  We study quasinormal modes for massive scalar fields in Schwarzschild-anti-de
Sitter black holes. When the mass-squared is above the Breitenlohner-Freedman
bound we show that for large angular momenta, $\ell$, there exist quasinormal
modes with imaginary parts of size $\exp(-\ell/C)$. We provide an asymptotic
expansion for the real parts of the modes closest to the real axis and identify
the vanishing of certain coefficients depending on the dimension.
