In a process for the preparation of C2- to C4-olefins, a feed stream comprising oxygenates and steam is passed through at least one fixed-bed zone comprising zeolite catalyst, where the oxygenates are converted catalytically into olefins with high selectivity for lower olefins, and the reaction mixture leaving the fixed-bed zone is separated into a first product stream comprising C2- to C3-olefins and inert gas components, at least one second product stream comprising C4+-olefins, and a third product stream consisting of aqueous phase. In order to improve the yield of lower olefins, the aim is to regulate the temperature of the catalytic reaction in accordance with a target temperature value in the range from 440 to 520° C. specified for the reaction mixture exiting the fixed-bed zone by means of a supplementary stream consisting of olefins and inert gas components fed into the feed stream.