A LEED and AES study on oxygen adsorption on Cu(100) and (h11) faces with 5 less-than-or-equal-to h less-than-or-equal-to 15 has been performed under various adsorption conditions (220 K less-than-or-equal-to T less-than-or-equal-to 670 K and 1 x 10(-8) less-than-or-equal-to P less-than-or-equal-to 6 x 10(-5) Torr of oxygen). The dependence of adsorption temperature on the oxygen surface superstructures is pointed out. At least, three oxygen surface states exist on a Cu(100) face. For low temperature exposures to oxygen, under conditions of slow surface diffusion, on the (100) face, two oxygen surface phases exist: a "four spots" and a c(2 x 2) superstructure, both observed even at saturation coverage; on all the stepped faces, a c(2 x 2) appears and no faceting is observed. For high temperature exposures, on the (100) face, two oxygen superstructures are observed, a "four spots" followed by a (2 square-root 2 x square-root 2)R45-degrees at higher coverages; on all the stepped faces, surface diffusion is activated and oxygen induced faceting occurs. The appearance of faceting is associated with the onset of the formation of the (2 square-root 2 x square-root 2)R45-degrees structure on the (100) face. The oxygen induced faceting and the oxygen surface meshes are reversible with coverages. At saturation coverage, a non-reversible surface transition between the c(2 x 2) and (2 square-root 2 x square-root 2)R45-degrees superstructures is observed at 420 +/- 20 K. The importance of impurity traces on the surface meshes is emphasized. Oxygen coverage at saturation is independent of the studied faces and adsorption temperature. Faceting occurs at a critical coverage value, whatever the stepped faces and adsorption temperature are. Models of the oxygen structure on the (h10) stepped faces are discussed.