  In this paper we investigate spectral properties of Lapla- cians on Rooms and
Passages domains. In the first part, we use Dirichlet- Neumann bracketing
techniques to show that for the Neumann Lapla- cian in certain Rooms and
Passages domains the second term of the asymptotic expansion of the counting
function is of order $\sqrt{\lambda}$. For the Dirichlet Laplacian our methods
only give an upper estimate of the form $\sqrt{\lambda}$. In the second part of
the paper, we consider the relation- ship between Neumann Laplacians on Rooms
and Passages domains and Sturm-Liouville operators on the skeleton.
