  A Kleinian manifold Y is a quotient of a rank-one symmetric space of
non-compact type by a convex-cocompact discrete group of isometries. We
describe the spectral decomposition of the space of square integrable sections
of locally homogeneous bundles on Y with respect to locally invariant
differential operators. In the course of the proof we obtain meromorphic
continuations of Eisenstein series and scattering matrices.
