At least a fraction of at least one branched, saturated aliphatic diacid having 6 carbon atoms, for example 2-methylglutaric acid and/or 2-ethylsuccinic acid and/or dimethylsuccinic acid, is separated from admixtures thereof with adipic acid, by at least partially converting such at least one aliphatic diacid into the corresponding anhydride thereof, and removing the corresponding anhydride or the adipic acid from the medium of conversion/anhydridization, for example by contemporaneous or subsequent distillation, or by crystallization.