TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The catalyst is a solid, acidic catalyst, preferably metal oxide or a mixture of metal oxides of the subgroups of the periodic table, such as aluminosilicate of zeolite type with acid and water-adsorbing properties.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The free fatty acid to be esterified is present in a mixture containing at least 20 wt.% of free fatty acid and mainly fatty acid glyceride. Preferred Process: The esterification process comprises several steps, where each step is performed in a phase separation device in the presence of a catalyst, a light water-/alcohol phase, resulting from the end or the first step, is gravimetrically separated from the resulting heavy fatty acid-/fatty acid-alkylester phase, and is replaced by adding alcohol to the reaction mixture for carrying out the following process steps, and the addition of adsorbent is carried out at the first or last in the process steps. The esterification is carried out at an atmospheric pressure and at a temperature ranging between the melting point of the free fatty acid and atmospheric boiling point of alcohol. The esterification is carried out in a stirred vessel, where the catalyst and adsorbent are distributed as fine-grained solids in the reaction mixture. The catalyst and the adsorbent are mixed and the mixture is added into a column by passing through the reaction mixture. The reaction mixture passes through several, preferably at least two columns filled with solid catalyst, where after each pass, the light alcohol-water phase is gravimetrically separated from the heavy fatty acid/fatty acid methyl ester phase, before the heavy phase passes through the next column, and then the heavy phase passes through a solid adsorbent-filled column. EXAMPLE - Oleic acid (282 g) was stirred with methanol (3 mole) in a stirring vessel with a solid esterification catalyst (styrene-divinylbenzene copolymer with sulfonic acid groups) (10 g) at 55 degrees C and atmospheric pressure for 30 minutes. A heavy phase was formed from oleic acid and the resulting oleic acid methyl ester, and a light phase was formed from methanol and water. The light phase was withdrawn and replaced by fresh methanol (100 g). Chinoptilolite powder (30 g) was added for the adsorption of the reaction water and stirred for 60 minutes to give oleic acid methyl ester end product.