Abstract—Some comparative nanoindentation results were presented for the Ti3AlC2 MAX phase (nanolayered material), the (001) plane of a LiF single crystal (elastoplastic material), and the PTFE polymer (viscoelastoplastic material). Using quasi-static nanoindentation, the hardness and elastic modulus of specimens were determined, and significant elastic energy dissipation was revealed the for Ti3AlC2 MAX phase under cyclic loading (as typical for some other nanolayered materials, such as graphite and high-temperature superconductors). To determine the viscoelastic characteristics for the MAX phase, the indentation depth change was measured in 60 s after fast indenter unloading. The relaxation time was determined for the MAX phase for the first time. In addition, fast unloading also made it possible to separate the components (elastic, viscoelastic, and plastic) of strain upon nanocontact for these materials. Although the share of viscoelastic strain in the total strain upon contact was negligible (~0.1%) for LiF, it was much higher for the Ti3AlC2 MAX phase and the PTFE polymer and equal to ~1 and ~17%, respectively.