  The characteristics of oxygen-rich and carbon-rich, large amplitude (dK>0.4
mag), asymptotic giant branch variables in the Large Magellanic Clouds are
discussed, with an emphasis on those obscured by dust. Near-infrared
photometry, obtained over about 8 years, is combined with published
mid-infrared observations from IRAS and ISO to determine bolometric magnitudes
for 42 stars. Pulsation periods of the O-rich stars are in the range 116<P<1393
days, while those for C-rich stars have 298<P<939 days. In addition to the
regular pulsations, one O-rich star and four C-rich stars show large amplitude,
dK> 0.6 mag, secular or very long period variations which may be associated
with changes in their mass-loss rates. We discuss and compare various methods
of determining the bolometric magnitudes and show, perhaps surprisingly, that
most of the very long period stars seem to follow an extrapolation of the
period-luminosity relation determined for stars with shorter periods - although
the details do depend on how the bolometric magnitudes are calculated. Three
stars with thin shells, which are clearly more luminous than the obscured AGB
stars, are undergoing hot bottom burning, while other stars with similar
luminosities have yet to be investigated in sufficient detail to determine
their status in this regard. We suggest that an apparent change in slope of the
period luminosity relation around 400-420 days is caused by variables with
luminosities brighter than the predictions of the core-mass luminosity
relation, due to excess flux from hot bottom burning.
