NOVELTY - Production of biodiesel grade, fatty acid alkyl esters involves reacting triglyceride, alcohol and catalyst in first reaction zone to form first intermediate reacted mixture (m1); removing glycerol and unreacted alcohol from mixture (m1) to form second intermediate reacted mixture (m2); feeding mixture (m2) to second reaction zone; adding fresh feed of alcohol and catalyst into the second zone to form fatty acid alkyl esters and glycerol from mixture (m2) to form third intermediate reacted mixture (m3); separating alcohol, glycerol and fraction of esters from mixture (m3); and recycling.    USE - For production of biodiesel grade, fatty acid alkyl esters; and for the production of biodiesel fuel fatty acid alkyl esters (claimed).    ADVANTAGE - The process is efficient, and cost-effective and provides high yield of fatty acid alkyl ester. The overall conversion of triglyceride to fatty acid alkyl ester in the process is greater than 99%.    DETAILED DESCRIPTION - Production of biodiesel grade, fatty acid alkyl esters involves: reacting triglyceride, alcohol and catalyst in a first reaction zone to form a first intermediate reacted mixture (m1) which includes trans-esterified fatty acid ester product, glycerol, unreacted alcohol, and unreacted and partially reacted triglyceride; removing glycerol and unreacted alcohol from the first mixture (m1) to form a second intermediate reacted mixture (m2); feeding the second mixture (m2) to a second reaction zone; adding a fresh feed of alcohol and catalyst into the second reaction zone to form fatty acid alkyl esters and glycerol from the second mixture (m2) to form a third intermediate reacted mixture (m3); separating alcohol, glycerol and a fraction of the fatty acid alkyl esters from the third mixture (m3); and recycling alcohol, glycerol and fatty acid alkyl esters recovered from the third mixture (m3) to the first reaction zone. An INDEPENDENT CLAIM is included for an apparatus for continuously producing biodiesel grade fatty acid alkyl esters comprising: a first tubular reactor adapted for receiving and reacting a mixture of an alkanol, triglyceride and catalyst at elevated temperature and pressure to form a first product stream containing fatty acid alkyl ester, glycerol, alkanol, triglycerides and optionally monoglycerides and diglycerides; a first separator configured to receive the first product stream and separate glycerol and alkanol from the first product stream and to provide a second product stream comprising fatty acid alkyl esters, triglycerides and optionally monoglycerides and diglycerides; a second tubular reactor coupled to the first separator configured to receive the second product stream and adapted for reacting the second product stream with additional alkanol at elevated temperature and pressure to generate additional fatty acid alkyl esters in a third product stream; a second separator adapted to generate a fourth product stream comprising alkanol and fatty acid alkanol esters from the third product stream, the second separator also being configured to provide a recycle stream from the third product stream including alkanol, glycerin and fatty acid alkyl ester (not less than 20 vol.%); and a recycle line adapted to provide the recycle stream to the first tubular reactor.