A mixing apparatus for mixing substances includes a single-use apparatus and a reusable apparatus. The single-use apparatus includes a flexible mixing tank configured to receive the at least two substances to be mixed, is plastic, and has a rotor arranged in the mixing tank. The rotor includes an impeller configured to mix the at least two substances, the impeller being magnetically contactlessly drivable and free of coils and permanent magnets. The reusable apparatus includes a support tank configured to receive the mixing tank and a stator configured to magnetically contactlessly drive the rotor about an axis of rotation in an operating state. The stator includes at least one permanent magnet configured to generate a permanent magnet flux and at least one winding configured to generate an electromagnetic flux, the permanent magnet flux and the electromagnetic flux together being capable of driving the rotor.