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