Reactor for producing C2- to C8-olefins, preferably propylene, from gaseous oxygenate, preferably dimethylether (DME) and/or methanol (MeOH) as well as H2O and a material flow containing one or more of the hydrocarbons C2-, C4-, C5-, C6-, C7-, C8-olefins and -paraffins, having a temperature of 400 to 470° C., with several reaction stages, arranged within an enclosed, vertical vessel through which the material flow flows from top to bottom, in each case composed of a tray with a fixed-bed zone formed by a layer of granular molecular-sieve catalyst arranged on top of it, wherein each tray is build-up from cells, arranged side by side without interspace and firmly connected with each other and freely suspended inside the vessel, the cells being filled with a layer of molecular-sieve catalyst, an atomizer system in the interspace delimited upwards and downwards by two adjacent reaction stages and formed by an assembly of nozzle tubes for the uniform atomization of a liquid phase containing DME and/or MeOH, mainly consisting of H2O and having a temperature of between 25 and 150° C., by means of a water-saturated gas phase mainly containing DME and/or MeOH and having a temperature of 170 to 300° C., in the direction of the next following downstream reaction stage.