The invention relates to a process for producing granular, particularly spherical activated carbon by carbonization of suitable carbonaceous polymers in the form of polymer granules, in particular polymer spherules, as a starting material, which are convertible by carbonization into carbon at least essentially, wherein the polymer granules, in particular the polymer spherules, are continuously moved through a carbonization apparatus comprising a plurality of temperature zones and/or a temperature gradient so that an at least essentially complete conversion of the starting material to carbon is effected.