Pyramidal tract lesions determine the clinical syndrome of Hereditary Spastic Paraplegia (HSP). The clinical impairments of HSP are typically exemplified by their deficits in mobility, leading to falls and injuries. The first aim of this study was to identify the cause for postural abnormalities caused by pyramidal tract lesions in HSP. The second aim was to specify the effect of treadmill training for postural abnormalities. We examined nine HSP patients before and after treadmill training, as well as nine healthy control subjects during perturbed and unperturbed stance. We found that HSP was associated with larger sway amplitudes and velocities. Body excursions following platform tilts were larger, and upper body excursions showed a phase lead. Model-based analysis detected a greater time delay and a reduced long-term error correction of postural reactions in the center of mass. HSP patients performed significantly better in clinical assessments after treadmill training. In addition, treadmill training reduced sway amplitudes and body excursions, most likely by increasing positional and velocity error correction gain as a compensatory mechanism, while the time delay and long-term error correction gain remained largely unaffected. Moreover, the upper body's phase lead was reduced. We conclude that HSP leads to very specific postural impairments. While postural control generally benefits from treadmill training, the effect seems to mainly rely on compensatory mechanisms, whereas the original deficits are not affected significantly.