In a method for the purifying of the waste gases of a sintering process of ores in the production of metals, in which ore material is sintered with a solid fuel, with the combustion of the solids and passage through a smoldering process, at least the pollutants SOx and/or HCl and NOx are reduced or extensively eliminated. To this end, the sintering waste gas is guided into a moving bed reactor (50) from below through a lower and upper layer (54B; 54A) of an adsorption and/or absorption agent already polluted with NOx and SOx and/or HCl, wherein at least the main quantity of SOx and/or HCl components is adsorbed from the sintering waste gas into the pore system of the NOx-loaded adsorption and/or absorption agent. The sintering waste gas, purified of the main quantity of SOx and/or HCl components, is intimately mixed with an ammonium-containing compound, such as ammonia or urea, and flows in below through an upper horizontal gas inflow and bulk material removal tray (52A) of the moving bed reactor into the upper layer of the adsorption and/or absorption agent already polluted with NOx and small quantities of SOx and/or HCl. In the throughflow of the upper layer (54A), at least the main quantity of NOx components is adsorbed from the sintering waste gas onto the surface of the adsorption/absorption agent, loaded with NOx or N2 and small quantities of SOx and/or HCl. Fresh and/or regenerated adsorption/absorption agent is delivered, via a bulk material-distributing tray (50C), at the upper end of the moving bed reactor and subsequently migrates, without interruption, through the upper and lower layers of the entire moving bed reactor, wherein initially, NOx and N2 and water vapor is adsorbed onto its surface, and subsequently, with SOx, and/or HCl, in its pore system.