Brake system for a motor vehicle having electromechanical wheel brakes (104, 106, 108, 110), a brake operating unit and a central brake control unit, wherein the wheel brakes (104, 106, 108, 110) each have a local brake control unit (118, 120, 122, 124), wherein the central brake control unit is connected directly to the brake operating unit and to the local brake control units (118, 120, 122, 124) of the wheel brakes (104, 106, 108, 110) via a first data connection, wherein the brake operating unit is connected directly to the local brake control unit (118, 120, 122, 124) of at least one wheel brake (104, 106, 108, 110) via a second data connection, wherein the central brake control unit in a normal operating mode of the brake system is configured to determine at least one brake demand from first operating information, received in particular via the first data connection, of the brake operating unit and to transmit control signals corresponding to the brake demand to the local brake control units (118, 120, 122, 124) of the wheel brakes (104, 106, 108, 110), and wherein the local brake control units (118, 120, 122, 124) of the wheel brakes (104, 106, 108, 110) in a fallback level operating mode of the brake system are configured to actuate the respective wheel brakes (104, 106, 108, 110) on the basis of second operating information, received via the second data connection, of the brake operating unit, characterized in that the brake operating unit is connected directly to the local brake control unit (118, 120, 122, 124) of exactly one wheel brake (104, 106, 108, 110), wherein the local brake control unit (118, 120, 122, 124) connected directly to the brake operating unit is configured to transmit second operating information received from the brake operating unit to the local brake control units (118, 120, 122, 124) of the further wheel brakes (104, 106, 108, 110) via a third data connection. wherein the wheel brakes (104, 106, 108, 110) each have a local brake control unit (118, 120, 122, 124), wherein the central brake control unit is connected directly to the brake operating unit and to the local brake control units (118, 120, 122, 124) of the wheel brakes (104, 106, 108, 110) via a first data connection, wherein the brake operating unit is connected directly to the local brake control unit (118, 120, 122, 124) of at least one wheel brake (104, 106, 108, 110) via a second data connection, wherein the central brake control unit in a normal operating mode of the brake system is configured to determine at least one brake demand from first operating information, received in particular via the first data connection, of the brake operating unit and to transmit control signals corresponding to the brake demand to the local brake control units (118, 120, 122, 124) of the wheel brakes (104, 106, 108, 110), and wherein the local brake control units (118, 120, 122, 124) of the wheel brakes (104, 106, 108, 110) in a fallback level operating mode of the brake system are configured to actuate the respective wheel brakes (104, 106, 108, 110) on the basis of second operating information, received via the second data connection, of the brake operating unit, characterized in that the brake operating unit is connected directly to the local brake control unit (118, 120, 122, 124) of exactly one wheel brake (104, 106, 108, 110), wherein the local brake control unit (118, 120, 122, 124) connected directly to the brake operating unit is configured to transmit second operating information received from the brake operating unit to the local brake control units (118, 120, 122, 124) of the further wheel brakes (104, 106, 108, 110) via a third data connection.