1. For 45 steel a nonlinear relationship between the strains in the longitudinal ex and transverse ey directions in tension-compression was established in loading above the cyclic proportional limit, which leads to the formation of a hysteresis loop. 2. For the investigated steel the interrelationship between the deformations in the longitudinal and transverse directions in cyclic tension-compression is the same for any number of cycles at which these deformations were determined, which is responsible for their unambiguous relationship to the degree of damage of the given material. 3. The formation of a hysteresis loop in ex−ey coordinates in cyclic tension-compression is related to the change in Poisson's ratio as the result of accumulation of microcracks in the material. 4. In tests under conditions of cyclic torsion, a strain hysteresis loop is not observed between the deformations in the directions perpendicular to the main planes since the ratio of these deformations is unchanged at all levels of stresses.