A high-frequency surgical appliance has a peak value detection and control unit, having a current or voltage sensor designed to detect the current strength or the voltage of a high-frequency alternating current output to the load. The control unit has a root-mean-square value former or is connected thereto, connected to the sensor and forms a root-mean-square value of a high-frequency alternating current detected by the sensor. The control unit deactivates the high-frequency generator when, in the steady state of the HF high-voltage circuit, a quantity of an instantaneous peak value of a signal representing an instantaneous value of the high-frequency alternating current detected during operation by the sensor exceeds a quantity of a value derived from the root-mean-square value of the high-frequency alternating current detected during operation by the sensor. The sensor continuously detects the instantaneous value of the current or voltage flowing during operation into the HF high-voltage circuit.
