A process is described for the co-production of maleic anhydride and at least one C4 compound selected from butane-1,4-diol, &ggr;-butyrolactone, and tetrahydrofuran in which maleic anhydride is produced by partial oxidation of a hydrocarbon feedstock selected from C4 hydrocarbons and benzene to yield a vaporous reaction effluent stream comprising maleic anhydride, water, unconverted hydrocarbon feedstock, and carbon oxides. A part of the maleic anhydride present in the vaporous reaction effluent stream is condensed to form a crude maleic anhydride stream and leave a residual vaporous stream containing residual amounts of maleic anhydride. Further maleic anhydride is absorbed from the residual vaporous stream by absorption in an organic solvent, water or an aqueous solution. Maleic anhydride is then recovered from the loaded liquid absorptions medium. Said at least one C4 compound is produced by hydrogenation of a C4+ hydrogenation feedstock selected from maleic anhydride, maleic acid, dialkyl maleates, and mixtures of two or more thereof. The process is characterised in that material of the crude maleic anhydride stream is used as the C4+ hydrogenation feedstock or is used to prepare the C4+ hydrogenation feedstock.