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The availability of suitable heavy-ion accelerators should make it possible to synthesize and identify additional heavy transuranium elements. Criteria for adequate proof that a new element has been synthesized or found in nature and identified are suggested. The basic criterion must be the proof that the atomic number of the new element is different from the atomic numbers of all previously known elements. Chemical identification constitutes an ideal proof; the procedure must be valid for application to individual atoms in an unequivocal manner. Also satisfactory is the identification of characteristic x rays in connection with the decay of the isotope of the new element. This is likely to involve measurement of the half-life and precise, unique energies of the alpha particles of the new element in coincidence with the characteristic x rays of the daughter nuclide. The proof of a genetic decay relationship through an alpha particle decay chain in which the isotope of the new element is identified by the observation of previously known decay products should be acceptable. Detection of a spontaneous fission activity and measurement of its half-life cannot per se establish that an element with a new atomic number has been produced, even with such informationmore » as fragment mass and kinetic energy distributions, for the systematics cannot be extrapolated reliably into new regions. Similarly, the use of the predicted half-lives for spontaneous fission and alpha decay and of predicted alpha decay energies cannot yet be considered sufficiently reliable. The present understanding of production yields, excitation functions, angular distributions, etc., is not sufficient to establish with certainity the discovery of a new element. Some anticipated features of the identification of ''superheavy'' elements are also mentioned. (RWR)« less