Electrosurgical apparatus for treating biological tissue by means of an RF current, comprising: - an electrosurgical instrument comprising a coagulation electrode and - an electrosurgical appliance comprising -- an RF generator for generating an RF voltage and for supplying the RF current to the coagulation electrode of the electrosurgical instrument and -- at least one control apparatus for completing the coagulation process, wherein the following is assigned to the control apparatus: - a measuring device, which is embodied in such a way that it detects at least one measurement value (u, i, t, θ) describing a measured tissue energy influx in a defined measured tissue region, wherein it detects at least one measurement value directly in the measured tissue region by means of a measuring electrode (32, 32'), wherein the coagulation electrode and the measuring electrode are arranged in such a way relative to one another that they tap the measured tissue region in respect of the extent thereof at least in a one-dimensional manner in one direction, - a computer apparatus, which is embodied in such a way -- that it determines the measured tissue energy influx in the defined measured tissue region and -- that it establishes a final value (w), which is predetermined for the coagulation process, for a target tissue energy influx in a target tissue region and/or adopts said final value as a stored final value (w), wherein the control apparatus is embodied in such a way that it controls or regulates the RF generator on the basis of the final value (w) in such a way that the required RF current is supplied to the target tissue region and that it then generates a shutdown signal (c) when the target tissue energy influx reaches the final value (w). - an electrosurgical instrument comprising a coagulation electrode and - an electrosurgical appliance comprising -- an RF generator for generating an RF voltage and for supplying the RF current to the coagulation electrode of the electrosurgical instrument and -- at least one control apparatus for completing the coagulation process, wherein the following is assigned to the control apparatus: - a measuring device, which is embodied in such a way that it detects at least one measurement value (u, i, t, θ) describing a measured tissue energy influx in a defined measured tissue region, wherein it detects at least one measurement value directly in the measured tissue region by means of a measuring electrode (32, 32'), wherein the coagulation electrode and the measuring electrode are arranged in such a way relative to one another that they tap the measured tissue region in respect of the extent thereof at least in a one-dimensional manner in one direction, - a computer apparatus, which is embodied in such a way -- that it determines the measured tissue energy influx in the defined measured tissue region and -- that it establishes a final value (w), which is predetermined for the coagulation process, for a target tissue energy influx in a target tissue region and/or adopts said final value as a stored final value (w), wherein the control apparatus is embodied in such a way that it controls or regulates the RF generator on the basis of the final value (w) in such a way that the required RF current is supplied to the target tissue region and that it then generates a shutdown signal (c) when the target tissue energy influx reaches the final value (w). -- an RF generator for generating an RF voltage and for supplying the RF current to the coagulation electrode of the electrosurgical instrument and -- at least one control apparatus for completing the coagulation process, - a measuring device, which is embodied in such a way that it detects at least one measurement value (u, i, t, θ) describing a measured tissue energy influx in a defined measured tissue region, wherein it detects at least one measurement value directly in the measured tissue region by means of a measuring electrode (32, 32'), wherein the coagulation electrode and the measuring electrode are arranged in such a way relative to one another that they tap the measured tissue region in respect of the extent thereof at least in a one-dimensional manner in one direction, - a computer apparatus, which is embodied in such a way -- that it determines the measured tissue energy influx in the defined measured tissue region and -- that it establishes a final value (w), which is predetermined for the coagulation process, for a target tissue energy influx in a target tissue region and/or adopts said final value as a stored final value (w), wherein the control apparatus is embodied in such a way that it controls or regulates the RF generator on the basis of the final value (w) in such a way that the required RF current is supplied to the target tissue region and that it then generates a shutdown signal (c) when the target tissue energy influx reaches the final value (w). -- that it determines the measured tissue energy influx in the defined measured tissue region and -- that it establishes a final value (w), which is predetermined for the coagulation process, for a target tissue energy influx in a target tissue region and/or adopts said final value as a stored final value (w),