Polyetherpolyols are prepared by reacting diols or polyols with ethylene oxide, propylene oxide, butylene oxide or a mixture thereof in the presence of a multimetal cyanide complex catalyst by a process which is carried out in a vertical upright cylindrical reactor comprising a jet nozzle which is arranged in the upper reactor region and is directed downward and via which the starting materials and the reaction mixture are fed in, and comprising a take-off, preferably in the lower reactor region, via which the reaction mixture is fed back to the jet nozzle in an external circulation by means of a pump via an equilibration container, comprising a concentric guide tube which extends over the total length of the reactor, except for the reactor ends, and comprising a heat exchanger integrated in the annular space.