Abstract: The device for magnetically suspending a rotor relative to a structure comprises at least one axial active magnetic bearing with a main electromagnet coil disposed in a stator and having load-bearing surfaces placed facing an armature extending essentially perpendicularly to the axis of the rotor. A device for detecting the axial position of the rotor is associated with circuits for servo-controlling the current carried by the main electromagnet coil. A compensation coil is disposed close to the main electromagnet coil, but in a position that is situated away from the load-bearing surfaces of the stator that co-operate with the rotor armature. The compensation coil is connected in series with the main electromagnet coil, but carries current in the opposite direction to that carried by said main electromagnet coil. The device constitutes an axial abutment of optimized capacity without magnetic leakage.