We present a relatively simple argument showing that H-dyon states req
uired by S-duality of the heterotic string on T-6 are present provided
that the BPS dyons required by S-duality of N = 4 supersymmetric Yang
-Mills theory are present. We also conjecture and provide evidence tha
t H-dyons at singularities where the non-perturbative gauge symmetry i
s completely broken behave like BPS dyons. (C) 1997 Elsevier Science B
.V.