  Let $\mathcal{F}$ be a family of $r$-graphs. An $r$-graph $G$ is called
$\mathcal{F}$-saturated if it does not contain any members of $\mathcal{F}$ but
adding any edge creates a copy of some $r$-graph in $\mathcal{F}$. The
saturation number $\operatorname{sat}(\mathcal{F},n)$ is the minimum number of
edges in an $\mathcal{F}$-saturated graph on $n$ vertices. We prove that there
exists a finite family $\mathcal{F}$ such that
$\operatorname{sat}(\mathcal{F},n) / n^{r-1}$ does not tend to a limit. This
settles a question of Pikhurko.
