  The series of perturbative fluctuations around a multi-instanton contribution
to a specific class of correlation functions of supercurrents in $\cal N=4$
supersymmetric SU(N) Yang-Mills theory is examined in the light of the AdS/CFT
correspondence. Subject to certain plausible assumptions, we argue that a given
term in the 1/N expansion in such a background receives only a finite number of
perturbative corrections in the 't Hooft limit. Such instanton
non-renormalisation theorems would explain, for example, the exact agreement of
certain weak coupling Yang-Mills instanton calculations with the strong
coupling predictions arising from D-instanton effects in string theory
amplitudes. These non-renormalisation theorems essentially follow from the
assumption of a well defined derivative $(\alpha^{\prime})$ expansion in the
string theory dual of the Yang-Mills theory.
