Abstract: An alkylene oxide is reacted in a loop reactor with an organic compound having a reactive hydrogen atom, a gas circulation and a liquid circulation around the reactor being provided and being coupled with one another via an ejector mixing nozzle. To ensure completeness of the reaction and suppression of the formation of by-products such as dioxane, it is essential to reduce the temperature of the entire alkylene oxide gas phase to a temperature below that of the liquid phase, and this is effected by feeding and evaporating liquid alkylene oxide and by cooling of the gas phase on the unit walls.