  We study Laplace-type operators on hybrid manifolds, i.e. on configurations
consisting of closed two-dimensional manifolds and one-dimensional segments.
Such an operator can be constructed by using the Laplace-Beltrami operators on
each component with some boundary conditions at the points of gluing. The large
spectral parameter expansion of the trace of the second power of the resolvent
is obtained. Some questions of the inverse spectral theory are adressed.
