  Let $k$ be a number field and $S$ a finite set of places of $k$ containing
the archimedean ones. We count the number of algebraic points of bounded height
whose coordinates lie in the ring of $S$-integers of $k$. Moreover, we give an
asymptotic formula for the number of $\bar{S}$-integers of bounded height and
fixed degree over $k$, where $\bar{S}$ is the set of places of $\bar{k}$ lying
above the ones in $S$.
