  We provide some additional evidence in favour of the strong - weak coupling
duality between the SO(32) heterotic and type I superstring theories by
comparing terms quartic in the gauge field strength in their low-energy
effective actions. We argue that these terms should not receive higher-loop
string corrections so that duality should relate the leading-order perturbative
coefficients in the two theories. In particular, we demonstrate that the
coefficient of the $F^4$-term in the one-loop (torus) part of the SO(32)
heterotic string action is exactly the same as the coefficient of the
$F^4$-term in the tree-level (disc) part of the type I action.
