The invention relates to a process for the catalytic hydrogenation of liquid saturated and unsaturated C.sub.6-24 fatty acid methyl esters for the production of saturated fatty alcohols and methanol in the presence of gaseous hydrogen and hydrogenation catalysts under pressures of 50 to 300 bar and at temperatures in the range from 160.degree. to 250.degree. C., characterized in that the hydrogenation reaction is carried out in a tube bundle reactor in which isothermal conditions are established by a cooling or heating fluid, the liquid phase and gas phase being passed together as a co-current trickle phase over catalyst packings in the individual tubes of the reactor without any back-mixing, and in that the load per unit volume of the reaction is between 0.2 and 2.5 liters starting material per liter reactor volume per hour and the load per unit area of each individual tube of the reactor is between 1.5 and 24 m.sup.3 starting material per m.sub.2 reactor cross-section per hour and the reaction parameters of temperature and pressure and correspondingly adapted to the particular activity of the catalyst.