NOVELTY - Producing fatty acid monovalent 1-5C alkyl esters, comprises: a multi-stage, alkali-catalyzed transesterification of fatty acid glycerides with monovalent 1-5C alkyl alcohols providing a fatty acid ester stream and many alcohol streams; removing alkyl alcohol (more than 80%) from fatty acid ester stream by evaporation providing an alkyl alcohol evaporate and a residue; washing the residue with water to deactivate the alkali catalyst and remove some residual 1-5C alkyl alcohol from the fatty acid ester stream; and subjecting the fatty acid stream to thermal treatment.    USE - The processes are useful for producing fatty acid monovalent 1-5C alkyl esters (claimed), which are used as biodiesel.    ADVANTAGE - The process provides fatty acid monovalent 1-5C alkyl esters, with improved cold-soak test results i.e. fatty acid monovalent 1-5C alkyl esters exhibit the cold soak filtration test time of less than 200 seconds, results from reduced methanol content in the residue in step of removing alkyl alcohol (more than 80%) from fatty acid ester stream and intensive thermal treatment.    DETAILED DESCRIPTION - Production of fatty acid monovalent 1-5C alkyl esters, comprises: a multi-stage, alkali-catalyzed transesterification of fatty acid glycerides with monovalent 1-5C alkyl alcohols providing a fatty acid ester stream and many alcohol streams comprising glycerol; removing more than 80% of the alkyl alcohol from the fatty acid ester stream by evaporation providing an alkyl alcohol evaporate and a residue; washing the residue with water to deactivate the alkali catalyst and remove some residual 1-5C alkyl alcohol from the fatty acid ester stream; and subjecting the fatty acid stream to thermal treatment thus providing fatty acid monovalent 1-5C alkyl esters with a cold soak filtration test time according to ASTM D6217 of less than 200 seconds. INDEPENDENT CLAIMS are also included for: (a) purification of fatty acid monovalent 1-5C alkyl esters containing residual monovalent 1-5C alkyl alcohol, comprising either providing fatty acid monovalent 1-5C alkyl esters with a cold soak filtration test time according to ASTM D 6217 of at least 200 seconds, removing the residual alkyl alcohol from the fatty acid monovalent 1-5C alkyl esters by evaporation providing monovalent alkyl alcohol evaporate and a residue, washing the residue with water, subjecting the washed residue to a thermal treatment by providing fatty acid monovalent 1-5C alkyl esters; or providing the fatty acid monovalent 1-5C alkyl esters with a cold soak filtration test time according to ASTM D 6217 of at least 200 seconds, washing the fatty acid monovalent 1-5C alkyl esters with water, subjecting the washed fatty acid monovalent 1-5C alkyl esters to thermal treatment; or providing the fatty acid monovalent 1-5C alkyl esters with a cold soak filtration test time according to ASTM D 6217 of at least 200 seconds and subjecting the fatty acid monovalent 1-5C alkyl esters to thermal treatment; and (b) the fatty acid monovalent 1-5C alkyl esters obtained by the processes.