  In this paper we obtain skew-product representations of the multidimensional
Dunkl processes which generalize the skew-product decomposition in dimension 1
obtained in L. Gallardo and M. Yor. Some remarkable properties of the Dunkl
martingales. S\'{e}minaire de Probabilit\'{e}s XXXIX, 2006. We also study the
radial part of the Dunkl process, i.e. the projection of the Dunkl process on a
Weyl chamber.
