  In this paper we first offer an alternative approach to extend the original
Fueter's Theorem in Dunkl-Clifford analysis to a version of the higher order
case. Then this result is used to prove a generlized version of Fueter's
Theorem with an extra homogeneous Dunkl-monogenic polynomial
$P_n(x_0,\underline{x})$ in $\R_1^d$ instead of the classical factor
$P_n(\underline{x})$ in $\R^d$.
