  We present a preliminary analysis of the effect of dynamical friction on the
orbits of part of the globular clusters in our Galaxy. Our study considers an
anisotropic velocity dispersion field approximated using the results of studies
in the literature. An axisymmetric Galactic model with mass components
consisting of a disc, a bulge, and a dark halo is employed in the computations.
We provide a method to compute the dynamical friction acceleration in
ellipsoidal, oblate, and prolate velocity distribution functions with similar
density in velocity space. Orbital properties, such as mean time-variations of
perigalactic and apogalactic distances, energy, and z-component of angular
momentum, are obtained for globular clusters lying in the Galactic region $R
\lesssim$ 10 kpc, $|z| \lesssim$ 5 kpc, with $R,z$ cylindrical coordinates.
These include clusters in prograde and retrograde orbital motion. Several
clusters are strongly affected by dynamical friction, in particular Liller 1,
Terzan 4, Terzan 5, NGC 6440, and NGC 6553, which lie in the Galactic inner
region. We comment on the more relevant implications of our results on the
dynamics of Galactic globular clusters, such as their possible
misclassification between the categories 'halo', 'bulge', and 'thick disc', the
resulting biasing of globular-cluster samples, the possible incorrect
association of the globulars with their parent dwarf galaxies for accretion
events, and the possible formation of 'nuclear star clusters'.
