The structural ordering properties of oxygen in YBa2Cu3O6 + x have been studied by neutron and high-energy synchrotron X-ray diffraction and by computer simulations based on an extension of the Asymmetric Next Nearest Neighbour Interaction (ASYNNNI) model. The observed structural phases are the tetragonal disordered and five orthorhombic ordered phases that result from Cu-O chains formation along the b-axis and ordering with different periodicity na along the a-axis: ortho-I (a), ortho-II (2a), ortho-in (3a), ortho-V (5a) and ortho-VIII (8a). Only the tetragonal and the ortho-I structure have long range order. The structural phase diagram of the superstructure ordering has been established from the experimental data, and it is concluded that the short-range superstructure ordering results from the formation of finite size domains that freeze before long range order is established. By an extension of the 2D ASYNNNI lattice gas model to include Coulomb interactions between oxygen atoms on chains that are 2a apart, we account for the observed structural phases, and confirm that the superstructures freeze into finite size domains at low temperatures. (C) 1999 Elsevier Science B.V. All rights reserved.