TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The heterogeneous catalysts used in stage 1 and stage 2 comprise a combination of at least one oxide of at least one metal M1 selected from group IIA, group IIB, group IIIA, group IIIB, group IVB, group IIIA, group IVA or group VA with alumina; or a combination of at least two oxides of at least one metal M1 and of at least one metal M2 selected from group IIA, group IIB, group IIIA, group IIIB, group IVB, group IIIA, group IVA or group VA possibly in the presence of alumina. The heterogeneous catalyst comprises a combination of oxides having the formula: (M1Ox)y(Al2O3)(1-y) (1), or (M1aM2bOc)y((Al2O3))(1-y) (2).x=1.2-2.6;y=0.005-2 (for formula 1), or 0.005-1 (for formula 2);a, b=0.5-5;c=number of oxygen atoms that satisfies the valence of metals M1 and M2.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: Each one of stages 1 and 2 is carried out at 165-240degreesC, with a contact time of 15 minutes to 3 hours and an alcohol/feedstock mass ratio of 20/80-80/20. The transesterification reaction is preceded by an esterification reaction of the free fatty acids present by means of the same alcohol as the alcohol used in the transesterification method in the presence of a strong acid selected from among sulfuric acid and soluble or supported sulfonic acids; or the transesterification reaction is preceded by an esterification reaction of the free fatty acids present by means of glycerin to form a total or partial glycerol ester, using a heterogeneous catalyst, at atmospheric pressure or under partial vacuum, and at 165-240degreesC. Preferred Components: The initial oil is palm oil (concrete or olein), soybean oil, palm nut oil, copra oil, babassu oil, colza oil (old or new), sunflower oil (conventional or oleic), corn oil, cotton oil, tallow and lard, peanut oil, pourgher oil, castor oil, lineseed oil and crambe oil, or all oils obtained from sunflower or colza by genetic engineering or hybridization. The initial oil is waste kitchen oil, slaughterhouse oil, fish oil, seal oil, or fowl fat. The initial oil is selected from among oils partly modified by polymerization or oligomerization. The initial oil has an acid number close to or above 10. EXAMPLE - Colza oil (100 g) and methanol (100 g) were fed into a fixed-bed reactor containing catalyst (110 ml) consisting of zinc aluminate (ZnAl2O4) in form of approximately 2 mm-diameter extrudates. The next stage consisted of removing all of the excess methanol, in decanting the glycerin formed. In a second reaction stage, the ester phase was fed with ethanol into a second reactor similar to the first one in order to be subjected to a conversion to fatty acid ethyl esters. The residual alcohol contained in the ester mixture thus obtained was again removed by evaporation. A second glycerin fraction representing 10-12% of the total glycerin formed during the transesterification reaction was then removed by decantation. The biodiesel fuel obtained consisted of 97.5% of a mixture of fatty acid ethyl esters and of fatty acid methyl esters with an ethyl ester/methyl ester mass proportion of 72/28. The reaction times in each one of the two stages was 55 minutes, instead of 110 minutes when the two stages are carried out each in the presence of ethanol.