A continuous process for the oxidative cleavage of vegetable oils containing triglycerides of unsaturated carboxylic acids, to obtain saturated carboxylic acids, comprising feeding to a first continuous reactor a vegetable oil, an oxidizing compound and catalyst capable of catalyzing the oxidation reaction of the olefinic double bond to obtain an intermediate compound containing vicinal diols: feeding to a second continuous reactor said intermediate compound, a compound containing oxygen and a catalyst capable of catalyzing the oxidation reaction of the vicinal diols to carboxylic groups, to obtain saturated monocarboxylic acids (i) and triglycerides containing saturated carboxylic acids with more than one acid function (ii); separating the saturated monocarboxylic acids (i) from the triglycerides (ii); hydrolyzing in a third reactor the triglycerides (ii) to obtain glycerol and saturated carboxylic acids with more than one acid function; and purifying said saturated carboxylic acids by fractioned crystallization by means of wash column (melt crystallization).