During developmental testing of a hydrogen-oxygen propulsion stage of the space launch vehicle, it is necessary to create storage tanks of liquid hydrogen and oxygen with working pressures considerably exceeding their critical parameters. On the basis of thermodynamic analysis of storage and delivery of hydrogen and oxygen from tanks with the supercritical parameters, we have developed recommendations on circuitry and structural solutions for maintaining pressure in the tanks for storage and delivery of cryogenic components on the propulsion stage of the launch vehicle. The paper discusses design features of cryogenic tanks for liquid hydrogen and oxygen at supercritical working pressures in storage tanks. The results of experiments on developing the technology of filling them with liquid nitrogen are analyzed. On the basis of these studies, recommendations on the technology of filling storage tanks with liquid hydrogen or oxygen at supercritical conditions have been developed.