N=2 supersymmetric SU(n) gauge theory for n>2
necessarily contains vacua with mutually non-local massless dyons, using only
analyticity of the effective action and the weak coupling limit of the moduli
space of vacua. A specific example is the Z_3 point in the exact solution for
SU(3), and we study its effective Lagrangian. We propose that the low-energy
theory at this point is an N=2 superconformal U(1) gauge theory containing both
electrically and magnetically charged massless hypermultiplets.
