Symmetrical and asymmetrical snares are used for endoscopically controlled methods by which tumors in hollow organs of the gastrointestinal tract can be ensnared and RF-surgically removed from the organ wall for diagnostic and/or therapeutic purposes. These snares are characterised in that one of the two snare portions, in the case of asymmetrical snares the longer of the two snare portions, is completely electrically insulated or is made from electrically non-conductive material and that the other of the two snare portions is made from electrically conductive material and its surface is not electrically insulated. In one embodiment, the asymmetrical snare is characterised in that the long snare portion is so much flexurally stiffer than the short snare portion that it tensions the short snare portion like the string of a bow.