Oxygen-deficient perovskites NdCuO3-delta (0 less than or equal to delta less than or equal to 0.5) were prepared for the first time at high pressures in a multianvil apparatus and characterized by X-ray and electron diffraction and by electron microprobe. Several new oxygen vacancy-order phases could be stabilized depending upon delta and synthetic conditions. The crystal structures of NdCuO3-delta are related to those previously observed in the LaCuO3-delta system, but are more highly distorted due to the smaller Nd cation size, leading to different symmetries, A-site coordination numbers and unit cell dimensions. Electron diffraction shows that NdCuO2.5; crystallizes in an orthorhombic root 2a(p) x 2 root 2a(p) x ap subcell with a 6 root/2a(p) x 4 root(2)ap x 2a(p), supercell, where a(p) is the simple cubic perovskite lattice parameter. NdCuO2.6 crystallizes in a monoclinic root 5a(p), x root 5a, x 2a(p) cell. In addition, two other phases with root 10a(p) x root 10a(p) x 2a(p) and root 5a(p) x 2 root 5a(p) x 2a(p) have been observed for delta = 0.3-0.4, each exhibiting superstructures related to NdCuO2.6. Oxygen vacancy ordering models are proposed to interpret these results. An orthorhombic GdFeO3-type phase with delta = 0-0.07, the first example of this structure-type in the rare earth cuprates, was found at the highest oxygen pressures investigated. The major structure-types, corresponding to delta = 0.07, 0.4, and 0.5, were refined by the Rietveld method. It was not possible to synthesize other LnCuO(3-delta) phases for rare earths smaller than Nd at pressures up to 150 kbar. Superconductivity was not observed in any of the new perovskites down to 4.2 K.