In a dual-circuit hydraulic motorcycle brake system with two hand or foot-operated master cylinders, at the commencement of the pump operation in one of the brake circuits, the change-over valve (20) and/or the separating valve (19) of that brake circuit assume a switching position in which the pressure which can be generated by the pump (9) is prevented from causing a reactive effect on the associated hand-operated or foot-operated master brake cylinder (7, 13). To this end, the separating valve (19) in the brake line may be switched to a closed or throttling position, while the change-over valve (20) in the suction path is closed. Alternatively, both the change-over valve (20) and the separating valve (19) can be opened at the same time so that the pump conveys brake fluid in a circle.