The braking system for the braking of a part which is moving relative to another part, of the type including a brake cylinder which is charged with a fluid under pressure when the brake is off, and which pressure is relieved for braking purposes, the system comprising a pressure accumulator connected with the brake cylinder through a nonreturn valve to receive part of the fluid escaping from the cylinder, the accumulator containing a gas under pressure, the pressure of which gas determines the value of the initial braking force, and a deceleration regulator connected to the brake cylinder through a throttle valve, the deceleration regulator including a casing, a cut-off valve, a flywheel rotated by a spindle rotatably mounted in said casing and which is driven by an axle of the moving part so as to be capable of overruning with respect to the spindle to cause the cut-off valve to operate to stop the passage of fluid into the regulator when a predetermined deceleration value is reached, and spring means opposing overrunning of the flywheel, the force of which spring determines the deceleration rate.