  The aim of this paper is to put the fundations of a new theory of functions,
called holomorphic Cliffordian, which should play an essential role in the
generalization of holomorphic functions to higher dimensions. Let R\_{0,2m+1}
be the Clifford algebra of R^{2m+1} with a quadratic form of negative
signature, D = \sum\_{j=0}^{2m+1} e\_j {\partial\over \partial x\_j} be the
usual operator for monogenic functions and $\Delta$ the ordinary Laplacian. The
holomorphic Cliffordian functions are functions f : \R^{2m+2} \fle
\R\_{0,2m+1}, which are solutions of D \Delta^m f = 0
