A cross-flow fan includes a cylindrical impeller having an annularly designed first magnetically effective core disposed at a first end, an annularly designed second magnetically effective core disposed at a second end, a plurality of vanes arranged between the first magnetically effective core and the second magnetically effective core, a first stator, which is a bearing and drive stator, and which interacts with the first magnetically effective core as a first electromagnetic rotary drive, and a second stator, which is at least a bearing stator, and with which the second magnetically effective core is capable of being magnetically levitated without contact with respect to the second stator. The impeller is magnetically driven without contact by the first and the second stators and magnetically levitated without contact with respect to the first stator and the second stator.