Triaxiality in nuclei influences many spectroscopic quantities related to the rotational band structure in deformed nuclei. Signature effects are expected in energies as well as in electromagnetic properties. Yet such effects may also arise as a result of the interplay of mechanisms not related to triaxiality. In contrast, the wobbling mode is uniquely related to triaxiality and introduces a series of bands with increasing wobbling phonon number,nw. The pattern of &ggr;‐transitions between the wobbling excitations will be influenced by the presence of an aligned particle. Recently, evidence for the wobbling mode was obtained, and even a two‐phonon wobbling excitation has now been identified in163Lu. The similarity between the data in163Lu and newly established bands and connecting transitions in the neighbouring nuclei,165Lu and167Lu, indicates that wobbling may be a more general phenomenon in this region. The higher phonon wobbling description shows some anharmonicity, but the characteristic large &Dgr;nw= 1 E2 strength is observed. The wobbling interpretation is based on comparison to particle‐rotor calculations in which ani13/2proton is coupled to a triaxial core. © 2003 American Institute of Physics