  We study quasinormal spectrum of massive scalar field in the $D$-dimensional
black hole background. We found the qualitatively different dependence on the
field mass of the fundamental modes for $D\geq6$. The behaviour of higher modes
is qualitatively the same for all $D$. Thus for some particular values of mass
(of the field and of the black hole) the spectrum has two dominating
oscillations with a very long lifetime. Also we show that the asymptotically
high overtones do not depend on the field mass. In addition, we present the
generalisation of the Nollert improvement of the continued fraction technique
for the numerical calculation of quasi-normal frequencies of $D$-dimensional
black holes.
