  We discuss properties of oscillatory convective modes in low-mass red giants,
and compare them with observed properties of the long secondary periods (LSPs)
of semi-regular red giant variables. Oscillatory convective modes are very
nonadiabatic g$^{-}$ modes and they are present in luminous stars, such as red
giants with $\log L/{\rm L}_\odot \ga 3$. Finite amplitudes for these modes are
confined to the outermost nonadiabatic layers, where the radiative energy flux
is more important than the convective energy flux. The periods of oscillatory
convection modes increase with luminosity, and the growth times are comparable
to the oscillation periods. The LSPs of red giants in the Large Magellanic
Cloud (LMC) are observed to lie on a distinct period-luminosity sequence called
sequence D. This sequence D period-luminosity relation is roughly consistent
with the predictions for dipole oscillatory convective modes in AGB models if
we adopt a mixing length of 1.2 pressure scale height ($\alpha = 1.2$).
However, the effective temperature of the red-giant sequence of the LMC is
consistent to models with $\alpha=1.9$, which predict periods too short by a
factor of two.
