C.sub.2 -C.sub.4 -olefins are prepared by catalytic conversion of methanol and/or dimethyl ether in the presence of a zeolite catalyst at elevated temperatures, by a process in which the catalyst used is a pure borosilicate zeolite which has been tableted or extruded without a binder and treated with hydrofluoric acid and hydrochloric acid. The treatment of the catalyst with hydrofluoric acid is carried out using 0.001-1N HF, and that with hydrochloric acid is carried out using 3-25% strength acid. The time-on-stream of the catalyst is improved.