  This article presents the study of the light-curves extracted from the MACHO
database of a sample of stars observed by the ISO in the SMC. These stars
belong to the ISO-Mini-Survey catalogue of the Magellanic Clouds (ISO-MCMS,
Loup et al. in preparation). Most of them are in the AGB and supergiant phases.
The dominant period and amplitude of pulsation have been derived and the stars
have been classified as Mira or Semi-Regular pulsators. Furthermore, the
cross-identification with near-infrared DENIS and 2MASS magnitudes available
within the ISO-MCMS allowed us: (i) to investigate the properties of these
stars in the combined near- and mid-infrared colour-magnitude diagrams, (ii) to
derive the bolometric magnitude by integrating the spectral energy distribution
and (iii) to estimate the mass-loss rate. The stars have been divided into
carbon- (C-) and oxygen-rich (O-rich) using the (J-Ks, Ks) colour-magnitude
diagram and their period and amplitude distributions have been compared. C-rich
AGB stars have a sharp peak in their period distribution at about 250 days and
have on average a larger amplitude than O-rich AGB stars. This effect, not
previously detected from the study of similar stars in the LMC and in the
Baade's window, might be closely related to the metallicity of the environment
in which the stars have formed.
