The paper presents a description of the numerical model of motion of artificial Moon satellites (AMS), developed by the authors, and the results of studying the features of the dynamics of objects in the circumlunar space. A numerical modeling of motion of 5180 objects uniformly distributed in the circumlunar space was carried out. It is shown that in a number of regions of the circumlunar space, the orbital lifetime of AMS is very short, depending on the choice of the initial value of the semi-major axis and inclination. The reasons for this phenomenon are elucidated. These results can be used in choosing a strategy of arrangement of satellite systems for long-term use in the circumlunar orbital space.