The invention concerns a rotary pump (3) having a housing (9) and a rotor (2) with blades (1b) which is placed inside the casing. The rotor (2) comprises a passive magnetically active rotor part (1) and the housing (9) is surrounded by a stator (7) having electrical windings (8a, 8b, 8c, 8d, 8e, 8f, 8g, 8h) and teeth (7a, 7b, 7c, 7d, 7e, 7f, 7g, 7h). The stator (7) and the rotor part (1) form a motor that has no bearings, whereby the rotor part (1) can be actively controlled and operated by means of the electrical windings (8a, 8b, 8c, 8d, 8e, 8f, 8g, 8h) through three degrees of freedom. The rotor part (1) and the teeth (7a, 7b, 7c, 7d, 7e, 7f, 7g, 7h) of the stator (7) are designed geometrically in a mutually adapted manner and are placed in such a way that the rotor part (1) is retained in the stator (7) through three additional degrees of freedom not actively controlled through passively operating reluctance forces, in order to mount the rotor (2) inside the housing (9) so that it can be driven and float frictionlessly.