The analysis of destruction events in near-Earth orbits and in GEO is presented. The analysis shows that in many cases the destruction was low energy and the velocity of fragments is limited in few meters per second. Long term evolution of fragments cloud formed as a result of destruction of the geostationary satellites was studied. The initial cloud of fragments was set within the model of low power explosion. Dimensions of considered fragments lay in the range 0.07 - 0.9 m with the initial velocities in the range 3 - 60 m/s. The movement of each fragment was simulated on a time interval of 11 years with the numerical model of a movement of the artificial satellites of the Earth, developed in Tomsk University (Russia). This model includes Earth's gravitational field up to 20th order, Sun, Moon, Earth's tides and light pressure. A number of explosions of low power were considered. The initial elements of orbits of destructed objects were accepted as: semimajor axis 42165 km, zero eccentricity, inclination 0° or 10°. Satellite longitudes were chosen near stable (75°E, 105°W) and unstable (165°E, 15°W) libration points and two intermediate (30°E, 120°E). The expansion of the cloud along the orbit and closing it to the torus is a result of the fragments moving in circular modes only. The inner structure of the cloud will stay heterogeneous on a long-term interval. During evolution in a cloud of fragments two areas with small cross section will arise. These areas correspond to the line of nodes of destructed object. Peculiarities of the evolution of longitudes of fragments orbits node allow to separate regions where the particle flow is maximal. These regions are most suitable for search explosion fragments; on the other hand this regions are present highest emergency for active geostationary objects.