The power supply system of orbital spaceships is expedient to make on the basis of hydrogen-oxygen electrochemical generators that during the flight produce electricity and water. All the processes implemented in the system of storage, preparation and supply of hydrogen can be represented in the form of three main stages: pre-flight fueling the on-board cryotanks with hydrogen and subsequent conversion of it into a liquid state under the supercritical pressure; taking a single-phase hydrogen out of the cryotanks performing the procedures of maintaining a constant pressure; a hydrogen evacuation from the cryotanks into a terrestrial stationary and transportable storage system. The thermodynamic features of the processes that take place within each of these stages are considered. It is shown that the conversion of the two-phase hydrogen which was fueled into the cryotanks to a single-phase liquid state with a supercritical pressure is carried out in the isochoric process as a result of the heat supply to it. The differential equations were obtained which describe the thermodynamic parameters of the hydrogen which is in the cryotank, and from which part of the product is continuously taken out. Numerical solution of the equations enabled us to find which should be the heat transferred to the cryotank in order to keep the constant pressure of hydrogen in it. The analysis of the processes of hydrogen evacuation from the cryotanks in the launch or landing complex of the orbital spaceship revealed that part of the hydrogen in liquid form can be supplied from the cryotanks into the system of its terrestrial storage.