Let $\dot x = f(t,x)$ be a smooth differential equation in 
${\bf R} \times {\bf R}^{n}$ and $M$ be 
an $s$--compact invariant set in ${\bf R} \times {\bf R}^{n}$. Assume 
the existence of a smooth invariant set $\Phi$ in 
${\bf R} \times {\bf R}^{n}$ containing $M$ such that $M$ is uniformly 
asymptotically stable with respect to the perturbations lying on $\Phi$. 
We analyze the influence of the stability properties of $\Phi$ ``near $M$''
on the unconditional stability properties 
of $M$.  A comparison with some classical results concerning the 
autonomous or the periodic 
case is given.