  We study the asymptotic behavior of the solutions related to a family of
singularly perturbed partial differential equations in the complex domain. The
analytic solutions are asymptotically represented by a formal power series in
the perturbation parameter. The geometry of the problem and the nature of the
elements involved in it give rise to different asymptotic levels related to the
so-called strongly regular sequences. The result leans on a novel version of a
multi-level Ramis-Sibuya theorem.
