A process for the preparation of 1,4-butanediol by catalytically hydrogenating maleic anhydride in the presence of an alcohol, at elevated temperature and elevated pressure and with the aid of a cobalt-containing catalyst comprises partially hydro- genating the reaction mixture in a first hydrogenation step at from 100 to 200.degree.C and at from 30 to 200 bar and subsequently post-hydrogenating the product of this first hydrogenation step, without further work-up at higher temperature and pressure than in the first hydrogenation step, in a second hydrogenation step at from 200 to 300.degree.C and at from 200 to 350 bar.