  We study hypercyclicity properties of a family of non-convolution operators
defined on spaces of holomorphic functions on $\mathbb{C}^N$. These operators
are a composition of a differentiation operator and an affine composition
operator, and are analogues of operators studied by Aron and Markose on
$H(\mathbb{C})$. The hypercyclic behavior is more involved than in the one
dimensional case, and depends on several parameters involved.
