A process for coproducing alkyl-substituted or unsubstituted THF and pyrrolidones by catalytically hydrogenating C4-dicarboxylic acids and/or derivatives thereof in the gas phase in the presence of copper catalysts and reacting GBL with ammonia or primary amines to give pyrrolidones comprises a) hydrogenating C4-dicarboxylic acids and/or derivatives thereof in the gas phase at from 200 to 300° C., from 0.1 to 100 bar, catalyst hourly space velocities of from 0.01 to 1 kg of reactant/l of catalyst*hour and reactant/hydrogen molar ratios of from 20 to 800 in the presence of catalysts comprising copper, aluminum and/or zinc to give mixtures of THF and GBL, b) separating the hydrogenation effluent obtained by distillation into a THF/water mixture as the top product and a GBL-containing bottom product, c) separating the THF/water mixture from step b) in a distillation facility consisting of three columns by withdrawing water from the bottom of the first column, recycling water-containing THF from the second into the first column, passing a side stream of the first into the second column, recycling the bottom product of the third column into the first column and withdrawing a distillate at the top of the first column, wherein a side stream of the second column is passed into the third column and the pure THF is obtained as the top product of the third column, d) recovering GBL from the GBL-containing bottom product from step b) by distillation and e) reacting the GBL obtained with ammonia or amines to give corresponding pyrrolidones.