  Given two systems $P=(P_j(D))_{j=1}^N$ and $Q=(Q_j(D))_{j=1}^M$ of linear
partial differential operators with constant coefficients, we consider the
spaces ${\mathcal E}_\omega^P$ and ${\mathcal E}_\omega^Q$ of
$\omega$-ultradifferentiable functions with respect to the iterates of the
systems $P$ and $Q$ respectively. We find necessary and sufficient conditions,
on the systems and on the weights $\omega(t)$ and $\sigma(t)$, for the
inclusion ${\mathcal E}_\omega^P\subseteq{\mathcal E}_\sigma^Q$. As a
consequence we have a generalization of the classical Theorem of the Iterates.
