Abstract: Based on results of numerical modeling, this paper shows for the first time the possibility of a long-term orbital existence of technogenic aluminum-oxide particles separating from the surface of an active geostationary satellite or a “debris” object “buried” in the vicinity of a geostationary orbit. It is shown that, under the conditions of low solar and geomagnetic activity, particles with radii exceeding a threshold value close to 1.1 μm have long orbital times of existence (more than 1 month). The times of orbital existence of technogenic particles with radii greater than the indicated threshold value virtually do not depend on the initial position of an injection point in a geostationary orbit and grow rapidly with increasing radius of a technogenic particle. So, the time of orbital existence of a particle with a radius of 3 μm is equal to 130 days, while for a particle with radius of 3.52 μm, this time is more than 2 years (!). The results of numerical experiments have shown that, under conditions of low solar and geomagnetic activity, submicron technogenic particles with radii less than 0.1 μm can also have long orbital existence times. The analysis of calculated data has shown that the long-lived particles with radii in the range from 0.01 to 0.1 μm have moved in the so-called “Keplerian” mode of motion. In addition, the possibility of long-term (more than 2 years) orbital existence of ultrasmall technogenic particles with radii less than 0.01 μm injected in a geostationary orbit was demonstrated. The analysis has shown that, in this case, the technogenic particle has moved in the “so-called magnetic–gravitational capture mode.”.