  We derive parts of the monopole and dyon spectra for N=2 super-Yang--Mills
theories in four dimensions with gauge groups G of rank r>1 and matter
multiplets. Special emphasis is put on G=SU(3) and those matter contents that
yield perturbatively finite theories. There is no direct interpretation of the
soliton spectra in terms of naive selfduality under strong--weak coupling and
exchange of electric and magnetic charges. We argue that, in general, the
standard procedure of finding the dyon spectrum will not give results that
support a conventional selfduality hypothesis --- the SU(2) theory with four
fundamental hypermultiplets seems to be an exception. Possible interpretations
of the results are discussed.

High Energy Physics - Theory