NOVELTY - A multistage fuel-synthesizing apparatus has a chromatography reactor (1) filled with a solid acid catalyst which absorbs water (W) produced during esterification of fatty acid, a raw-material-oil supply unit (12) to supply raw material oil to chromatography reactor, an eluting solvent-supply unit (11) to supply alcoholic eluting solution to chromatography reactor, a control unit (3), a catalyst apparatus (2) and a fats-and-oils supply unit.    USE - Multistage apparatus is used for synthesizing biodiesel fuel (claimed).    ADVANTAGE - The multistage apparatus enables stable and continuous synthesizes of biodiesel fuel.    DETAILED DESCRIPTION - A multistage fuel-synthesizing apparatus has a chromatography reactor filled with a solid acid catalyst which absorbs water produced during esterification of fatty acid, a raw-material-oil supply unit to supply raw material oil to chromatography reactor, an eluting solvent-supply unit to supply alcoholic eluting solution to chromatography reactor, a control unit which controls value of reaction characteristic factor of material balance of fatty acid in chromatography reactor, eluting solvent (E), fatty acid ester as biodiesel fuel (b1), water and fats and oils, and separates water, a catalyst apparatus filled with metal oxide catalyst (C2) which synthesizes fatty acid ester as biodiesel fuel (b2) by transesterification with fats and oils and alcohol, an alcohol supply unit to supply alcohol solution to catalyst apparatus, and fats-and-oils supply unit to supply fatty acid ester and fats and oils to catalyst apparatus. The biodiesel fuel is synthesized from raw material oil containing fatty acid and fats and oils. An INDEPENDENT CLAIM is included for synthesizes of biodiesel fuel.    DESCRIPTION OF DRAWING(S) - The drawings show the schematic view of the multistage fuel-synthesizing apparatus. (Drawing includes non-English language text)    Chromatography reactor (1)    Catalyst apparatus (2)    Control unit (3)    Eluting solvent-supply unit (11)    Raw-material-oil supply unit (12)    Hydrogen-type ion-exchange resin (C1)    Metal oxide catalyst (C2)    Eluting solvent (E)    Water (W)