For many disordered materials, knowing their average crystal structure is insufficient for explaining and predicting their macroscopic properties. It has been found that a description of the short-range atomic arrangements is needed to understand such materials. In order to understand the conduction pathways in ionic conductors which have random distributions of vacancies it is imperative to know the local structures which are present. In this study the local structures of three oxygen-deficient double perovskites, Sr(2)MSbO(5.5) (M = Ca, Sr, Ba), have been investigated by neutron pair distribution function analysis. The ions in these compounds are all found to have local coordination environments which are radically different than those given by their average structures. While there is no long-range ordering of the oxygen vacancies in these compounds, a considerable amount of short-range order does exist. The conditions which drive the short-range ordering are discussed as are the possible mechanisms for achieving it. It is proposed that the SbO(5) polyhedra form distorted trigonal bipyramids by moving oxygen atoms into interstitial positions. In the M = Sr compound 45° rotations of SbO(6) octahedra are also present, which add additional oxygen atoms into the interstitial sites. Large displacements of the Ca(2+), Sr(2+), and Ba(2+) cations are also present, the directions of which are correlated with the occupancies of the interstitial oxygen sites. Reverse Monte Carlo modeling of the pair distribution function data has provided the actual bond length distributions for the cations.