Electroadhesive systems are promising for creating delicate robotic manipulators operating both in the natural environment and in space conditions. Using thermosetting epoxy resin, polyurethane and polyester resin as examples, the influence of the polymers’ natures, potential differences and current strengths on electroadhesive interactions in polymer–polymer systems was studied. The investigations were carried out by recording the force of normal separation of substrates from electroadhesives using contact and contactless methods at various electrical parameters of the systems and their components. A correlation was established between the relative permittivity and the electroadhesive force. The relaxation nature of the electroadhesion phenomenon after removing the electrical voltage was revealed. The influence of the potential difference and current strength on the effect of electroadhesion for polymer substrates of various natures was established. The obtained dependencies describe the main regularities of electroadhesive interactions necessary for creating promising electroadhesive materials.