In order to address a problem with the effectiveness of a brake booster device, provision is made for the latter to be produced in the form of hydraulic servo control. In such an instance, a master cylinder (7-10) of a braking circuit (3-4) is provided with a pressure chamber (19) upstream of the braking circuit. This pressure chamber is then subjected to an injection (28) of hydraulic fluid by a pump (34). The pump is operated (39) according to the braking requirements. The servo control comprises a set of moving gear (54) sensitive to these requirements and that work an injection valve (29-30).