  We study the population of asymptotic giant branch (AGB) stars in the Small
Magellanic Cloud (SMC) by means of full evolutionary models of stars of mass
1Msun < M < 8Msun, evolved through the thermally pulsing phase. The models also
account for dust production in the circumstellar envelope. We compare Spitzer
infrared colours with results from theoretical modelling. We show that ~75% of
the AGB population of the SMC is composed by scarcely obscured objects, mainly
stars of mass M < 2.5Msun at various metallicity, formed between 700 Myr and 5
Gyr ago; ~ 70% of these sources are oxygen--rich stars, while ~ 30% are
C-stars. The sample of the most obscured AGB stars, accounting for ~ 25% of the
total sample, is composed almost entirely by carbon stars. The distribution in
the colour-colour ([3.6]-[4.5], [5.8]-[8.0]) and colour-magnitude ([3.6]-[8.0],
[8.0]) diagrams of these C-rich objects, with a large infrared emission, traces
an obscuration sequence, according to the amount of carbonaceous dust in their
surroundings. The overall population of C-rich AGB stars descends from
1.5-2Msun stars of metallicity Z=0.004, formed between 700 Myr and 2 Gyr ago,
and from lower metallicity objects, of mass below 1.5Msun, 2-5 Gyr old. We also
identify obscured oxygen-rich stars (M ~ 4-6Msun) experiencing hot bottom
burning. The differences between the AGB populations of the SMC and LMC are
also commented.
