  New results on metric ultraproducts of finite simple groups are established.
We show that the isomorphism type of a simple metric ultraproduct of groups
$X_{n_i}(q)$ ($i\in I$) for $X\in\{{\rm PGL},{\rm PSp},{\rm
PGO}^{(\varepsilon)},{\rm PGU}\}$ ($\varepsilon=\pm$) along an ultrafilter
$\mathcal{U}$ on the index set $I$ for which $n_i\to_{\mathcal{U}}\infty$
determines the type $X$ and the field size $q$ up to the possible isomorphism
of a metric ultraproduct of groups ${\rm PSp}_{n_i}(q)$ and a metric
ultraproduct of groups ${\rm PGO}_{n_i}^{(\varepsilon)}(q)$. This extends
results of Thom and Wilson.
