Process for the continuous hydrogenation of triglyceride containing raw materials in a fixed bed reactor system having several catalyst beds arranged in series and comprising at least one hydrogenation catalyst comprising an active phase constituted by a nickel and molybdenum element. The raw material feed, hydrogen containing gas and diluting agent are passed together through the catalyst beds at hydrogenation conditions. The raw material feed stream as well as the stream of hydrogen containing gas are divided into an equal number of different partial streams. These are each passed to one catalyst bed in such a manner 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. The claimed process is preferably conducted at low temperatures and allows the utilization of existing units due to the low recycle ratio.