The invention relates to a motor vehicle brake system having a hydraulically actuatable service brake system and an electromechanically actuatable brake system, including an operating element HMI, in particular for activating a parking brake function, an electronic control device (EPB-ECU) for activating an electromechanical actuator of the electromechanically actuatable brake system, and an electrohydraulic control unit (HECU) associated with a service brake and serving to control or regulate hydraulically implemented service brake functions, driving stability functions and/or braking assistance functions. It is an aim of the invention to contribute to reducing the stress on parts or components of the brake system. It is proposed that an electronically controlled hydraulic pressure conditioning process is carried out in integrated brake calipers after hydraulic actuation of the brake, it being further provided that the electromechanical brake system generates additional application forces only after the hydraulic pressure conditioning process.