An air filter system with an air filter element having an inflow and an outflow face and comprising alternating flat and pleated layers, which are configured to form channels. The channels are alternately sealed in inflow and outflow direction, such that the medium to be filtered must pass through one of the layers as it flows from the inflow face through the filter to the outflow face. An adsorber element made of an activated carbon coated honeycomb structure is disposed adjacent the air filter element.