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We present a preliminary analysis of the effect of dynamical friction on theorbits of part of the globular clusters in our Galaxy. Our study considers ananisotropic velocity dispersion field approximated using the results of studiesin the literature. An axisymmetric Galactic model with mass componentsconsisting of a disc, a bulge, and a dark halo is employed in the computations.We provide a method to compute the dynamical friction acceleration inellipsoidal, oblate, and prolate velocity distribution functions with similardensity in velocity space. Orbital properties, such as mean time-variations ofperigalactic and apogalactic distances, energy, and z-component of angularmomentum, 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. Severalclusters are strongly affected by dynamical friction, in particular Liller 1,Terzan 4, Terzan 5, NGC 6440, and NGC 6553, which lie in the Galactic innerregion. We comment on the more relevant implications of our results on thedynamics of Galactic globular clusters, such as their possiblemisclassification between the categories 'halo', 'bulge', and 'thick disc', theresulting biasing of globular-cluster samples, the possible incorrectassociation of the globulars with their parent dwarf galaxies for accretionevents, and the possible formation of 'nuclear star clusters'.

Orbits of globular clusters computed with dynamical friction in the Galactic anisotropic velocity dispersion field