  Let $M$ be a complex- or real-analytic manifold, $\theta$ be a singular
distribution and $\mathcal{I}$ a coherent ideal sheaf defined on $M$. We prove
the existence of a local resolution of singularities of $\mathcal{I}$ that
preserves the class of singularities of $\theta$, under the hypothesis that the
considered class of singularities is invariant by $\theta$-admissible
blowings-up. In particular, if $\theta$ is monomial, we prove the existence of
a local resolution of singularities of $\mathcal{I}$ that preserves the
monomiality of the singular distribution $\theta$.
