An axial flux machine has an annular stator and two rotor elements mounted rotatably relative to the stator about an axis of rotation. A first rotor element is arranged axially adjacent to a first end face of the stator and a second rotor element is arranged axially adjacent to a second end face of the stator. The stator has a plurality of stator cores distributed in a circumferential direction of a circular line extending about the axis of rotation, wherein at least one stator core has a plurality of radially extending guide segments that are stacked on top of one another in the circumferential direction and are of plate-like design. At least a partial quantity of the guide segments have, on the radial outer side thereof and/or the radial inner side thereof, a retaining contour accommodated in an interlocking manner on at least one supporting region fixed to the housing.