A process for preparing ethylene amines and ethanolamines by hydrogenative amination of monoethylene glycol and ammonia in the presence of a catalyst, wherein the process is carried out in two process stages in which in the first process stage, the amination is carried out over a hydroamination catalyst to a monoethylene glycol conversion of not more than 40% and in the second process stage, a supported catalyst having an active composition comprising ruthenium and cobalt and no further additional metal of group VIII and also no metal of group IB is used in the form of shaped catalyst bodies which in the case of a spherical shape or rod shape in each case have a diameter of <3 mm, in the case of a pellet shape have a height of <3 mm and in the case of all other geometries in each case have an equivalent diameter L=1/a' of <0.70 mm, is proposed.