The gas-phase hydrogenolysis of dimethyl maleate has been studied over copper/zinc oxide catalysts at temperatures between 473 and 513 K in the pressure range from 2 to 35 bar. A Cu/ZnO catalyst with a low copper content of 15 mol % was found to be the most active for the conversion of dimethyl maleate. At very low residence times, significant amounts of dimethyl maleate isomerize to dimethyl fumarate. The reaction then proceeds via the saturated ester, dimethyl succinate, until 1,4-butanediol and gamma-butyrolactone are formed together with methanol. Furthermore, the chosen catalyst produces low amounts of tetrahydrofuran and water and only traces of undesirable butanol and CO2. It was found that the production of high amounts of 1,4-butanediol in one step is not possible, because the simultaneous presence of diesters and butanediol gives rise to the formation of a polymeric material via transesterification. Therefore, a two-step process including the complete conversion of dimethyl maleate to gamma-butyrolactone, carried out at high temperature and moderate pressure, without formation of butanediol followed by the hydrogenation of gamma-butyrolactone to 1,4-butanediol at low temperature and high pressure was proposed. It could be shown by systematic investigation of the hydrogenation of gamma-butyrolactone that the amount of 1,4-butanediol formed is limited by thermodynamic constraints. The dependence of the equilibrium constant for the reaction between gamma-butyrolactone and 1,4-butanediol was determined as a function of temperature and pressure.