TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The step of obtaining the low-boiling components removed liquid by removing the low-boiling components or fraction from the effluent liquid of a last reactor is carried out in the absence of the catalyst. Separation of the fatty acid alkyl esters and glycerine from the low-boiling components removed liquid involves phase separation of the low-boiling components removed liquid into an ester phase and a glycerine phase. The method further involves reaction of an ester phase separated from an effluent of a reactor with an alcohol in the next reactor in the presence of the insoluble solid catalyst; and distillation purifying at least one of the ester phase and the glycerine phase obtained in the step of phase separation of the low-boiling components removed liquid. At least one of the purification residues is used as one of the raw materials for the reaction. The glycerine phase obtained during phase separation of the low-boiling components removed liquid contains not less than 70 pbw of glycerine per 100 pbw of the glycerine phase. The alcohol is recovered from the low-boiling components or fraction distilled off and at least part of the recovered alcohol is used as a raw material. A fixed bed reaction apparatus packed with the insoluble solid catalyst is used for a production and the fatty acid alkyl esters and/or glycerine is produced continuously.    TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The insoluble solid catalyst is a catalyst capable of catalyzing the esterification of free fatty acids contained in the fat or oil. The insoluble solid catalyst contains at least one metal element selected from Group 4 and 5 in the periodic table (preferably a layered compound of formula ATixMO(2X+3)); or an oxide whose crystal structure comprises an octahedral skeleton formed by coordination of the essential metal component with oxygen atoms in a six-coordinate complex-forming manner.A = H or an alkali metal atom;M = niobium or tantalum atom;X = natural number not more than 7. EXAMPLE - The straight tubular reactor was packed with the molded catalyst e.g. HTiNbO5 (540 g). For enabling pressure control, the reactor outlet was equipped with a filter and a backpressure regulator via an air-cooled condenser. Using high-pressure constant delivery precision pumps, the palm oil (205 g/h) and methanol (68. 8 g/h) were mixed together in a line and continuously passed through the reactor downward from the top. The pressure within the tubular reactor was set at 3.5 MPa. The supply of methanol relative to the palm oil was 3.0 times the theoretical amount to be fed. The tube inside temperature was set at 200 degrees C by externally heating the tubular reactor portion. At 3 hours after stabilization of the temperature and pressure, the total flow rate of fatty acid methyl esters at the outlet of the reactor was 194 g/h, the total flow rate of free fatty acids was 1.31 g/h, that of monoglycerides was 10.4 g/h, and that of diglycerides was 0.646 g/h. Thus, the whole amount of triglycerides had been consumed. The flow rate of free glycerine at the outlet of the reactor was 19.9 g/h that of methanol was 46.9 g/h, and that of byproduct water was 0.750 g/h. The yield of fatty acid methyl esters and free glycerine were 91 mol% and 91 mol%, respectively.