  As a motivation, we first recall the possible connection of electric-magnetic
duality to finiteness in N=1 super-Yang-Mills theories (SYM). Then, we present
the criterion for all-order finiteness (i.e., vanishing of the beta-functions
at all orders) in N=1 SYM. Finally, we apply this finiteness criterion to an
SU(5) SGUT. The latter turns out to be all-order finite if one imposes
additional symmetries.
