  We present a novel approach to the study of Yang-Mills instantons on
quaternionic K\"ahler manifolds, based on an extension of the harmonic space
method of constructing instantons on hyperk\"ahler manifolds. Our results
establish a bijection between local equivalence classes of instantons on
quaternionic K\"ahler manifolds M and equivalence classes of certain
holomorphic maps on an appropriate SL_2(C)-bundle over the Swann bundle of M.
