In this note we obtain two different types of skew-product representations of the multidimensional Dunkl Markov processes which generalize the skew-product decomposition in dimension 1 obtained in [GY05] and the skew-product of an n-dimensional Brownian motion into its radial and angular parts. We also study the radial part of the Dunkl Markov process, i.e. the projection of the Dunkl Markov process on a Weyl chamber.