The invention concerns a rotary machine which comprises a driven rotor (2) and an electric motor (4, 14), with a stator (4) and a driving rotor. The stator (4) is also in the form of an electromagnetic bearing (4, 14) for the driving rotor (14). The driving rotor (14) of the electric motor (4, 14) forms a rotor unit (2, 14) with the driven rotor (2), i.e. the two rotors (2, 14) form an integral rotor (2, 14). The rotary machine can, for example, be a rotary pump, centrifugal pump, centrifuge or an agitator. The rotor (2, 14) can be constructed such that it is easily removable from the stator (4).