A process for the preparation of polyether alcohols by reacting at least one alkylene oxide with at least one unsaturated starter having at least one active hydrogen atom per molecule under basic catalysis, that the alkoxylation is carried out in at least two stages, in stage (I) the alkoxylation of the starter or starters being carried out with not more than 10 mol of alkylene oxide per mole of starter with a catalyst concentration of not more than 0.0085 mol of basic catalyst per mole and in stage (II) and the optionally following stages, the alkoxylated starter or starters from stage (I) being reacted with further alkylene oxide at a catalyst concentration of at least 0.01 mol of basic catalyst per mole of starter.