We know what the étalés on an affine variety are. The étalés on any object $X$ of $\Sh{M}$ are defined to be the morphisms $Y\to X$ whose inverse image by each morphism $\Yo{V}\to X$ is étalé over $V$. The étalés have properties 1–4 of étalés elementaires. They also obtain a local character: if $\prn{X_i\to X}\Sub{j\in J}$ is a covering family, $Y\to X$ is étalé when each $Y\times_X X_j\to X_j$ is.