I will talk about the construction of Penner-like coordinates on
the co-called N=1 and N=2 super-Teichmueller spaces for punctured Riemann
surfaces. These are higher Teichmueller spaces for supergroups OSP(1|2) and
OSP(2|2). I will discuss about all important ingredients such as a combinatorial
approach to spin structures on Riemann surfaces, super-version of the
Ptolemy transformations and the explicit formula for the analogue of the
Weil-Petersson 2-form.