We have carried out an infrared search for obscured AGB stars in the Magellanic Clouds. The survey uncovered a number of obscured AGB stars as well as some supergiants with infrared excess. We present photometry of the sources and discuss the colour diagrams and bolometric luminosities. Most of the AGB stars are luminous, often close to the classical limit of $M_{rm bol}=-7.1$. To determine whether the stars are oxygen-rich or carbon-rich, we have acquired narrow-band mid-infrared photometry with the ESO TIMMI camera for several sources. All but one are found to show the silicate feature and therefore to have oxygen-rich dust: the colours of the remaining source are consistent with either an oxygen-rich or a carbon-rich nature. A method to distinguish carbon and oxygen stars based on H$-$K versus K$-$[12] colours is presented. We discuss several methods of calculating the mass-loss rate: for the AGB stars the mass-loss rates vary between approximately 5 times 10**-4 and 5 times 10**-6 solar masses per year, depending on assumed dust-to-gas mass ratio. We present a new way to calculate mass-loss rates from the OH-maser emission. We find no evidence for a correlation of the mass-loss rates with luminosity in these obscured stars. Neither do the mass-loss rates for the LMC and SMC stars differ in any clear systematic way from each other. Expansion velocities appear to be slightly lower in the LMC than in the Galaxy. Period determinations are discussed for two sources: the periods are comparable to those of the longer-period galactic OH/IR stars. All of the luminous stars for which periods are available, have significantly higher luminosities than predicted from the period--luminosity relations.
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