  We compute precise values of quasinormal modes of a massive scalar field in
the background of the Schwarzschild-like brane-localised black holes. It is
shown that the quasinormal spectrum of the massive field differs qualitatively
from that previously known for other black hole models, due to the presence of
two kinds of modes: those whose damping rate vanishes as the mass of the field
$\mu$ increases up to some critical value, and those whose real oscillation
frequency vanishes at a certain value of $\mu$. While the first type of modes,
which are arbitrarily long-lived, are recognized in various four-dimensional
backgrounds as quasi-resonances, the second type is a novel feature for
asymptotically flat black holes. When $Re (\omega)$ reaches zero, the
fundamental mode disappears from the spectrum and the first overtone becomes
the fundamental mode. We also demonstrate that quasi-resonances may not exist
for brane-localised black holes immersed in $D\geq 6$ - dimensional bulk.
