Surgical tissue fusion instrument having two gripping structures which are movable relative to each other, are designed for gripping and bringing together biological tissue sections, and are assigned heat-generating means designed in such a way that tissue fusion takes place between the biological tissue sections by heat being supplied in the area of the gripping structures. At least one gripping structure is assigned a fluid-conducting system, which is designed to supply at least one liquid or flowable additive to the tissue sections during a tissue fusion process.