  We show that the tensor product $A\otimes B$ over $\mathbb{C}$ of two $C^*
$-algebras satisfying the \textit{NCDL} conditions has again the same property.
We use this result to describe the $C^* $-algebra of the Heisenberg motion
groups $G_n = \mathbb{T}^n \ltimes \mathbb{H}_n$ as algebra of operator fields
defined over the spectrum of $G_n $.
