The characteristics of oxygen-rich and carbon-rich , large amplitude ( \Delta K > 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 , \Delta K > 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 .