Supersymmetric extreme dyonic black holes of toroidally compactified h
eterotic or type-II string theory can be viewed as lower-dimensional i
mages of solitonic strings wound around a compact dimension. We consid
er conformal sigma models which describe string configurations corresp
onding to various extreme dyonic black holes in four and five dimensio
ns. These conformal models have regular short-distance region equivale
nt to a WZW theory with level proportional to magnetic charges. Argume
nts are presented suggesting a universal relation between the black ho
le entropy (area) and the statistical entropy of BPS-saturated oscilla
tion states of solitonic string.