Abstract: The invention relates to a method and apparatus for purifying the exhaust gases from plants for the production of cement clinker, in which in a multi-stage filter zone hot exhaust gases coming from a preheating zone are first of all cleaned of dust in a first filter stage and then in a further stage are purified of NH.sub.x compounds, heavy metals and trace pollutants, SO.sub.z and NO.sub.x. In order to achieve a particularly efficient and economic purification, the exhaust gases from the preheating zone are set before the first filter stage to such a filter zone inlet temperature that in this first filter stage at least a proportion of the easily volatile pollutant elements and pollutant compounds are precipitated out of the exhaust gases in addition to the dust.