Brake system for motor vehicles, with - an actuation device, in particular in the form of a brake pedal, - a travel simulator to generate a feedback force on the actuation device, - a first piston-cylinder device, wherein the piston-cylinder device has at least one piston and at least one working chamber (A 1, A 2) is connected via at least one hydraulic connecting line (VL 1, VL 2) to at least one wheel brake (RB 1-4) of a brake circuit (BK1, BK2), - a control device, wherein at least one wheel brake (RB1, RB2, RB3, RB4) is assigned to each brake circuit (BK1, BK2) and each wheel brake (RB1, RB2, RB3, RB4) can be connected to its assigned connecting line (VL 1, VL 2) via an assigned controllable switching valve (SV1, SV2, SV3, SV4), wherein the controllable switching valve (SV1, SV2, SV3, SV4) is opened unpowered, and at least one pressure supply unit driven by an electric motor and having a double-stroke piston, a first working chamber and a second working chamber, wherein by means of the pressure supply unit the brake pressure can be reduced optionally in one or more wheel brakes (RB1, RB2, RB3, RB4) simultaneously, wherein the first working chamber is connectable via a first controllable switching valve with a storage container and the second working chamber is connectable via a second controllable switching valve with the storage container, characterized in that the wheel brake pressure is reducible via establishing a hydraulic connection of one of the working chambers (4, 4a) of the pressure supply unit, in particular the double-stroke piston, with the storage container by opening the respective controllable switching valve (PD1, PD3) as follows: a) in at least one or more wheel brakes (RB1, RB2, RB3, RB4) the controlled pressure reduction takes place via the controllable switching valve (SV1, SV2) assigned to the respective wheel brake (RB1, RB2) via a pressure volume control by means of a return stroke of the double-stroke piston into the storage container and/or, b) in at least one or more wheel brakes (RB1, RB2, RB3, RB4), the controlled pressure reduction takes place via the controllable switching valve (SV1, SV2) assigned to the respective wheel brake (RB1, RB2) via a pressure volume control by means of a forward stroke of the double-stroke piston into the storage container. - an actuation device, in particular in the form of a brake pedal, - a travel simulator to generate a feedback force on the actuation device, - a first piston-cylinder device, wherein the piston-cylinder device has at least one piston and at least one working chamber (A 1, A 2) is connected via at least one hydraulic connecting line (VL 1, VL 2) to at least one wheel brake (RB 1-4) of a brake circuit (BK1, BK2), - a control device, wherein at least one wheel brake (RB1, RB2, RB3, RB4) is assigned to each brake circuit (BK1, BK2) and each wheel brake (RB1, RB2, RB3, RB4) can be connected to its assigned connecting line (VL 1, VL 2) via an assigned controllable switching valve (SV1, SV2, SV3, SV4), wherein the controllable switching valve (SV1, SV2, SV3, SV4) is opened unpowered, and at least one pressure supply unit driven by an electric motor and having a double-stroke piston, a first working chamber and a second working chamber, wherein by means of the pressure supply unit the brake pressure can be reduced optionally in one or more wheel brakes (RB1, RB2, RB3, RB4) simultaneously, wherein the first working chamber is connectable via a first controllable switching valve with a storage container and the second working chamber is connectable via a second controllable switching valve with the storage container, characterized in that the wheel brake pressure is reducible via establishing a hydraulic connection of one of the working chambers (4, 4a) of the pressure supply unit, in particular the double-stroke piston, with the storage container by opening the respective controllable switching valve (PD1, PD3) as follows: a) in at least one or more wheel brakes (RB1, RB2, RB3, RB4) the controlled pressure reduction takes place via the controllable switching valve (SV1, SV2) assigned to the respective wheel brake (RB1, RB2) via a pressure volume control by means of a return stroke of the double-stroke piston into the storage container and/or, b) in at least one or more wheel brakes (RB1, RB2, RB3, RB4), the controlled pressure reduction takes place via the controllable switching valve (SV1, SV2) assigned to the respective wheel brake (RB1, RB2) via a pressure volume control by means of a forward stroke of the double-stroke piston into the storage container. a) in at least one or more wheel brakes (RB1, RB2, RB3, RB4) the controlled pressure reduction takes place via the controllable switching valve (SV1, SV2) assigned to the respective wheel brake (RB1, RB2) via a pressure volume control by means of a return stroke of the double-stroke piston into the storage container and/or, b) in at least one or more wheel brakes (RB1, RB2, RB3, RB4), the controlled pressure reduction takes place via the controllable switching valve (SV1, SV2) assigned to the respective wheel brake (RB1, RB2) via a pressure volume control by means of a forward stroke of the double-stroke piston into the storage container.