Method for operating a braking system for motor vehicles, comprising • hydraulically actuatable wheel brakes ; • an electrically controllable pressure-providing device for hydraulically actuating the wheel brakes , which device is formed by a cylinder-piston arrangement with a hydraulic pressure chamber , the pressure piston of which can be displaced by an electric motor and a rotation-translation gear mechanism; • an actuating device which can be actuated by means of a brake pedal and which comprises a tandem master brake cylinder with a primary pressure chamber , into which a primary piston is pushed on actuation of a brake pedal , and a secondary pressure chamber and a floatingly mounted secondary piston , wherein the primary pressure chamber can be hydraulically separated from a first set of the wheel brakes by means of a first, normally open separating valve , and wherein the secondary pressure chamber can be hydraulically separated from a second set of the wheel brakes by means of a second, normally open separating valve ; • a pressure medium reservoir , which is under atmospheric pressure and which is hydraulically connected to the secondary pressure chamber of the master brake cylinder in the unactuated state of the secondary piston ; • a hydraulically configured simulator with a simulator piston and a simulator spring, which is configured to simulate the hydraulic volume absorption of pressurized wheel brakes, wherein the braking system is activated in order to actively build up pressure in the wheel brakes in a by-wire operating mode by means of the pressure-providing device , characterized in that in the event of a pressure medium surplus in the wheel brakes (42-48), the second separating valve is opened in the by-wire operating mode if a release of the brake pedal by the driver is detected, so that surplus pressure medium can flow into the secondary pressure chamber . • hydraulically actuatable wheel brakes ; • an electrically controllable pressure-providing device for hydraulically actuating the wheel brakes , which device is formed by a cylinder-piston arrangement with a hydraulic pressure chamber , the pressure piston of which can be displaced by an electric motor and a rotation-translation gear mechanism; • an actuating device which can be actuated by means of a brake pedal and which comprises a tandem master brake cylinder with a primary pressure chamber , into which a primary piston is pushed on actuation of a brake pedal , and a secondary pressure chamber and a floatingly mounted secondary piston , wherein the primary pressure chamber can be hydraulically separated from a first set of the wheel brakes by means of a first, normally open separating valve , and wherein the secondary pressure chamber can be hydraulically separated from a second set of the wheel brakes by means of a second, normally open separating valve ; • a pressure medium reservoir , which is under atmospheric pressure and which is hydraulically connected to the secondary pressure chamber of the master brake cylinder in the unactuated state of the secondary piston ; • a hydraulically configured simulator with a simulator piston and a simulator spring, which is configured to simulate the hydraulic volume absorption of pressurized wheel brakes, wherein the braking system is activated in order to actively build up pressure in the wheel brakes in a by-wire operating mode by means of the pressure-providing device , <EOS>