Process for the continuous hydrogenation of triglyceride containing raw materials like vegetable oils to produce diesel and/or kerosene fraction in a fixed bed reactor system having several catalyst beds comprising hydrogenation catalyst, which beds are arranged in series, wherein the raw material feed, hydrogen containing gas and diluting agent are passed together through the catalyst beds of the reactor system at hydrogenation conditions, wherein a) the raw material feed stream is divided into a number of different partial stream F1 to Fn identical to the number of catalyst beds n in the reactor system at a temperature of less than 80°C, the stream of hydrogen containing gas is also divided into the same number of different partial stream H1 to Hn at a temperature of less than 110°C, then partial raw material feed stream F1 and partial stream of hydrogen containing gas H1 are passed to the first catalyst bed, and before the first partial mixed stream F1+H1 enters the first catalyst bed, it is mixed with added diluting agent which is a specific fraction of the hydrogenation product obtained by the present process leaving the last bed, partial raw material feed stream F2 and partial stream of hydrogen containing gas H2 are passed to the second catalyst bed and so on, if n is greater than 2, each partial stream of raw material feed following in downstream direction being that much larger than the preceding one, that the weight ratio of diluting agent to raw material feed is essentially the same at the entrance of all catalyst beds and does not exceed 4:1, said diluting agent comprising the hydrogenation product formed in every catalyst bed as well as the specific fraction recycled to the reactor inlet at the first catalyst bed and is referred to as added diluting agent, b) the temperature at the reactor inlet at the first catalyst bed after start up phase is adjusted by adding diluting agent called added diluting agent, which is recovered from the reactor exit product mixture by separation in one or two steps without controlled pressure reduction, c) added diluting agent is only added 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, and d) hydrogen is used in excess of the theoretical hydrogen consumption, wherein the hydrogenation takes place at hydrogen partial pressures in the range of 1 to 8 MPa, at temperatures of 145 to 280°C, and with the LHSV of the raw material feed in each bed from 0.1 to 5 m 3 /m 3 catalyst/h characterized in that a hydrogenation bulk or supported catalyst comprising an active phase constituted by at least one element from group VIB and at least one element from group VIII, said elements being in the sulfide form, and the atomic ratio of the metal or metals from group VIII to the metal or metals from group VIB being strictly more than 0 and less than 0.095, is used in at least the first catalyst bed of the fixed bed reactor system. a) the raw material feed stream is divided into a number of different partial stream F1 to Fn identical to the number of catalyst beds n in the reactor system at a temperature of less than 80°C, the stream of hydrogen containing gas is also divided into the same number of different partial stream H1 to Hn at a temperature of less than 110°C, then partial raw material feed stream F1 and partial stream of hydrogen containing gas H1 are passed to the first catalyst bed, and before the first partial mixed stream F1+H1 enters the first catalyst bed, it is mixed with added diluting agent which is a specific fraction of the hydrogenation product obtained by the present process leaving the last bed, partial raw material feed stream F2 and partial stream of hydrogen containing gas H2 are passed to the second catalyst bed and so on, if n is greater than 2, each partial stream of raw material feed following in downstream direction being that much larger than the preceding one, that the weight ratio of diluting agent to raw material feed is essentially the same at the entrance of all catalyst beds and does not exceed 4:1, said diluting agent comprising the hydrogenation product formed in every catalyst bed as well as the specific fraction recycled to the reactor inlet at the first catalyst bed and is referred to as added diluting agent, b) the temperature at the reactor inlet at the first catalyst bed after start up phase is adjusted by adding diluting agent called added diluting agent, which is recovered from the reactor exit product mixture by separation in one or two steps without controlled pressure reduction, c) added diluting agent is only added 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, and d) hydrogen is used in excess of the theoretical hydrogen consumption,