A process for preparing 1,4-butanediol and, if desired, &ggr;-butyrolactone and THF by oxidizing butane or benzene to form a product stream including maleic anhydride, absorbing maleic anhydride from the product stream with a high-boiling inert solvent in an absorption stage to give a liquid absorption product, esterifying the liquid absorption product with a C1-C5 esterifying alcohol in an esterification stage to form an esterification product comprising the corresponding diester and high-boiling inert solvent, then hydrogenating the esterification product to give a hydrogenation product which comprises the products of value, 1,4-butanediol and, if desired, &ggr;-butyrolactone and tetrahydrofuran and the esterifying alcohol and which is separated by distillation into the products of value and the esterifying alcohol, and recycling the esterifying alcohol to the esterification zone, which comprises separating the esterification product into the diester and the inert solvent by distillation under reduced pressure prior to the hydrogenation, recycling the inert solvent to the absorption stage, and hydrogenating the diester in the liquid phase over a fixed-bed catalyst.