TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The catalyst is an alkali selected from sodium hydroxide, potassium methoxide, sodium methoxide and/or sodium methylate.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Apparatus: The first and second tubular reactors are adapted to operate at a temperature of 70-200degreesC. The first and second tubular reactors are adapted to operate at a pressure of 150-400 psi. The first and second separators are hydroclones. The first and second tubular reactors have a diameter of one quarter-4 inches.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: The reaction of triglyceride and alcohol is carried out in the presence of a catalyst. The first and second reaction zones are tubular plug flow reactors operated at a pressure of 50-300 psi. The alcohol and triglyceride are introduced into the first reaction zone in a mole ratio of alcohol to triglyceride of 4:1 to 8:1. The triglyceride feed stream is introduced into the first reaction zone at a temperature of 70-200degreesC. The triglyceride and the alcohol are introduced into the first reaction zone at a pressure of 150-400 psi. The residence time in the tubular plug flow reactors is less than 3 minutes. The residence time in the first reaction zone is 20-30 seconds. The residence time in the second reaction zone is 30-60 seconds. The amount of catalyst used is 0.2-2 (preferably 0.25-1.25) wt.% of triglyceride. The glycerol and unreacted alcohol is removed from the first intermediate reacted mixture with a hydroclone. The alcohol, glycerol and fatty acid ester are separated from the third intermediate reacted mixture with a hydroclone. The process for the production of biodiesel fuel fatty acid alkyl esters involves: feeding a fatty acid triglyceride, an alkanol and catalyst to a first tubular reaction zone; transesterifying the fatty acid triglyceride in the first tubular reaction zone to produce a first intermediate stream comprising fatty acid alkyl ester and glycerol; removing glycerol from the first intermediate stream to produce a second intermediate stream; feeding the second intermediate stream along with additional catalyst and additional alkanol to a second tubular reaction zone; transesterifying fatty acid triglyceride to produce fatty acid alkyl ester in the second tubular reaction zone to produce a third intermediate stream; separating the third intermediate stream into a crude product stream and an alkyl ester containing recycle stream; and recycling the recycle stream to the first reaction zone, where the overall conversion of triglyceride to fatty acid alkyl ester in the process is greater than 95%. The conversion of triglyceride at the end of the first reaction zone is 60-80%. The recycle stream contains alkyl ester (at least 20, preferably at least 35) vol.%. Preferred Components: The alcohol is methanol. EXAMPLE - No suitable example is given.