Mechanisms of deformation under nanoindentation (NI) and microindentation (MI) remain topics of great interest in order to understand the reasons of specific deformation of various materials as a function of structure, composition and loading conditions with the end aim of designing materials with desired mechanical properties.       The deformation behavior of any material under very non-uniform gradient stress field created under point-contact deformation (NI, MI) depends on the possibility of a specific inherent structure to dissipate external mechanical energy for the relaxation of induced internal stresses. The relaxation of internal stresses begins just at the loading stage by dissipating the stored elastic energy onto irreversible plastic deformation. Depending on the structure of material this irreversible deformation is realized through translation mechanism (dislocation movement), rotation mechanism (disclinations, twinning) and densification one (phase transition, polyamorphism, interstitial plasticity). For materials, in which the plastic deformation is poorly developed, the initial stages of fracture are involved in the first relaxation phase. The relaxation of material continues, entering the second phase, during unloading stage, when the external stresses are being removed. This stage is accompanied by elastic recovery, restructuring of the plastic zone and, in case of brittle materials, crack growth and fracture development. The third and final relaxation phase set in after full load release.   Another factor, along with the structure, influencing the relaxation processes, is strain created by the indenter depending on its geometry and load applied. On the example of CaF2 and LiF crystals it was shown that higher strain, induced by sharper indenter and higher load, results in rotation plasticity and fracture involving (Fig. 1) in the relaxation process, in addition to the dislocation plasticity [1]. The third group of factors, influencing the relaxation processes, can be identified as time-dependent ones that include strain rate, prolonged holding under the peak load and cyclic loading. It was shown that unloading rate and holding can induce changes in phase transition evolution in Si [2]. As well, it was shown that strain rate changes the mutual contribution of densification and plastic flow in phosphate glasses [3]. And the fourth factor is temperature of deformation, which influences almost whole range of relaxation processes.