The exact solution of N = 2 supersymmetric QCD found by Seiberg and Wi
tten includes a prediction for all multiinstanton contributions to the
low-energy dynamics. In the case where the matter hypermultiplets are
massless, the leading non-perturbative contribution at weak coupling
comes from the two-instanton sector. We calculate this contribution fr
om first principles using the exact two-instanton solution of the self
-dual Yang-Mills equation found by Atiyah, Drinfeld, Hitchin and Manin
. We find exact agreement with the predictions of Seiberg and Witten f
or all numbers of flavours, We also confirm their predictions for the
case of massive hypermultiplets.