These conference proceedings discussed the problems of producing and the investigation of the properties of nuclei in extreme states, in particular, of nuclei situated on the limits of particle stability. They dealt with the synthesis and study of the properties of the heaviest isotopes of the lightest elements, with the properties of neutron- and proton-rich nuclei, and with some astrophysical problems. Reports were also made on the present status and perspectives of producing and the application of radioactive nuclear beams Radioactive nuclear beams are produced in principle by means of high intensity proton- or heavy-ion beams. The possibility of using intense neutron fluxes for this purpose is also discussed.