The paper examines issues of introducing the distributed computational technologies in constructing the fail-safe and fault-tolerant control systems for spacecraft constellations of various purposes. Various target objectives require various tools to achieve the task. Comparative analysis of the existing distributed computational technologies operating with the responsive application systems was performed including the spacecraft constellation control systems, to identify the most acceptable solutions. Principles of constructing the network-centric systems in controlling the spacecraft constellations were considered. Distributed computational technologies were analyzed not only from the point of view of solving the target problems by the spacecraft constellations, but also from the point of view of ensuring their reliability, as well as in organizing the spacecraft constellation control systems.