  Formulations of some Grassmann-valued systems of ordinary differential
equations invariant under (infinitesimal) supersymmetry transformations,
including $N$-superspace extended types, are reviewed and discussed, with use
of superfields. Different new examples are shown, and some aspects on methods
for obtaining solutions are offered. Notions inspired from Darboux theory are
considered for some general polynomial systems, involving Grassmann variables.
