NOVELTY - Producing a liquid fuel composition involves: providing oil selected from vegetable oil and/or animal oil; and hydrodeoxygenating and hydroisomerizing the oil, involving feeding oil to a tubular reaction unit containing a acidic catalyst and metal component; feeding effluent from tubular reaction unit to vapor-liquid separator; and feeding a vapor phase separated from effluent from tubular reaction unit to adiabatic reaction unit containing same catalyst as in tubular reaction unit.    USE - For production of liquid fuel (claimed), particularly diesel, jet and naphtha fuel from vegetable and animal oils.    ADVANTAGE - The produced fuel composition has acceptable lubricity (I.e. of less than 400, preferably less than 300, especially less than 200 mu m). The process provides high yield of high quality diesel fuel composition, with properties and minimized production of lighter components e.g. naphtha, carbon oxides and 1-4C hydrocarbons. The use of both tubular and adiabatic reaction units allows for optimization of hydrodeoxygenating and hydroisomerizing and improved performance and stability of the catalyst. The process is carried out at relatively mild conditions, e.g. the tubular reaction unit is operated at a liquid hourly space velocity of 0.5-5 (preferably 0.6-3 especially 1-2.5) per hour, at 300-450 degrees C, at a pressure of 10-60 (preferably 20-40) atm, and a H2/oil ratio of 300-1200 (preferably 500-1000) NL/L. The diesel fuel composition produced by methods comprises mixture of 2-8C or 4-8C paraffins with a ratio of iso to normal paraffins of 0.5-8 (preferably 1-4, especially 4-7), they have a sulfur content of less than 5 (preferably less than 1) ppm.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for a reaction system for producing a liquid fuel composition comprising tubular reaction unit; an adiabatic reaction unit comprising same catalyst as in tubular reaction unit; and a vapor-liquid separator disposed between tubular reaction unit and adiabatic reaction unit.