The article analyzes the interaction of carbon nanotubes with polymer matrices, considers methods to increase the dispersibility of nanotubes in epoxy resin in order to obtain modified composite materials. Solutions of carbon nanotubes in a polymer binder are considered as lyophobic dispersed media with a significant difference in the intermolecular interaction between the dispersion medium and the dispersed phase. Based on the micellar theory of colloidal systems, a mathematical model of the aggregate stability of solutions of carbon nanotubes in a polymer binder is developed. It was found that the dispersibility of carbon nanotubes in a polymer binder depends on a large number of parameters, among which the length, diameter and number of layers are of great importance. At the same time, the agglomeration of nanotubes in binder solutions increases the settling rate of nanotubes by several tens of times in comparison with dispersed nanotubes, which emphasizes the importance of their dispersion in the processes of obtaining modified composites with high physical and mechanical properties for the space industry. © 2021, Univelt Inc. All rights reserved.