In 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 a hydrogenation catalyst under a pressure of from about 50 to about 300 bar and at a temperature in the range of from about 160 to about 250.degree. C., the improvement wherein the process (a) is carried out under substantially isothermal conditions in a multiplicity of discrete tubular reaction zones (b) the reaction mixture comprises both a liquid phase and a gas phase, and the liquid phase and the gas phase are passed together in co-current flow over a stationary catalyst in each reaction zone without back-mixing, (c) between about 0.2 and about 2.5 liters of ester per liter of tubular reaction zone per hour is employed, (d) between about 1.5 and about 24 m.sup.3 of ester is used per m.sup.2 cross section of tubular reaction zone per hour, (e) the temperature and pressure in the tubular reaction zones are determined based on the activity of the catalyst employed in the reaction, and (f) the gas phase exiting the tubular reaction zones is received in the process.