Wobbling is a rotational mode unique to a triaxial body. The Lu–Hf isotopes with N∼94 at high spin provide a possible region of nuclei with pronounced triaxiality. We have investigated 163Lu through the fusion-evaporation reaction 139La(29Si,5n)163Lu with a beam energy of 152 MeV. Three excited bands decaying into the known, presumably triaxial, superdeformed (TSD) band built on the i13/2 proton orbital are observed. The electromagnetic properties of the connecting transitions from the two strongest populated excited TSD bands have been investigated. New particle-rotor calculations in which one i13/2 quasiproton is coupled to the core of triaxial shape produce a variety of bands, whose properties can clearly be interpreted either as “wobbling” or “cranking” motion of the core. Evidence for the assignment of the excited TSD bands as one, and possibly even two wobbling phonon modes built on the yrast TSD band in 163Lu is given. These triaxial bands coexist with bands built on quasiparticle excitations in the normal deformed (ND) minimum for which new data are also presented.