Abstract The structure of an oxygen-deficient perovskite BaLa 4Cu 5O 13+δ has been determined by neutron powder diffraction and high-resolution electron microscopy. It has been resolved in the space groupP4m(a ∼ a p√5, c ∼ a p). The framework [Cu 5O 13] is built up from corner-sharing CuO 5 pyramids and CuO 6 octahedra forming hexagonal tunnels and perovskite cages where the La 3+ and Ba 2+ ions are located in an ordered manner. The barium ions are located in the perovskite tunnels whereas the lanthanum ions are located in the hexagonal tunnels. One typical feature of the host lattice [Cu 5O 13] deals with the geometry of the hexagonal tunnels which is rather different from the ideal model derived from the stoichiometric perovskite. O-O-O angles are close to 70° (instead of 90°) and O(5)-O(5) distances are close to 3A˚(instead of 3.8A˚). A great number of crystals exhibit a single oxygen-deficient perovskite which can be considered as having the stoichiometry BaLa 4Cu 5O 13; the excess of oxygen, δ, corresponds to the formation in other crystals of superstructures (∼ a p√10 × a p√10 × a p) and of microdomains which are interpreted as the result of a distortion of the [Cu 5O 13] matrix induced by the introduction of oxygen in half of the hexagonal tunnels.