  We establish a Bohr-Sommerfeld type condition for quasi-normal modes of a
slowly rotating Kerr-de Sitter black hole, providing their full asymptotic
description in any strip of fixed width. In particular, we observe a
Zeeman-like splitting of the high multiplicity modes at a=0 (Schwarzschild-de
Sitter), once spherical symmetry is broken. The numerical results presented in
Appendix B show that the asymptotics are in fact accurate at very low energies
and agree with the numerical results established by other methods in the
physics literature. We also prove that solutions of the wave equation can be
asymptotically expanded in terms of quasi-normal modes; this confirms the
validity of the interpretation of their real parts as frequencies of
oscillations, and imaginary parts as decay rates of gravitational waves.
