An air filter (10) includes an openable filter housing (12) and a filter element (18). The filter housing (12) includes an inlet (26) and an outlet. A filter element (18) with a filter medium (46) is disposed replaceably in the filter housing separating the inlet (26) from the outlet (22). The filter element (18) features on an exterior side facing away from the element interior space (52) on an axial front face relative to the element axis (32) at least one supporting element (58) having at least one supporting lateral surface (60, 61) with at least one cylindrical portion and/or at least one portion with a variable cross-section in the direction of a main axis. The supporting element (58) is supported at least transversely in relation to the element axis (32) with the at least one supporting lateral surface (60, 61) against at least one corresponding support portion (42) on the side of the filter housing (12).