  In this letter, we investigate corrections to quartic gauge couplings in
compactifications of string theories on a 2-torus without vector structure.
First, we calculate the threshold corrections to F^4 terms in the heterotic CHL
string. Then, using the CHL string/type I duality dictionary, we map these
corrections to perturbative and non-perturbative effects in type I string
compactified on 2-torus without vector structure. Comparing the perturbative
terms provides a quantitative test of the S-duality conjecture. The
non-perturbative contributions are due to D-strings wrapping the torus. A
T-duality along one of the compactified directions allows us to compare these
instanton corrections to the ones obtained in a standard type I
compactifications. The most striking feature is that these non-perturbative
couplings turn out to be identical for both models.
