Abstract: A method for the surveillance of a brake device includes an indirect measurement of temperature of a selected device component, for example a brake drum, of a brake device. A warning signal is furnished, if this measured temperature reaches a maximum permissible value. The invention method is quick by employing the pressure-dependent deformation characterizing curve (11) of the device component heated to the permissible temperature. The device component represented by the brake drum (1) can heat to the maximum permissible temperature and is placed under surveillance during a brake actuation based on deformation and pressure measurement. It is then determined if the actual values reach or exceed the deformation characterizing curve (11). The invention apparatus is used in connection with brake devices in vehicles.