  We introduce the so-called Clifford-Hermite polynomials in the framework of
Dunkl operators, based on the theory of Clifford analysis. Several properties
of these polynomials are obtained, such as a Rodrigues formula, a differential
equation and an explicit relation connecting them with the generalized Laguerre
polynomials. A link is established with the generalized Hermite polynomials
related to the Dunkl operators (see [R\"osler M., Comm. Math. Phys. 192 (1998),
519-542, q-alg/9703006]) as well as with the basis of the weighted $L^{2}$
space introduced by Dunkl.
