The apparatus for the esterification of a fatty acid F includes a column with a packing. In addition to functioning as a catalytic reactor, the packing functions as a stripping section. A heteregenous catalysis of a fatty acid is carried out with an alcohol used in the same molar ratio or in excess. A gaseous alcohol-rich counter-flow is produced in a sump of the column by vaporization. Water is removed from the reaction zone by means of the counter-flow acting as a stripping gas. The loaded stripping gas is at least partially liquefied at the head of the column. The head product is separated into a water-rich fraction as well as an alcohol-rich fraction. The alcohol-rich fraction is returned to the process as a starting material for the esterification and for the production of the stripping gas.