We consider the slow and fast systems that belong to a small neighborhood of an unperturbed problem. We study the general case where the slow equation has a compact positively invariant subset which is asymptotically stable, and meanwhile the fast equation has asymptotically stable equilibria (Tykhonov's theory) or asymptotically stable periodic orbits (Pontryagin-Rodygin's theory). The description of the solutions is by this way given on infinite time interval. We investigate the stability problems derived from this results by introducing the notion of practical asymptotic stability. We show that some particular subsets of the phase space of the singularly perturbed systems behave like asymptotically stable sets. Our results are formulated in classical mathematics. They are proved within Internal Set Theory which is an axiomatic approach to Nonstandard Analysis. RESUME. On considere les systemes lents-rapides appartenant a un petit voisinage d'un probleme non perturbe. On etudie le cas general ou l'equation lente admet un sous-ensemble compact positive- ment invariant qui soit asymptotiquement stable tandis que l'equation rapide a des equilibres asymp- totiquement stables (theorie de Tykhonov) ou des cycles limites stables (theorie de Pontryagin). La description des solutions est de ce fait donnee sur des intervalles de temps infinis. On examine les problemes de stabilite decoulant de ces resultats en introduisant la notion de stabilite pratique. On montre que certains sous-ensembles de l'espace de phases des systemes singulierement perturbes se comportent comme des ensembles asymptotiquement stables. Les resultats sont formules classi- quement mais sont demontres dans le cadre de la theorie IST, une approche axiomatique de l'Analyse Non Standard.
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