Method for operating a brake system for motor vehicles having a) hydraulic wheel brakes , wherein two wheel brakes are hydraulically assigned to a first brake circuit (I) and two wheel brakes are hydraulically assigned to a second brake circuit (II); b) a pressure medium reservoir which is under atmospheric pressure; c) in particular an electronic open-loop and closed-loop control unit ; d) a pressure modulation unit for setting wheel-specific brake pressures, which are derived from the brake system pressure; e) an electrohydraulic pressure provision device which is connected to the pressure modulation unit and to the pressure medium reservoir and which outputs the brake system pressure to the pressure modulation unit and which, for the compensation of its volume balance, draws in pressure medium from the pressure medium reservoir , wherein the pressure provision device comprises a double-acting piston-cylinder arrangement , wherein a piston of the piston-cylinder arrangement separates two pressure spaces from one another, wherein a pressure build-up occurs in the first pressure space during a backward movement of the piston and occurs in the second pressure space during a forward movement of the piston ; f) a first pressure activation valve for connecting the first pressure space of the pressure provision device to the pressure modulation device , and a second pressure activation valve for connecting the second pressure space of the pressure provision device to the pressure modulation device , characterized in that, during a brake pressure build-up by a forward stroke of the piston of the piston-cylinder arrangement in a predefined situation, in particular in the case of demand for a particularly high brake system pressure, the first pressure activation valve is opened and the first pressure space is hydraulically separated from the pressure medium reservoir , wherein the two pressure spaces are hydraulically connected to one another. a) hydraulic wheel brakes , wherein two wheel brakes are hydraulically assigned to a first brake circuit (I) and two wheel brakes are hydraulically assigned to a second brake circuit (II); b) a pressure medium reservoir which is under atmospheric pressure; c) in particular an electronic open-loop and closed-loop control unit ; d) a pressure modulation unit for setting wheel-specific brake pressures, which are derived from the brake system pressure; e) an electrohydraulic pressure provision device which is connected to the pressure modulation unit and to the pressure medium reservoir and which outputs the brake system pressure to the pressure modulation unit and which, for the compensation of its volume balance, draws in pressure medium from the pressure medium reservoir , wherein the pressure provision device comprises a double-acting piston-cylinder arrangement , wherein a piston of the piston-cylinder arrangement separates two pressure spaces from one another, wherein a pressure build-up occurs in the first pressure space during a backward movement of the piston and occurs in the second pressure space during a forward movement of the piston ; f) a first pressure activation valve for connecting the first pressure space of the pressure provision device to the pressure modulation device , and a second pressure activation valve for connecting the second pressure space of the pressure provision device to the pressure modulation device , <EOS>