The mechanical relaxation was examined by a resonance piezoelectric method for a 3,5 wt % Y2O3-ZrO2 polycrystal and 4 wt % Y2O3-ZrO2 tetragonal single crystals with orientations in the [100] and [111] directions. The relaxation was observed for the [111]-oriented crystal, but not far the [100]-crystal. The results indicated that the relaxation was active only for the elastic compliance, s(44), and inactive for (s(11)-s(12)). The amplitude of the anelastic relaxation measured for the polycrystalline and the [111]-crystal body was 4.2 x 10(-12) m(2) N-1 and 6.7 x 10(-12) m(2) N-1, respectively. An observed broad relaxation peak suggested that complex processes exist even in single crystals.