The device and method according to the invention allow a particularly fast, gentle, and secure fusion of vessels between two coagulation electrodes. Resistance oscillations are generated in the biological tissue, said oscillations alternatingly moving above and below a tissue resistance value of, e.g., 50 Ohm. Subsequently, a phase of slowed tissue cooling is passed, during which phase a current is applied to the tissue with chronologically decreasing coagulation voltage to achieve a substantially slowed cooling process compared to the instant voltage disconnection. In doing so, a good fusionof the collagen of the pressed-together vessel walls and a mechanically stable solidification of the collagen is achieved. Due to the mentioned process control, the required fusion time is shortened compared to conventional methods, the unwanted damage to surrounding tissue is reduced, and the closure of the vessel is more secure.