The present invention relates to a continuous process for hydrogenating organic compounds in a polyphasic system in the presence of a homogeneous or heterogeneous catalyst, which comprises performing the process in two stages, the first stage being performed in a loop reactor with an external heat exchanger and the second stage in a bubble column reactor with limited backmixing.The present invention further relates to a hydrogenation reactor (1) in a tall cylindrical design comprising a concentric guide tube (2) arranged in the lower reaction region and a mixing nozzle (3) directed upward, through which reactants and reaction mixture can be supplied, a pump (4) and a heat exchanger (5), which are present in an external pump circulation system which leads from the reactor to the mixing pump, and with one or more gas- and liquid-permeable internals (10) mounted in the upper region of the reactor, where the ratio of total length to diameter of the hydrogenation reactor (1) is in the range from 5:1 to 100:1 and the ratio of the volume of the upper region of the reactor to the volume of the lower region of the reactor is from 0.05:1 to 10:1.