We have searched for near-infrared stellar counterparts of IRAS point sources in the Large Magellanic Cloud (LMC), in J and K-bands. This resulted in the detection of 21 counterparts, of which 19 are new discoveries. Using colour-magnitude and colour-colour diagrams, we identify 13 Asymptotic Giant Branch (AGB) stars with thick circumstellar dust envelopes, 7 possible early post-AGB stars or stars recovering from a thermal pulse, and 1 red supergiant or foreground star. For 10 of the IRAS targets we do not succeed in detecting and/or identifying a near-infrared counterpart. We serendipitously detect 14 other red sources, of which 2 are known Long Period Variables, and a few galaxies. The near-infrared and optical colours of the galaxies may indicate considerable interstellar extinction through the LMC, as much as A_V about 2-4 mag. The relative number of AGB carbon stars over oxygen stars is shown to decrease as the luminosity increases. Yet amongst the faintest mass-losing AGB stars oxygen-rich stars still exist, which puts constraints on current convection theories that predict the occurrence of third dredge-up and Hot Bottom Burning. We investigate the nature of some LMC stars that have infrared properties very similar to suspected Galactic post-AGB stars.
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