Stability of the heaviest atomic nuclei

Calculations of the alpha-decay and the spontaneous-fission of the heaviest nuclei are described. Main attention is given to the presentation of the results of the author, obtained in recent few years. One of the important modification, with respect to earlier studies, is the use of a multidimensional deformation space, which is especially important for the calculation of the fission barrier. Even-even nuclei with atomic number Z=92-110 are considered. Much attention is paid to the description of shell effects in the half-lives. These effects are especially important for the heaviest nuclei as they decide the question of their existence. (author)