The invention relates to a process and a plant for producing cement clinker, which has a furnace system and has essentially the following process steps:—raw material is preheated in a preheater by means of hot offgases from the furnace system,—dust is removed from the hot offgas downstream of the preheater in a preliminary dust removal apparatus to a residual dust concentration of max. 20 g/standard m3,—the offgas which has been subjected to preliminary dust removal is purified in a selective catalytic flue gas purification plant (selective catalytic reduction, SCR),—at least part of the offgas purified in the flue gas purification plant is conveyed in a bypass around a raw material milling plant to a cooling device and cooled there to temperatures of max. 140° C.,—before the residual dust in the offgas is precipitated in a process filter and—at least part of the residual dust precipitated in the process filter is discharged for removal of mercury.