Dehydrogenation of five species including CH3OH, CH3O, H2COO, NH3, and H2O over clean and oxygen-modified copper surfaces has been investigated by the first-principle density functional calculations within the generalized gradient approximation. The reaction enthalpies and the activation energies have been calculated for 10 elementary steps corresponding to the direct and oxygen-assisted cleavage of X-H bonds (X = O, N, C). The DFT-GGA results showed that the pre-adsorbed oxygen always facilitates the dehydrogenation reaction by decreasing the reaction enthalpies and the activation energies. The obtained results are in general agreement with experimental observations.