Electron-diffraction techniques have been used to study the ordering of oxygen atoms within the Cu(1)O1-δ plane of YBa2Cu3O7-δ. The results show that ordering along a single axis and ordering along two orthogonal axes both occur and alternate systematically across the composition range 0.06 < δ < 0.75. Where the ordering is restricted to a single axis, it is found to be the crystallographic a axis. Various models of oxygen ordering are proposed to explain the observed diffraction phenomena. In addition to the ordering of oxygen atoms that give the diffuse diffraction spots at (h∗/2,0,0) and (0, k∗/2,0), a second type of ordering reflection that occurs at (h∗/3,0,0) and (0,k∗/3,0) was also observed. These sharper and more strongly streaked diffraction maxima are explained in terms of a defect in the cation sublattice.