The present invention relates to a process for preparing optionally alkyl-substituted 1,4-butanediol by two-stage catalytic hydrogenation in the gas phase of C4-dicarboxylic acids and/or of derivatives thereof having the following steps: a) introducing a gas stream of a C4-dicarboxylic acid or of a derivative thereof at from 200 to 300° C. and from 2 to 60 bar into a first reactor and catalytically hydrogenating it in the gas phase to a product which contains mainly optionally alkyl-substituted γ-butyrolactone; b) removing succinic anhydride from the product obtained in step a), preferably to a residual level of from