Coagulation electrodes are described which are intended for the thermal coagulation of biological tissue by means of high-frequency electrical alternating current. The area adjoining the contact surface of the coagulation electrode is designed as a heat sink with such a great heat capacity value and is cooled to such a low temperature that, during the time span necessary for at least one coagulation procedure, the contact surface has a temperature within a temperature range whose upper temperature limit is below the temperature of the operating room and whose lower limit is above the freezing temperature of water. The heat sink can comprise a cooling facility with an inlet and a discharge line for liquid or gaseous coolant.; According to one exemplary embodiment relating to the application of the invention to bipolar coagulation forceps (Fig. 6), metallic tubular lines (34, 35) run to the area of the two contact surfaces (20, 21) for the supply and the discharge of the coolant, these lines being connected in series via a connection line (38), which is formed by a tube made of electrically non-conducting synthetic material.