  We discuss non-perturbative corrections to the gauge kinetic functions in a
four-dimensional N=2 gauge theory realized with a system of D7/D3-branes in a
compactification of type I' theory on T_4/Z_2 x Z_2. The non-perturbative
contributions arise when D(-1) branes, corresponding to stringy instantons, are
added to the system; such contributions can be explicitly evaluated using
localization techniques and precisely match the results predicted by the
heterotic/type I' duality. This agreement represents a very non-trivial test of
the stringy multi-instanton calculus.
