  We present Spitzer Space telescope spectroscopic observations of 14
carbon-rich AGB stars in the Small Magellanic Cloud. SiC dust is seen in most
of the carbon-rich stars but it is weak compared to LMC stars. The SiC feature
is strong only for stars with significant dust excess, opposite to what is
observed for Galactic stars. We argue that in the SMC, SiC forms at lower
temperature than graphite dust, whereas the reverse situation occurs in the
Galaxy where SiC condenses at higher temperatures and forms first. Dust input
into the interstellar medium by AGB stars consists mostly of carbonaceous dust,
with little SiC or silicate dust. Only the two coolest stars show a 30-micron
band due to MgS dust. We suggest that this is due to the fact that, in the SMC,
mass-losing AGB stars generally have low circumstellar (dust) optical depth and
therefore effective heating of dust by the central star does not allow
temperatures below the 650 K necessary for MgS to exist as a solid. Gas phase
C$_2$H$_2$ bands are stronger in the SMC than in the LMC or Galaxy. This is
attributed to an increasing C/O ratio at low metallicity. We present a
colour-colour diagram based on Spitzer IRAC and MIPS colours to discriminate
between O- and C-rich stars. We show that AGB stars in the SMC become carbon
stars early in the thermal-pulsing AGB evolution, and remain optically visible
for $\sim 6 \times 10^5$ yr. For the LMC, this lifetime is $\sim 3 \times 10^5$
yr. The superwind phase traced with Spitzer lasts for $\sim 10^4$ yr. Spitzer
spectra of a K supergiant and a compact HII region are also given.
