The claim that the two-phonon gamma-vibrational configuration constitutes a major component for the I-K(pi)=4(4)(+) states in osmium nuclei is based on solid experimental evidence, such as the systematics of the excitation energies, the absolute E2 strengths, the branching ratios, and the static quadrupole moments. Nevertheless, a non-negligible two-quasiparticle or hexadecapole component must exist in order to explain the observed E4 strength and the cross sections for the nucleon-transfer reactions.