  Using weakly non-linear theory of oscillation, we estimate the amplitudes of
low frequency modes in a slowly pulsating B (SPB) star, taking account of the
effects of rotation on the modes. Applying the formulation by Schenk et al
(2002), we compute non-linear coupling coefficient between the low frequency
modes and estimate the equilibrium amplitudes of the modes excited in the star,
assuming the amplitudes of the unstable modes are saturated as a result of
non-linear coupling with stable modes, that is, as a result of parametric
instability expected between one unstable mode and two stable modes. We use the
traditional approximation to calculate adiabatic and non-adiabatic oscillations
in a rotating star. We find $r$-modes in a rapidly rotating star play a
significant role in the amplitude determination through non-linear coupling. We
also find that for low $m$ modes, the fractional amplitudes of the radiative
luminosity caused by the low frequency modes are of order $10^{-4}$ to
$10^{-3}$ at the surface.
