  We study the pulsational properties of rapidly rotating main-sequence B-type
stars using linear non-adiabatic analysis of non-radial low-frequency modes
taking into account the effect of rotation. We compare the properties of
prograde sectoral $g$ and retrograde $r$ modes excited by the $\kappa$
mechanism at the Fe opacity peak with the newly discovered period-luminosity
relation that is obeyed by a group of fast-rotating B-type stars in the young
open cluster NGC 3766. The observed relation consists of two sequences in the
period versus magnitude diagram, at periods shorter than 0.5 days. We find that
this property is consistent with similar period-luminosity relations predicted
for excited sectoral prograde $g$-modes of azimuthal orders $m=-1$ and $m=-2$
in fast-rotating stars along an isochrone. We further show that some of the
rapidly rotating stars that have photometric variability with periods longer
than a day may be caused by $r$-mode pulsation predicted to be excited in these
stars. One fast-rotating star, in particular, shows both short and long periods
that can be explained by the simultaneous excitation of $g$- and $r$-mode
pulsations in models of fast-rotating stars.
