The article presents arguments in favor of existence of relatively stable transuranium elements with atomic numbers Z>110.1 A review is given of experimental attempts to detect such elements in accelerators, among materials of earthly, lunar, and meteoric origin, and in the most detail, in cosmic rays. The properties of the detectors used in these searches are discussed. A summary is presented of data on the composition of nuclei of cosmic origin in the region Z>30, and recommendations are given further investigations.