  Based on earlier work of the latter two named authors on the higher
super-Teichmueller space with $\mathcal{N}=1$, a component of the flat
$OSp(1|2)$ connections on a punctured surface, here we extend to the case
$\mathcal{N}=2$ of flat $OSp(2|2)$ connections. Indeed, we construct here
coordinates on the higher super-Teichmueller space of a surface $F$ with at
least one puncture associated to the supergroup $OSp(2|2)$, which in particular
specializes to give another treatment for $\mathcal{N}=1$ simpler than the
earlier work. The Minkowski space in the current case, where the corresponding
super Fuchsian groups act, is replaced by the superspace $\mathbb{R}^{2,2|4}$,
and the familiar lambda lengths are extended by odd invariants of triples of
special isotropic vectors in $\mathbb{R}^{2,2|4}$ as well as extra bosonic
parameters, which we call ratios, defining a flat $\mathbb{R}_{+}$-connection
on $F$. As in the pure bosonic or $\mathcal{N}=1$ cases, we derive the analogue
of Ptolemy transformations for all these new variables.
