The present invention relates to a process for producing polyether polyols having primary hydroxyl end groups, comprising the steps of reacting a starter compound containing active hydrogen atoms with an epoxide under double metal cyanide catalysis, reacting the resulting product with a cyclic carboxylic anhydride and reacting this resulting product with ethylene oxide in the presence of a catalyst containing at least one nitrogen atom per molecule, excluding non-cyclic, identically substituted tertiary amines. The invention further relates to polyether polyols obtainable by this process, compositions containing said polyols and polyurethane polymers based on said polyols.