The SIS300 ion synchrotron is the last stage of the FAIR facility for antiproton and ion research. Its magnet structure is based on rapid-cycling superconducting magnets, making it possible to increase the energy and time-averaged intensity of particle beams. In 2008, the Institute of High Energy Physics (IFVE) developed and successfully tested the SIS300 model dipole, which reached a central magnetic field 6.8 T with ramping 1.15 T/sec, which is higher than that of existing analogues. At the present time, the IHEP is developing with the financial support from Rosatom prototypes of rapid-cycling quadrupole and corrector magnets for SIS300 and is developing in collaboration with the Bochvar All-Russia Research Institute for Inorganic Materials (VNIINM) a superconducting conductor for these magnets and developing the SIS300 cryostating system, which will be built by Kriogenmash and Geliimash. The status of this work is presented.The SIS300 superconducting ion synchrotron is the last stage of the FAIR accelerator complex, where U 92+ ions are accelerated to energy 33 GeV/nucleon [1]. In the future, the synchrotron will be used as a stretching ring with the possibility of increasing the energy of U 28+ ions from 400 to 1000 MeV/nucleon with maximum intensity 1·10 12 ions/sec. As the principal magnetic structure of the synchrotron, superconducting rapid-cycling magnets make it possible to increase considerably the energy and time-averaged intensity of the accelerated ion beams.A temperature margin (minimum difference between the critical and working temperature) at 1 K in all operating regimes of the accelerator must be provided for stable operation of the superconducting rapid-cycling magnets. This is accomplished by decreasing the thermal losses and by effective cooling. The rate of change of the magnetic field in superconducting magnets of large charged-particle accelerators, for example, the Tevatron (USA), HEA (Germany, RHIC (USA), and LHC (Switzerland), with amplitude exceeding 3 T does not exceed 0.1 T/sec. Its 10-fold increase in SIS300 will increase considerably the heat losses in the winding and in the magnetic conductor. This will cause considerable heating of the superconducting winding, which will lower the temperature margin, and greatly increase the load on the cryogenic system and, as a consequence, increase the operational costs of operating the accelerator.