  The main goal of this paper is to study compactifications of polynomial
slow-fast systems. More precisely, the aim is to give conditions in order to
guarantee normal hyperbolicity at infinity of the Poincar\'e-Lyapunov sphere
for slow-fast systems defined in $\mathbb{R}^{n}$. For the planar case, we
prove a global version of the Fenichel Theorem, which assures the persistence
of invariant manifolds in the whole Poincar\'e-Lyapunov disk. We also discuss
the appearence of non normally hyperbolic points at infinity, namely: fold,
transcritical and pitchfork singularities.
