[en] The inequalities which must be satisfied the characteristics of elastic state of the materials of contacting bodies at their adhesion (coalescence) and its absence (antiadhesion) were obtained. These are the result of the analysis of adhesion phenomena and its absence. The analysis is made on the basis of a special variant of a nonlocal theory of elasticity. Its main hypothesis is infinitely small particles of the continuous elastic medium interact with each other at finite distances with the help of many-particle potential forces. The results of using criterial inequalities were confirmed by known experimental data. (paper)