  Let $\V$ be a mixed characteristic complete discrete valuation ring with
perfect residue field. Let $\X$ be a smooth formal scheme over $\V$. We prove
than a $\D ^\dag_{\X,\Q} $-module which is overcoherent after any change of
basis is an holonomic $\D ^\dag_{\X,\Q} $-module. Furthermore, we check that
this implies than a bounded complex $\E$ of $\D ^\dag_{\X,\,\Q}$-modules is
overholonomic after any change of basis if and only if, for any integer $j$,
$\mathcal{H} ^{j} (\E) $ is overholonomic after any change of basis.
