A flat air filter element for an air filter has a filter medium of cellulose material and a sealing element extending circumferentially about the filter medium. Sealing element and filter medium have at least one recess at an outer contour of the flat air filter element. The sealing element has a circumferentially extending holding groove to be engaged by a housing part of a filter housing. The filter housing has a housing pot, a housing cover to cover the housing pot, and a closure element for closing the filter housing. The flat air filter element is secured in the closed state of the filter housing by circumferentially clamping the sealing element between housing pot and housing cover. The circumferentially extending holding groove of the sealing element is engaged by housing pot or housing cover. The closure element of the filter housing is arranged in the region of the recess.