In producing C2-C4 olefins, in particular propylene, from an educt mixture containing steam and oxygenates, such as methanol and/or dimethyl ether, the educt mixture is reacted in a reactor on a catalyst to a reaction mixture comprising low-molecular olefins and gasoline hydrocarbons, which in a first separating device is separated into a mixture rich in C5− olefins, a mixture rich in C5+ gasoline hydrocarbons, and an aqueous phase. To increase the yield of propylene the mixture rich in C5+ gasoline hydrocarbons is supplied to a second separating device, in which the aromatics contained in the mixture are separated. The residual stream largely free from aromatics is at least partly recirculated to the reactor.