A process for preparing polyether alcohols by reacting 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, wherein the one or more alkylene oxides are introduced into the reactor 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, with the proviso that the temperature at the end of a runaway reaction is at any point in time at least 100 K below the onset temperature of the decomposition reaction of the liquid reaction mixture, is proposed.