The invention relates to a multistage coordinated overvoltage arrester circuit having at least one first coarse protection arrester path in the transverse branch and at least one second fine protection arrester path in the longitudinal and transverse branch, an electrically isolated surge current measuring device and a monitoring device for a physical state of the over voltage arrester located in the first arrester path being arranged in the first arrester path. According to the invention, a monitoring device for a physical state is likewise assigned to the overvoltage arresters in the second arrester path, wherein a determination of the temperature of the respective overvoltage arrester is carried out as state monitoring, wherein the energy converted in the respective overvoltage arrester is determined from the measured temperatures and the temperature rise time and, from this, a determination of possible damage to the respective overvoltage arrester is performed.