TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Conditions: The fatty acid is formed by reacting fats and oils with water in a subcritical or supercritical state at 200-400degreesC and 2-45 MPa pressure. The fatty acid ester is formed by adding alcohol to the dehydration residue and reacting in a subcritical or supercritical state at 50-350degreesC and 0.2-45 MPa pressure. Alternately, the reaction between fats and oils with water, and the reaction between alcohol and dehydration residue is carried out under same temperature and pressure conditions.Preferred Composition: The fatty acid ester composition contains water (3-1000 mol) and alcohol (3-200 mol) w.r.t a fatty acid glyceride (1 mol) contained in fats and oils. The fats and oils are animal fats and oils, vegetable fats and oils or waste fats and oils, containing fatty acid. The alcohol is monovalent alcohol.Preferred Process: The fatty acid ester composition is subjected to purification for removing the alcohol and/or water contents. The time for performing steps (A, B) is 1 minute-10 hours.Preferred Apparatus: The apparatus for manufacturing a fatty acid ester composition has a dehydration apparatus for removing water content from the reaction material produced in the primary processing device. At least one of the primary and secondary processing devices are equipped with a thermostat and/or a pressure adjusting device. A refiner is provided for refining the obtained fatty acid ester composition. Pre-heating and pre-pressurizing devices are provided for heating and pressurizing the fats and oils, water and alcohol supplied to steps (A, B). EXAMPLE - A reaction material containing water and triglyceride in a molar ratio of 217:1 was fed into a primary processing device along with rapeseed oil (1 kg). A hydrolysis reaction was carried out for 30 minutes at 270degreesC and 17 MPa pressure (step A). The reaction mixture obtained in step A was cooled to 150degreesC and transferred to a decanter that separates a light liquid containing fatty acid and a heavy liquid containing water, under a pressure of 17 MPa. The light liquid containing fatty acid was transferred to a secondary processing device. Methanol (4.7 kg) that was previously pre-heated and pressurized was added to the light liquid supplied to the secondary processing device, and esterification was carried out for 30 minutes at 270degreesC and 17 MPa pressure. Subsequently, the obtained fatty acid ester composition was purified in a refiner. The yield of fatty acid ester composition was 93%. The total glycerin content in the composition was 0.18%, which satisfied the biodiesel fuel standards.