We present a fully quantum-mechanical, microscopic, unified treatment of gr
ound-state band and multiphonon gamma-vibrational bands using shell model d
iagonalization with the triaxial projected shell model. The results, which
agree very well with data on the g- and gamma-band spectra in Er156-170, as
well as with recently measured 4(+) two-phonon gamma-bandhead energies in
Er-166 and Er-168, are discussed in terms of the K mixing. Multiphonon gamm
a-excitation energies are predicted.