This invention relates to a system for fixing a window regulator on a frameless door of a vehicle equipped with a fixed front window pane and a mobile rear pane, the front edge of the mobile pane being guided by a slideway which extends between the panes and of which the lower part is fixed in the door. The window regulator comprises a front rail and a rear rail parallel to the slideway, on which slide sliders displaced by cables actuated by a drive. The front rail is rigidly connected to the slideway in order to ensure parallelism between these two elements.