Abstract: The tool-holding spindle assembly, particularly for a grinding machine, comprises means for supporting the shaft of the spindle and a power drive, for example an electric motor for rotating the spindle. The support means comprise at least one electromagnetic radial bearing controlled by a radial detector, having an annular armature mounted on the shaft of the spindle and a fixed armature surrounding this annular armature, an electromagnetic axial bearing having a disc-shaped armature mounted on the shaft of the spindle and a fixed armature, a chain for controlling the radial and/or axial position of the spindle, said chain being connected on the one hand to at least one detector of the radial and/or axial position of the spindle, and on the other hand to excitation coils of the armatures of each magnetic bearing, and means for selectively modifying the signal generated by said at least one position detector.