[en] The essence of talk is the mass limit of the atomic nuclei. In this connection one of the fundamental and prediction of the modern theory about possible existence of the 'stability islands' in the domain of the hypothetical very heavy (superheavy) elements are considered. The enhanced stability has been expected for the deformed nuclei near Z = 108 and N = 162, yet much stronger effect has been predicted for heavier spherical nuclei close to the shells Z = 114 and N = 184, next to the doubly-magic nucleus ²⁰⁸Pb (Z = 82, N = 126). The talk is devoted to the experimental verification of these predictions - the synthesis and study of both the decay and chemical properties of the superheavy elements. For the synthesis of the heaviest elements with atomic number 104-113 fusion reactions of the nuclei of ²⁰⁸Pb, ²⁰⁹Bi with the projectiles of ⁵⁰Ti, ⁵⁴Cr,... ⁷⁰Zn have been used. In this reactions the most heavy compound nuclei have an excitation energy of about 12-15 MeV only (cold fusion). They cool down to the ground state by emission one neutron and gamma-rays. Cold fusion reaction allowed to investigate decay properties of the nuclides with Z = 104-113 and N = 151-165 in the region of the deformed shells Z = 108 and N = 162. The nuclides Z = 110-113 (T_1/2 ≅ ms) produced in these reactions undergo sequential α-decays with total decay time of few seconds. The synthesis of even heavier nuclei (Z = 112-118) has been carried out in the fusion reactions of ²²⁶Ra, ^233,238U, ²³⁷Np, ^242,244Pu, ^245,248Cm, ²⁴⁹Bk and ²⁴⁹Cf with the 48-- projectiles. The maximal yield of the superheavy elements was obtained at the excitation energy of about 40-45 MeV (hot fusion); the compound nuclei cool down mostly by emission 3 and 4 neutrons and gamma-rays. Eight more neutrons compare with above mentioned cold fusion reaction (Pb-based target) made possible to study decay properties of the nuclides with - Z = 104-118 with the higher neutron number, N = 161 -177. The decay properties of 48 synthesized nuclei were compared with the theoretical calculations made in various theoretical models. It is shown that the obtained results provide direct experimental evidence of the existence of the superheavy nuclei that considerably changing the mass limits of atomic nuclei and expand the Periodical Table of the chemical elements. The experiments were carried out at the U-400 heavy ion cyclotron of the Flerov Laboratory of Nuclear Reactions (FLNR, JINR). In the talk are used the results obtained in collaboration FLNR (Dubna, Russia), LLNL (Livermore, USA), ORNL (Oak Ridge, USA) and PSI (Villigen, Switzerland)