The kinetics of HD and water formation during admission of H atoms to D- and O-covered Cu(110) surfaces was measured and compared to the kinetics of the analogous reactions on Cu(100), Cu(111), and other metal surfaces. The phenomenology of the HD abstraction kinetics on Cu(100) is according to an Eley-Rideal (ER) mechanism with a cross-section of 2.4 Angstrom(2) and only a small contribution of D-2 products provides evidence for the operation of a hot-atom mechanism. Similar features were observed on the other Cu surfaces. As origin of the ER-phenomenology on Cu surfaces the inefficiency of electron-hole excitation for hot-atom sticking due to the small density of states at the Fermi level of Cu is proposed. Unlike at Cu(100), the H adsorption-induced reconstruction of the surface does not affect the abstraction kinetics. The interaction of gaseous H with oxygen adsorbed on Cu(100) leads to adsorbed and gaseous water products at 100 K. The occurrence of a considerable fraction of gaseous water at reaction temperatures 60 K below the water desorption temperature indicates that the substantial exothermicity of the reaction leads to energetically ejected product upon their formation. In accordance with other water formation reactions between gaseous H and adsorbed oxygen the mechanism is identified as two sequential hydrogenation reactions, O to adsorbed OH and OH to gaseous and adsorbed water, of which the latter is rate-determining with a cross-section of 0.6 Angstrom(2). At reaction temperatures well above the water desorption temperature, isothermal desorption is absent in the water kinetics and only gaseous water was monitored. The coverage of oxygen has no effect on the water kinetics.