  Nuclear magnetic dipole properties of ground bands and gamma-vibrational
bands are studied for the first time using the triaxial projected shell model
approach. The study is carried out for the Dy and Er isotopic chains, ranging
from transitional to well-deformed region. It is found that the g-factor ratio
of the 2^+ state in ground bands to that of gamma-bands, r=g(2^+,
gamma-vib)/g(2^+, ground), varies along an isotopic chain. With the
gamma-deformations, which best reproduce the energy levels for both bands, we
obtain a qualitative agreement with the experimental data. This result thus
suggests that study of the ratio may provide an important information on the
triaxial deformation of a nuclear system. The angular-momentum dependence of
the ground band g-factor on the triaxial deformation is also investigated.
