A brake controller is connected downstream of a primary vehicle dynamics computer and has a channel for controlling the yaw velocity at a desired value, and a channel for limiting the sideslip angle. The computer prescribes the desired value and the limit value, and determines which channel is effective on the basis of the driving situation. The two channels generate a control signal which is routed via a control amplifier having a proportional component and a differential component. An actuating signal which is used to input braking pressure at the wheel brakes is formed from the resulting signal components, the instantaneous driving situation being assigned in both cases to one of a plurality of classes, and this assignment being co-used to determine the wheels at which braking pressure is input.