Using resonant and off-resonant X-ray emission spectroscopy, in combination with ground-state density functional calculations, we examine the electronic structure of chemisorbed ethylene and benzene on the Cu(110) surface to investigate the suitability of the donation/back-donation bonding model given by Dewar and Chatt and Duncanson (DCD) for the interaction of unsaturated hydrocarbons with metal surfaces. We give an experimental verification of the DCD model and find donation/back-donation to be twice as large for ethylene as for benzene. In particular, the degree of