Hydraulic brake system for a vehicle having: a master brake cylinder which can be activated by means of a brake activation element and has a floating piston between a first pressure chamber and a second pressure chamber; a first brake circuit which is connected to the first brake-activation-element-side pressure chamber of the master brake cylinder via a first switching valve of the first brake circuit and has at least a first wheel brake cylinder; a second brake circuit which is connected to the second pressure chamber of the master brake cylinder via a second switching valve of the second brake circuit, and has at least a second wheel brake cylinder, wherein the switching valves (28, 40) each have a non-return valve (28a, 40a), which opens in the direction of the wheel brake cylinders (32, 42), in a bypass line (28b, 40b) which runs parallel to the switching valves (28, 40); and a control device having an actuation device which, at least in a first operating mode, taking into account at least one supplied sensor signal of at least one brake activation-element sensor, is configured to output, at least temporarily during an activation of the brake activation element which is connected to the master brake cylinder of the hydraulic brake system, at least a first control signal to at least one blending valve of the first brake circuit, as a result of which the at least one blending valve can be placed in an at least partially opened state in such a way that brake fluid from the at least one first wheel brake cylinder can be displaced into at least one storage chamber of the first brake circuit, and at least a first brake pressure which is present in at least a first wheel brake cylinder of the first brake circuit can be limited to a response pressure of the at least one storage chamber, wherein the actuation device is also configured, at least in the first operating mode, taking into account the at least one supplied sensor signal, to output at least a second control signal to a pressure discharge valve of the second brake circuit, as a result of which the pressure discharge valve can be placed in an at least partially opened state in such a way that brake fluid can be displaced into a brake fluid reservoir which is connected on the output side to the pressure discharge valve, and at least the first brake pressure which is present in the at least one first wheel brake cylinder of the first brake circuit can additionally be reduced below the response pressure of the at least one storage chamber. a master brake cylinder which can be activated by means of a brake activation element and has a floating piston between a first pressure chamber and a second pressure chamber; a first brake circuit which is connected to the first brake-activation-element-side pressure chamber of the master brake cylinder via a first switching valve of the first brake circuit and has at least a first wheel brake cylinder; a second brake circuit which is connected to the second pressure chamber of the master brake cylinder via a second switching valve of the second brake circuit, and has at least a second wheel brake cylinder, wherein the switching valves (28, 40) each have a non-return valve (28a, 40a), which opens in the direction of the wheel brake cylinders (32, 42), in a bypass line (28b, 40b) which runs parallel to the switching valves (28, 40); and a control device having an actuation device which, at least in a first operating mode, taking into account at least one supplied sensor signal of at least one brake activation-element sensor, is configured to output, at least temporarily during an activation of the brake activation element which is connected to the master brake cylinder of the hydraulic brake system, at least a first control signal to at least one blending valve of the first brake circuit, as a result of which the at least one blending valve can be placed in an at least partially opened state in such a way that brake fluid from the at least one first wheel brake cylinder can be displaced into at least one storage chamber of the first brake circuit, and at least a first brake pressure which is present in at least a first wheel brake cylinder of the first brake circuit can be limited to a response pressure of the at least one storage chamber, wherein the actuation device is also configured, at least in the first operating mode, taking into account the at least one supplied sensor signal, to output at least a second control signal to a pressure discharge valve of the second brake circuit, as a result of which the pressure discharge valve can be placed in an at least partially opened state in such a way that brake fluid can be displaced into a brake fluid reservoir which is connected on the output side to the pressure discharge valve, and at least the first brake pressure which is present in the at least one first wheel brake cylinder of the first brake circuit can additionally be reduced below the response pressure of the at least one storage chamber.