Hydrostatic transmission apparatus having an elementary motor with a feed enclosure and a discharge enclosure; a displacement selector suitable for taking up a bypass position, in which the feed and discharge enclosures are interconnected via a bypass link; and constriction means for constricting said bypass link. When the selector is in the bypass position, the constriction means can be activated to restrict the flow of fluid through the bypass link when the discharge pressure in the discharge enclosure exceeds a constriction threshold, said threshold being a function of a control pressure prevailing in a control chamber.