A process is described for purifying polyalkylene glycols obtained by adding alkylene oxide to alkylene glycol, in which, after addition is complete, the resultant polyalkylene glycol is treated at a pH of >7 with a bleaching agent selected from the group consisting of peroxides, peracids, percarbonates, perborates, peroxodisulfates or oxygen, in each case with or without addition of a bleaching activator.The process is suitable in particular for preparing polyethylene glycol having molar weights from 196 to 203 g/mol which meets requirements of pharmacopeias.