Process for preparing allyl alcohol alkoxylates

What is proposed is a process for preparing polyether alcohols by reaction of one or more unsaturated starters having at least one active hydrogen atom per molecule with one or more alkylene oxides in the liquid phase, in the presence of a basic catalyst, in a reactor, which is characterized in that the metered addition of the one or more alkylene oxides into the reactor is effected in such a way that the concentration of unreacted alkylene oxide in the liquid reaction mixture in the reactor is increased as far as possible with increasing degree of addition of the alkylene oxide onto the starter, it being necessary at all times to meet the condition that the temperature at the end of a runaway reaction is at least 100 K below the onset temperature of the decomposition reaction of the liquid reaction mixture.