The invention relates to the production of olefins from dimethyl ether. Gaseous dimethyl ether with a purity of 70 - 100 wt.% together with recycled gas, which contains olefinic, paraffinic, and/or aromatic hydrocarbons, and water vapor is fed to a first catalyst stage of a reactor. The aim of the invention is to form the temperature profile over the catalyst stages as flatly as possible but as close as possible to the optimal operating temperature. This is achieved in that gaseous dimethyl ether with a purity of 70 - 100 wt.% together with recycled gas, which contains olefinic, paraffinic, and aromatic hydrocarbons, is fed to at least one downstream catalyst stage. Said downstream catalyst stage is additionally supplied product gas from the upstream catalyst stage. The system for this method consists of a reactor with at least two catalyst stages, each of which has a feed line. The ratio of dimethyl ether and recycled gas in said feed lines is determined by a control or regulating device that is attached in the feed or discharge line.