A turbo-machine for compressing or expanding a fluid comprises a housing, a rotary shaft, an electric machine, an impeller mounted at an end of the rotary shaft, radial magnetic bearings, an axial magnetic bearing, an axial detector, radial detectors, a control circuit, and auxiliary bearings. An auxiliary bearing is integrated within a stator portion of the axial magnetic bearing and this stator portion of the axial magnetic bearing is located opposite a rotor armature of the axial magnetic bearing. The rotor armature is made of iron or of a material which is adapted to be attracted in a magnetic field and is constituted by a rear face of the impeller.