A machine (1) for stabilization of a track (2) has a machine frame (5), mobile on the track by means of on-track undercarriages, on which a stabilizing unit (4) is arranged which has vertical adjustment drives (6) as well as a vibration exciter (7). The stabilizing unit is designed to be displaceable relative to the machine frame (5) in a longitudinal direction (23) of the machine by means of a longitudinal displacement drive (24).