Snare instrument, in particular a medical snare instrument, with - a snare structure which is formed in one piece from a tube section, by the latter being slit and bent open, and which has a proximal base portion and, extending axially forward from the latter, a distal snaring portion, and which is movable between a snaring position, in which it is moved forward out of an enclosure with the snaring portion folded open, and a securing position, in which it is moved back at least partially into the enclosure with the snaring portion folded in and providing a securing action, and - a pulling-wire actuation element which is guided axially movably in the enclosure, wherein the proximal end region of the snare structure is coupled to a distal end region of the pulling-wire actuation element, characterized in that - the snaring portion, in the folded-open state, has a cup shape with a distal snare opening, and, for this purpose, a distal end region of the tube section is provided with open axial slits of suitable length introduced from the direction of the distal end of the tube section, and, lying between these, with associated closed axial slits which terminate at a distance in front of the distal end of the tube section and are of greater length than the open axial slits, wherein, by means of the open and closed axial slits, wire sections are formed from the tube section and, when the tube section is bent open, the wire sections form circumferential portions of the snare opening, - further characterized in that a maximum diameter (D E) of the cup shape of the snaring portion in the folded-open state is greater than a diameter (Do) of the snare opening. - a snare structure which is formed in one piece from a tube section, by the latter being slit and bent open, and which has a proximal base portion and, extending axially forward from the latter, a distal snaring portion, and which is movable between a snaring position, in which it is moved forward out of an enclosure with the snaring portion folded open, and a securing position, in which it is moved back at least partially into the enclosure with the snaring portion folded in and providing a securing action, and - a pulling-wire actuation element which is guided axially movably in the enclosure, wherein the proximal end region of the snare structure is coupled to a distal end region of the pulling-wire actuation element, characterized in that - the snaring portion, in the folded-open state, has a cup shape with a distal snare opening, and, for this purpose, a distal end region of the tube section is provided with open axial slits of suitable length introduced from the direction of the distal end of the tube section, and, lying between these, with associated closed axial slits which terminate at a distance in front of the distal end of the tube section and are of greater length than the open axial slits, wherein, by means of the open and closed axial slits, wire sections are formed from the tube section and, when the tube section is bent open, the wire sections form circumferential portions of the snare opening, - further characterized in that a maximum diameter (D E) of the cup shape of the snaring portion in the folded-open state is greater than a diameter (Do) of the snare opening.