We search for dual gauge theories of all-loop finite, N = 1 supersymme
tric gauge theories. It is shown how to find explicitly the dual gauge
theories of almost all chiral, N = 1, all-lopp finite gauge theories,
while several models have been discussed in detail, including a reali
stic finite SU(5) unified theory. Out of our search only one all-loop,
N = 1 finite SO(10) theory emerges, so far, as a candidate for exhibi
ting also S-duality. (C) 1998 Elsevier Science B.V.