  The prevailing evidence suggests that most large-amplitude AGB variables
follow the period luminosity (PL) relation that has been established for Miras
in the LMC and galactic globular clusters. Hipparcos observations indicate that
most Miras in the solar neighbourhood are consistent with such a relation.
There are two groups of stars with luminosities that are apparently greater
than the PL relation would predict: (1) in the LMC and SMC there are large
amplitude variables, with long periods, P> 420 days, which are probably
undergoing hot bottom burning, but which are very clearly more luminous than
the PL relation (these are visually bright and are likely to be among the first
stars discovered in more distant intermediate age populations); (2) in the
solar neighbourhood there are short period, P<235 days, red stars which are
probably more luminous than the PL relation. Similar short-period red stars,
with high luminosities, have not been identified in the Magellanic Clouds.
