Method for manufacture of poly-fatty acids and maleic anhydride-added fatty acids

A method for the manufacture of a maleic anhydride-added fatty acid, which comprises causing maleic anhydride and at least one ethylenically unsaturated fatty acid selected from the group consisting of oleic acid, linoleic acid, linolenic acid, .alpha.-eleostearic acid, .beta.-eleostearic acid, ricinoleic acid, ricinelaidic acid and fatty acids derived from tall oil, soybean oil, linseed oil, cotton-seed oil, safflower oil, castor oil and tung oil, to flow continuously and come into contact with a synthetic silica-alumina catalyst having a composition of 69 to 72 wt.% of SiO.sub.2, 27 to 30 wt.% of Al.sub.2 O.sub.3, not more than 1 wt.% of Fe.sub.2 O.sub.3, not more than 1 wt.% of CaO and not more than 1 wt.% of MgO, having phosphoric acid supported thereon, and maintained in a temperature range of from 150.degree. C. to 330.degree. C., whereby the addition of maleic anhydride to said fatty acid is effected.