The nanoindentation tests have been carried out for the quasicrystalline polygrain Al62.4Cu25.3Fe12.3 alloy with the icosahedral structure i; the load P-displacement h diagrams have been used to estimate the contributions of plastic deformation (monotonic and intermittent), and the structures of the transverse microscopic sections have been studied in the vicinity of indentations by electron microscopy. It is shown that several systems of deformation bands are formed in the elasto-plastic zone in the vicinity of the indentations along the close-packed planes of the i lattice with the five-fold and two-fold symmetry axes; the bands often begin from cracks and manifest the signs of the dislocation structure. The traces of the phase transformation with the formation of the β-phase areas are observed only in a thin layer under an indenter. The effects of intermittent deformation are up to 50% of the total inelastic deformation and are related to the plastic behavior of the quasicrystal-activation and passage of deformation bands and also the formation of undersurface micro- and nanosized cracks.