The addition of hydrogen atoms to ethylene and benzene on a Cu(111) surface has been studied by temperature‐programmed desorption and integrated desorption mass spectrometry. The results show that adsorbed ethylene and benzene react with atomic hydrogen from the gas phase at temperatures as low as 110 K. The reaction intermediates, ethyl groups and partially hydrogenated benzene, can be isolated on the surface at this low temperature. When the surface is heated to above 150 K, hydrogen elimination reactions occur to produce ethylene, benzene, cyclohexadiene, and cyclohexene. Complete hydrogenation to alkanes also occurs for larger H‐atom exposures. The absence of these addition reactions when H atoms are adsorbed onto the surface before ethylene or benzene suggests Eley–Rideal mechanisms for these processes.