A track leveling and tamping machine has a plurality of tamping units whose distance from each other may be changed. Each tamping unit is mounted on a respective machine frame or frame portion which are pivotally coupled together, and a track lifting mechanism is mounted on the frame. At least one running gear mounting the frame or frame portions on the track rails is arranged between each two spaced apart tamping units, and each trailing tamping unit is arranged between a respective pair of the running gears. A reference system controls the leveling of the track.