  We study the irregularity of hypergeometric D-modules $\mathcal{M}_A (\beta
)$ via the explicit construction of Gevrey series solutions along coordinate
subspaces in $X =\mathbb{C}^n$. As a consequence, we prove that along
coordinate hyperplanes the combinatorial characterization of the slopes of
$\mathcal{M}_A (\beta)$ given by M. Schulze and U. Walther in [21] still holds
without any assumption on the matrix A. We also provide a lower bound for the
dimensions of the spaces of Gevrey solutions along coordinate subspaces in
terms of volumes of polytopes and prove the equality for very generic
parameters. Holomorphic solutions outside the singular locus of $\mathcal{M}_A
(\beta)$ can be understood as Gevrey solutions of order one along X at generic
points and so they are included as a particular case.
