The wobbling mode of the collective angular momentum expressed as a phonon excitation with a phonon quantum number, n_w, and wobbling frequency, \hbar\omega_w, is unique to the rotational motion of a triaxial nucleus. The presence of quasiparticle alignment introduces characteristic trends in the electromagnetic decay properties for transitions between bands with different wobbling quantum number. Evidence for the wobbling mode, and thereby triaxiality, has been obtained in several even-N Lu isotopes, ¹⁶³Lu being the best studied case with the strongest population of the wobbling excitations. As an important support for the wobbling interpretation, recent lifetime measurements in ¹⁶³Lu have shown that the quadrupole moments of the bands with n_w = 0 and n_w = 1 are very similar. Triaxial strongly deformed shapes are expected also for neighbouring Hf nuclei, but efforts to identify wobbling in the Hf isotopes where many bands are established, resembling those found in the Lu isotopes, has so far failed. To date the even-N Lu isotopes, ^{161,163,165,167}Lu, are the only nuclei in which wobbling excitations are identified.

PACS numbers: 27.70.+q, 23.20.-g, 21.10.Re