An improvement in the process for extracting alumina from gibbsitic bauxites, wherein the basic, known process comprises mixing the bauxites with a sodium hydroxide-sodium aluminate digestion liquor, digesting the bauxites at a temperature in the range of 100.degree.-180.degree. C., diluting the resulting slurry, separating the red mud therefrom, precipitating alumina hydrate by cooling and agitation of the sodium aluminate liquor, and calcining the alumina hydrate precipitate to obtain alumina, wherein the improvement is characterized by so controlling the process that, in the liquid phase of the slurry leaving the digestion reactor, the reactive hydroxide ion concentration is maintained below 6 g/l, and preferably between 0 and 2 g/l, where the reactive hydroxide ion concentration is defined by the following formula: ##EQU1## where: C.sub.Al.sbsb.2 O.sub.3,gi.sup.eq is the equilibrium solubility of Al.sub.2 O.sub.3 for gibbsite, in g/l.C.sub.Al.sbsb.2 O.sub.3 is the actual concentration of Al.sub.2 O.sub.3, in g/l andC.sub.SiO.sbsb.2 is the actual concentration of SiO.sub.2, in g/l.Desirably, control of the process is maintained by regulating the ratio of bauxite to digestion liquor.