A method for purifying waste gases of an at least partially burnt solid fuel to reduce pollutants such as SOx and/or HCl and NOx. The waste gas flows into a moving bed reactor from below through a lower and upper layer of an adsorption and/or absorption agent already polluted with NOx, SOx and/or HCl. SOx and/or HCl components are adsorbed from the waste gas into the NOx loaded adsorption and/or absorption agent. Thereafter, the waste gas is mixed with an ammonium-containing compound and flows through an upper horizontal gas inflow and bulk material removal tray 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. During the throughflow of the upper layer, NOx components are adsorbed from the waste gas onto the adsorption/absorption agent.