TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Process: In process (P1), each partial raw material feed stream is mixed with the corresponding partial stream of hydrogen containing gas to form a partial mixed stream (F1+H1, F2+H2) before entering the reactor system, and each partial stream of hydrogen containing gas following in downstream direction is larger than the preceding one by the same factor as the corresponding partial streams of raw material feed with which they are mixed. The hydrogen excess is at least 50%, 75-400% or 100-300%. The weight ratio of added diluting agent to total raw material feed is less than 1, or less than 0.5. The partial feed streams and the corresponding partial streams of hydrogen containing gas are all mixed at the same ratio of standard cubic meter of gas to cubic meter of raw material feed. The amount of the partial streams or the partial mixed streams to the second and, if present, the following catalyst beds is controlled so as to adjust the temperature at the inlet of every catalyst bed to essentially the same temperature as at the reactor inlet at the first catalyst bed. The hydrogenation takes place at hydrogen partial pressures in the range of 1-8 MPa, at 145-280 degrees C. The weight ratio of added diluting agent to raw material feed at the reactor entrance is less than or equal to 4:1 and each partial stream of fresh raw material feed as well as each partial stream of hydrogen containing gas is by a factor of greater than or equal to 1.25 larger than the previous partial stream. The triglyceride containing raw materials are processed together with mineral oil. The part of the hydrogenation product, which is not recycled for addition to the streams of raw material feed F1 and hydrogen containing gas H1 entering at the reactor inlet and passing through the first catalyst bed, is further processed to obtain upgraded kerosine or diesel fuels. Preferred System: The reactor system comprises more than 3, more than 4 and more than 5, less than 20, less than 15 or less than 10 catalyst beds. Preferred Catalyst: The hydrogenation catalyst is selected from at least one sulfide elements of Groups 6, 8, 9 and 10 of the Periodic System (preferably nickel, molybdenum, tungsten and/or cobalt). The space velocity (LHSV) of the raw material feed is 0.1-1 m3/m3 catalyst/h. The linear velocity of the liquid material is in the range of 1-6 mm/s in each bed. EXAMPLE - No suitable example given.