Abstract: An air filter, including: an openable filter housing having an inlet for air to be cleaned, an outlet for cleaned air, a filter element exchangeably arranged with the filter housing. The filter element includes a filter medium radially surrounding and defining an interior space within the filter element and a support element secured to the filter element. The support element faces away from the filter medium and has a lateral support surface having a cylindrical section and/or a section with a cross section that changes in the direction of the element axis, whose main axis runs axially or parallel to the element axis and with which the support element is supported at least transversely to the element axis against a corresponding support section arranged on a side of the filter housing.