A review of the current state of Russian Space Surveillance System (SSS), its general structure, information sources (radar and optical) are given. The basic SSS information processing principles are considered in particular in automatic mode and with the help of an operator at all stages from receiving the measurements through forming and maintaining the Space object Catalog. The basic Catalog information characteristics are presented. Particular attention is paid to organizing the tracking of space debris and realization in the SSS of the real space objects mutual approach calculation program and forming the warning about possible collision and dangerous close -encounters. A brief analysis of the preliminary results of running the program is carried out. All the data obtained may be used for qualitative decision of many practical tasks for estimation and providing the safe space activities.