A hydrostatic transmission circuit for a vehicle having at least two displacement members (12) driven by at least one hydraulic motor (10) having a feed main duct and a discharge main duct (16, 18). Skid control means for controlling skidding of at least one displacement member comprise a skid control valve (20) and an additional valve (22) that are disposed in parallel on a main duct (16). At least the skid control valve (20) has a constriction of variable section, while the additional valve has two end positions (22A, 22B), in which its through sections are respectively at their maximum and at their minimum. Control means (UC, 26, 28) make it possible to cause said valves to move as a function of a skid situation detected by detection means (24).