In order to provide a transport device having a planar motor, which gives greater flexibility in the movement of the transport units, at least one multiple-action transport unit is provided on the transport device. On the multiple-action transport unit, at least first drive magnets for electromagnetic interaction with the drive coils of a first planar motor and at least second drive magnets for electromagnetic interaction with the drive coils of a second planar motor are provided. The multiple-action transport unit can be moved two-dimensionally on the transport plane of one of the planar motors, or can be moved simultaneously, unidimensionally on neighboring transport planes of the first and second planar motor.