<p>Process for the preparation of 1,4-butanediol by catalytic hydrogenation of maleic anhydride in the presence of alcohols at elevated temperature and at elevated pressure and with the aid of a cobalt-containing catalyst by partial hydrogenation of the reaction mixture in a first hydrogenation step at temperatures of 100 to 200 DEG C and a pressure of 30 to 200 bar and subsequent full hydrogenation of the hydrogenation product obtained from this first step without further workup at higher temperatures and at a higher pressure than in the first hydrogenation step in a second hydrogenation step at temperatures of 200 to 300 DEG C and a pressure of 200 to 350 bar.</p>